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# Microkelvin 2013

Microkelvin Workshop 2013

Workshop – Review – Users’ Meeting of the EU Microkelvin Collaboration

Sannäs Manor House, Porvoo, Finland

9 – 13 September, 2013

The past 2012 Microkelvin Workshop was organized to provide a wide overview of latest research at ultra-low temperatures, emphasizing nanophysics applications. This time the 2013 Workshop is planned to

• review Microkelvin research progress during the past four grant years
• highlight promising future projects
• introduce novel research which could be part of a future Microkelvin programme
• prepare for a collection of research papers in Microkelvin Proceedings

The four workshop days 9-12 September are followed by the final public Review of the Microkelvin grant programme on Friday 13 September. The arrival to Sannäs is on Monday morning before the first session which starts at 11 am (You get the program by downloading a pdf-file, by clicking HERE). The departure is on Friday, either in the morning or after the Review at 4 pm. The venue is Sannäs Manor House, a convention centre [link] recently acquired by the Aalto University, which is located 60 km to the east from the Helsinki airport and 10 km from the small historic town of Porvoo/Borgå. Transportation from and to Helsinki airport will be available. Travel and boarding at Sannäs are provided from the Microkelvin grant.

The structure and topics of the workshop are organized as follows:

Monday 9 September

Workshop start Monday at 11 am with lunch (Welcome.ppt)

Refrigeration, thermalization, and thermometry – JRA1

Chair George Pickett <g.pickett(at)lancaster.ac.uk>

• Refrigeration in the mK regime – George Pickett (Lancaster)
• Cooling of nanoelectronics – Dominik Zumbühl (Basel)
• Dominik Zumbuhl (University of Basel): Towards microkelvin quantum transport experiments in nanosamples

I will present an overview of our activities working towards μK temperatures in electronic transport measurements in semiconductor nanostructures. The Basel approach employs individual, separate nuclear refrigerators to directly cool each of the electrical wires connecting the sample, thus enabling efficient thermal to a microkelvin bath. Recently, the nuclear refrigerators have cooled to 185±25 μK (in collaboration with the Pickett group in Lancaster), thus establishing the required experimental microkelvin platform. Nevertheless, cooling samples, their electrons and nuclear spins rather than only the nuclear stages, remains a formidable challenge. Recently, we have cooled a metallic Coulomb blockade thermometer to 5.2 +/- 0.2 mK (collaboration with the Pekola group in Aalto University). Though this is a new record and well below 10 mK, these temperatures are still clearly above the μK range. We are currently developing further strategies for reaching temperatures below 1 mK.

Already temperatures just below 10 mK are beginning to reveal exciting new physics. I will present striking data demonstrating the effects of density gradients on the integer and fractional quantum Hall effects in ultra-high mobility GaAs 2D electron gases. In ever cleaner samples measured at ever lower temperatures, gradient effects will inevitably appear and become important. Finally, I will also briefly outline ultralow temperature quantum transport experiments in GaAs quantum wires, presenting evidence for helical nuclear spin order in the Luttinger liquid regime – a novel quantum state of matter.

• Aya Shibahara (Royal Holloway): Pulse-tube precooled and hyperfine-field-enhanced nuclear refrigeration with noise thermometry (.pptx)

We report the experimental demonstration of the feasibility of reaching temperatures below 1 mK using cryogen-free technology. Our prototype system comprises an adiabatic nuclear demagnetisation stage, based on hyperfine-enhanced nuclear magnetic cooling, integrated with a commercial cryogen-free dilution refrigerator and 8 T superconducting magnet. Thermometry was provided by a current-sensing noise thermometer. The minimum temperature achieved at the experimental platform was 600 μK. The platform remained below 1 mK in excess of 24 hours, indicating a total residual heat-leak into the experimental stage of 5 nW. We also discuss improvements in the performance of current sensing noise thermometers. When optimised for speed 1% precision in 0.1 seconds measurement time was achieved. This work opens the way to widening the accessibility of temperatures in the microkelvin regime, of potential importance in areas from the application of strongly correlated electron states in nanodevices to quantum computing.

We present an advanced network of 16 parallel nuclear refrigerators operated on a BlueFors pulse-tube dilution refrigerator platform (cryogen-free, "dry" system) and demonstrate nuclear refrigeration, with the goal of cooling nanosamples for quantum transport experiments. Numerous measures were implemented to reduce vibrations originating mainly from the pulse-tube. Further, we show cooling of a metallic Coulomb blockade thermometer down to 5.2 $\pm$ 0.2 mK on a similar nuclear stage operated in a traditional 4He bath ("wet") system. Striking deviations from electron-phonon cooling were observed and are strong indication of the effectiveness of cooling through the sample leads.

• Pulse-tube precooled nuclear demagnetization cooling of liquid 3He and thermometry – Igor Todoshchenko (Aalto) (.ppt)
• Jost Engert (PTB Berlin): Thermometry and temperature scales below 1 K (.pptx)

Traceable thermometry requires the application of the international temperatures scales ITS-90 and PLTS-2000. Recent developments in temperature metrology have led to the adoption of the ‘Mise en pratique for the definition of the Kelvin’ by the Comité Consultatif de Thermométrie of the BIPM, enabling a more flexible approach. In future, also direct measurements of temperature by primary methods will be allowed for the realization and dissemination of the Kelvin in accordance with the system of units SI.

In this presentation the current status of temperature scales at low temperatures is described. A new calibration service for the dissemination of the PLTS-2000, which PTB has started recently, is presented. Also an overview will be given of the activities of PTB in the temperature range below 1 mK, where no internationally agreed temperature scale exists at all.

Tuesday 10 September

Nanorefrigeration – JRA2

Chair Jukka Pekola <jukka.pekola(at)aalto.fi>

The topic of quantum fluctuations in quasi-1D superconductors, also called quantum phase slips (QPS), has attracted significant attention [1]. It has been shown that the phenomenon is capable to suppress the zero resistivity of ultra-narrow superconducting nanowires at low temperatures T << Tc [2-4] and quench persistent currents in tiny nanorings [5]. The coherent QPS effect enables the fabrication of a new generation of quantum logic devices – qubits [6]. It has been predicted that a superconducting nanowire in the regime of QPS is dual to a Josephson junction [7]. In the particular case of an extremely narrow superconducting nanowire imbedded in a high-impedance environment the duality leads to an intuitively controversial result: the superconductor can enter an insulating state [8].

Here we experimentally demonstrate that the I-V characteristics of such a wire indeed show Coulomb blockade which disappears with the application of a critical magnetic field and/or above the critical temperature proving that the effect is related to superconductivity [9]. Such a system can be considered as a junctionless single electron transistor (with charge 2e), where the QPSs provide the dynamic equivalent of weak links in conventional devices containing static (in space and time) tunnel junctions. Application of external RF radiation can be synchronized with the internal Bloch oscillations of the current-biased superconducting nanowire in the regime of QPS. The phenomenon is dual to the well-known Shapiro effect: the voltage steps for a Josephson junction are substituted by the current steps for a QPS wire: the proof-of-principle demonstration of the long-awaited metrological application - the quantum standard of electric current

[1] K.Yu. Arutyunov, D.S. Golubev, A.D. Zaikin, Phys. Rep. 464, 1 (2008)

[2] M. Zgirski, K.-P. Riikonen, V. Touboltsev, K. Arutyunov, NanoLett. 5, 1029 (2005)

[3] M. Zgirski, K.-P. Riikonen, V. Touboltsev, K.Yu. Arutyunov Phys. Rev. B. 77, 054508 (2008)

[4] J.S. Lehtinen, T. Sajavaara, K.Yu. Arutyunov, M.Yu. Presnjakov, A. Vasiliev, Phys. Rev. B 85, 094508 (2012)

[5] K.Yu. Arutyunov, T.T. Hongisto, J.S. Lehtinen, L.I. Leino, A.L. Vasiliev. Nature: Sci. Rep. 2, 293 (2012)

[6] O.V. Astafiev, L B. Ioffe, S. Kafanov, Yu.A. Pashkin, K.Yu. Arutyunov, D. Shahar, O. Cohen, J.S. Tsai, Nature 484, 355 (2012)

[7] J.E. Mooij, Yu.V. Nazarov, Nature Physics 2, 169 (2006)

[8] T.T. Hongisto, A.B. Zorin, Phys. Rev. Lett. 108, 097001 (2012)

[9] J. Lehtinen, K. Zakharov, K. Arutyunov, Phys. Rev. Lett. 109, 187001 (2012)

• Hervé Courtois (CNRS - Grenoble): Existence of an independent phonon bath in a quantum device (.pdf)

At low temperatures, the thermal wavelength of acoustic phonons in a metallic thin film on a substrate can widely exceed the film thickness. It is thus generally believed that a mesoscopic device operating at low temperaturs does not carry an individual phonon population. In this work, we provide direct experimental evidence for the thermal decoupling of phonons in a mesoscopic quantum device from its substrate phonon heat bath at a sub-Kelvin temperature. A simple heat balance model assuming an independent phonon bath following the usual electron-phonon and Kapitza coupling laws can account for all experimental observations.

• Pepita Martinez (NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa): Heat interference in Josephson nanocircuits: toward coherent caloritronics (.pptx)

The Josephson effect [1] represents perhaps the prototype of macroscopic phase coherence and is at the basis of the most widespread interferometer, i.e., the superconducting quantum interference device (SQUID) [2]. Yet, in analogy to electric interference, Maki and Griffin [3] predicted in 1965 that thermal current flowing through a temperature-biased Josephson tunnel junction is a stationary periodic function of the quantum phase difference between the superconductors. The interplay between quasiparticles and Cooper pairs condensate is at the origin of such phase-dependent heat current, and is unique to Josephson junctions. In this scenario, a temperature-biased SQUID would allow heat currents to interfere [4,5], thus implementing the thermal version of the electric Josephson interferometer. The dissipative character of heat flux makes this coherent phenomenon not less extraordinary than its electric (non-dissipative) counterpart. Surprisingly, this striking effect has never been demonstrated so far.

In this presentation we shall report the first experimental realization of a heat interferometer [6,7]. We investigate heat exchange between two normal metal electrodes kept at different temperatures and tunnel-coupled to each other through a thermal `modulator' [5] in the form of a DC-SQUID. Heat transport in the system is found to be phase dependent, in agreement with the original prediction. With our design the Josephson heat interferometer yields magnetic-flux-dependent temperature oscillations of amplitude up to ~ 21 mK, and provides a flux-to-temperature transfer coefficient exceeding ~ 60mK/Φ0 at 235 mK (Φ0 is the flux quantum). Besides offering remarkable insight into thermal transport in Josephson junctions, our results represent a significant step toward phase-coherent mastering of heat in solid-state nanocircuits, and pave the way to the design of novel-concept coherent caloritronic devices, for instance, heat transistors, thermal splitters and diodes [8] which exploit phase-dependent heat transfer peculiar to the Josephson effect.

In this latter context, we shall also present the concept for a further development of a Josephson heat interferometer based on a double superconducting loop [9] which allows, in principle, enhanced control over heat transport. We shall finally conclude presenting some preliminary results on a quite different prototypical thermal interferometer which could add complementary flexibility in mastering heat flux at the nanoscale.

[1] B. D. Josephson, Phys. Lett. 1, 251 (1962).

[2] J. Clarke and A.I. Braginski, The SQUID Handbook (Wiley-VCH, 2004).

[3] K. Maki and A. Griffin, Phys. Rev. Lett. 15, 921 (1965).

[4] G.D. Guttman, E. Ben-Jacob, and J. Bergman, Phys. Rev. B 57, 2717 (1998).

[5] F. Giazotto and M.J. Martínez-Pérez, Appl. Phys. Lett. 101, 102601 (2012).

[6] F. Giazotto and M.J. Martínez-Pérez, Nature 492, 401 (2012).

[7] R.W. Simmonds, Nature 492, 358 (2012).

[8] M.J. Martínez-Pérez and F. Giazotto, Appl. Phys. Lett. 102, 182602 (2013).

[9] M.J. Martínez-Pérez and F. Giazotto, Appl. Phys. Lett. 102, 092602 (2013).

• Tero Heikkilä (University of Jyväskylä): Enhancing the optomechanical coupling via the Josephson coupling

Connecting an optical or a microwave cavity to a high-quality mechanical resonator allows for accurate control and measurement of mechanical vibrations down to a level of only a few quanta of mechanical motion. Traditionally this has been done in a regime of weak bare coupling of mechanics to optics, and the enhancement of the coupling has been done via a strong side-band driving of the cavity. The drawback of this method is that it converts the initially non-linear radiation pressure coupling to the mechanics to an essentially linear coupling, leaving the entire system to the correspondence limit, where quantum effects can only be observed in signal correlations. In this talk I show how the charge tuning of the Josephson inductance in a superconducting single-electron transistor [1] can be employed to arrange a strong radiation pressure -type coupling between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high radiation pressure couplings. We also show how a strong coupling between the qubit and the mechanics hybridizes the two systems, and as a result, the effective mechanical degree of freedom can reside at a much lower effective temperature than the bare mechanics. If time allows, I will also detail the main nonlinearities of such a system and discuss the possibility of observing quantum effects in the resulting effective optomechanical system.

[1] Tero T. Heikkilä, J. Tuorila, F.K. Massel, R. Khan, and M.A. Sillanpää, in preparation.

• Nikolai Kopnin (Aalto): Information flow and optimal protocol for Maxwell's demon single electron pump (.pdf)

We study the entropy and information flow in a Maxwell's demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages which minimize irreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems where barriers between different regions can be manipulated.

• Sergey Kubatkin (Chalmers): Electronic properties and metrological applications of epitaxial graphene on Silicon Carbide (.pdf)

Graphene grown from SiC by high-temperature annealing (SiC/G) is a strong contender in the race to large-scale graphene electronics. To this end there is a need for quality control of this material, because the surface of silicon carbide reconstructs uncontrollably during high-temperature annealing, leading to the appearance of stepped terraces and nucleation of multilayer graphene domains. These topographic features introduce electron scattering and lead to uneven doping profiles, which limit the performance of SiC/G electronic devices and prevent their large-scale integration. I shall discuss a technique that allows surprisingly simple and accurate identification of single and multilayer domains in SiC/G and informs on nanoscopic details of the SiC topography, making it ideal for rapid and non-invasive quality control of as-grown SiC/G. I shall make a link with experiments, where the homogeneity of this form of graphene was particularly important. In particular, I shall review the recent extraordinary progress in the development of a new quantum standard for resistance based on SiC/G, where the unique properties of this material system suit perfectly the requirements of resistance metrology and allow the most precise ever direct comparison of the Hall resistance between graphene and traditional GaAs/AlGaAs 2DEG.

• Stefan Ludwig (LMU, München): Quantum dot qubits at ultra-low temperatures - a perpective (link)

Semiconductor based mesoscopic systems allow us to study fundamental many body quantum physics and provide promising possibilities for quantum information processing. Ultra low temperatures will boost the former and simplify the latter. However, controlling the temperature of mesoscopic systems connected to hot leads becomes increasingly difficult below a few tens of mK. Accepting the challenge, we teamed up with the Ultra-Low-Temperature Group at Lancaster University where we presently prepare first test measurements on the newly built Microkelvin Access Facility cryostat.

In this talk I will motivate our goal of cooling mesoscopic systems to sub-mK temperatures by discussing a recent experiment in which we investigated the electron-phonon coupling in a double-quantum-dot (DQD) charge-qubit. We performed Landau-Zener-Stueckelberg-Majorana interferometry in a GaAs-based DQD charged by two electrons. The coherence time of our charge qubit of > 200 ns (allowing for > 600 qubit operations) is limited by the electron-phonon interaction at our presently lowest temperature of 18 mK. The coherence could be further increased by further lowering the temperature which could make semiconductor charge qubits one of the strongest candidates for quantum information processing.

• Matthias Meschke (Aalto University): Thermometry for solid state NIS refrigerators operating at low temperatures

A specially designed solid state NIS cooler offers the possibility to cool the electron system in an isolated normal metal islands to temperatures below 10 mK from a phonon bath temperature of about 100 mK. In practice, the realization is not straightforward when considering the back side of the cooler, where a noticeable amount of heat has to be deposited into a superconducting electrode. Heat conduction within the superconductor drastically weakens at low temperatures and therefore effective quasiparticle traps are required. A quasiparticle drain through magnetic vortices demonstrates this effect, improves thermalization of the superconducting electrode and enhances the cooling performance. As usual, reaching the low temperatures is only the first step, reliable thermometry at the lowest electronic temperatures needs a new approach: standard NIS thermometry fails at the lowest temperature end where the influence of the probe current is no longer negligible. Alternatively, we explore SNS proximity thermometers, where no dissipation occurs as long as the probe current stays below the critical current of the junction. I discuss recent progress in experimental fabrication and readout of such a proximity thermometer and show how to use the NIS cooler to detect voltages on the order of few tens of pV across the SNS junction. This possibly leads to new experimental insight in phase jumps across the weak link of the SNS junction.

• Hung Nguyen (Aalto University): High power electronic coolers based on superconducting tunnel junctions (.pdf)

We develop a technique to fabricate large area normal metal - insulator - superconductor (NIS) junctions based on metal etching and photolithography. A quasiparticle drain is added underneath the superconductor with a fine tuned tunnel barrier. We demonstrate both with a model and experiments that the drain thermalises the hot superconducting electrodes very well and is crucial to the performance of the coolers. The resulted SINIS coolers have 1nW cooling power per device and cool from 300 mK to 130 mK, reaching the lowest temperature of 30 mK from 150 mK. We present a robust cooling platform based on this new technology.

• Yuri Pashkin (Lancaster University): Low-temperature thermometry with nanomechanics (.pdf)

A number of fundamental physical phenomena provide the basis for primary thermometry at low temperatures, relating the observed quantities to the absolute temperature through Boltzmann's constant. The successful realisations of practical sensors operating in the mK temperature range include, e.g., noise and Coulomb blockade thermometers. However, these tools measure the temperature of electrons. The lattice temperature, which may differ from that of electrons due to poor electron-phonon coupling, remains largely unknown. I propose to use the thermal (Brownian) motion of a nanoscale mechanical resonator as a measure of the absolute phonon temperature. The underlying physics of this thermometer is similar to the physics of noise thermometry: due to the finite temperature, the resonator oscillates with the mean square amplitude of mechanical displacement proportional to the phonon temperature. Thus, if the mean square amplitude is measured, the resonator's temperature can be inferred. Some technical details of the proposal as well as basic estimates of the device performance will be presented.

• Jukka Pekola (Aalto University): Szilard’s engine for electrons

I discuss dissipation and energy fluctuations in classical single-electron tunneling [1,2]. Our recent experiment demonstrates an electronic analogue of Szilard’s engine, where ideally the process extracts heat kT ln(2) from the bath in one cycle [3].

[1] O.-P. Saira et al., PRL 109, 180601 (2012)

[2] J.V. Koski et al., Nat. Phys. doi:10.1038/nphys2711 (2013)

[3] J.V. Koski, D.V. Averin et al., in preparation (2013)

• Mika Sillanpää (Aalto University): Optomechanics with a Josephson junction cavity

One of the next challenges in optomechanics is to increase the single-quantum coupling strength to exceed the cavity dissipation rate. Motivated by this goal, we present a new design of the circuit optomechanical experiment, where the on-chip microwave cavity includes a Josephson charge qubit. This creates an effective cavity whose frequency is tunable by charge. The cavity is coupled to a micromechanical resonator whose motion is visible as charge, and hence affects the cavity frequency. We thereby obtain a radiation pressure interaction between the mechanical resonator and cavity. This way we were able to boost the coupling in the setup by six orders of magnitude up to (2 \pi) 1.5 MHz. We observe basic optomechanical phenomena, for example, effective mechanical damping rates up to (2 \pi) 0.5 MHz.

• Nathan Vercruyssen (Technische Universiteit Delft): Evanescent states and nonequilibrium in driven superconducting nanowires (.pdf)

We study the nonlinear response of current transport in a superconducting diffusive nanowire between normal reservoirs [1]. We demonstrate theoretically and experimentally the existence of two different superconducting states appearing when the wire is driven out of equilibrium by an applied bias, called the global and bimodal superconducting states. The different states are identified by using two-probe measurements of the wire, and measurements of the local density of states with tunneling probes. The analysis is performed within the framework of the quasiclassical kinetic equations for diffusive superconductors.

[1] N. Vercruyssen, T.G.A. Verhagen, M.G. Flokstra, J.P. Pekola, T.M. Klapwijk, Phys. Rev. B 85, 224503 (2012)

Wednesday 11 September

Ultra-low temperatures – JRA3

Chair Henri Godfrin <henri.godfrin(at)grenoble.cnrs.fr>

• Yuriy Bunkov (Institut Néel, CNRS, Grenoble): Magnon condensation (.ppt)

Magnons are magnetic excitations in magnetic materials, such as magnetically ordered systems like ferromagnets, antiferromagnets, etc., and paramagnetic systems with external magnetic ordering such as Fermi liquids, or nuclear systems with Suhl-Nakamura interaction. We will review the current understanding of magnon Bose-Einstein condensation and the spin supercurrent of magnons. We discuss the differences from false interpretations of BEC and magnetic superfluidity, currently used in some publications.

• Vladimir Eltsov (Aalto University): Trapped Bose-Einstein condensates of magnons in superfluid 3He-B

In superfluid 3He-B traps for magnon excitations can be formed by the order-parameter texture and the applied profile of the static magnetic field. At temperatures around 0.2Tc and below one can pump magnons to the trap using NMR techniques to create a macroscopic occupation of the ground level or of a selected excited level. Such magnons form Bose-Einstein condensates as demonstrated by the long-lived coherent spin precession after switching off the pumping. One of the remarkable properties of such condensates is the self-modification of the trapping potential which makes them analogous to the Q-balls of high-energy physics.

At the lowest temperatures the lifetime of the magnon condensates reaches minutes. They become a very sensitive probe for the properties of superfluid 3He connected with the orbital texture or magnetic relaxation, including the properties of the free surface, vortex lines, and the interface between the A and B phases.

• Shaun Fisher (Lancaster University): Quantum turbulence in superfluid 3He-B at low temperatures (.ppt)

We briefly review studies of quantum turbulence in superfluid 3He-B at very low temperatures. Vortex lines have a large cross-section for Andreev scattering thermal quasiparticle excitations. This provides a convenient passive probe of quantum turbulence in the zero temperature limit. Andreev reflection from single vortex lines and vortex rings is well understood, but quantum turbulence is more challenging. We discuss results from recent simulations. We also discuss on-going experiments to develop a quasiparticle camera for imaging vortices and quantum turbulence.

Understanding the quantum dynamics of many-body systems is one of the major goals of present physics. For this reason, many studies have been devoted to liquid 4He (bosons) and liquid 3He (fermions). The elementary excitations of a strongly interacting 2D Fermi liquid have been investigated by neutron inelastic scattering at very low temperatures [1,2]. The collective mode (zero-sound, or plasmon) traverses the particle-hole band in a Fermi system, an effect observed for the first time. The collective mode is mainly determined by the strong correlations, and not by quantum statistics. The results are compared to dynamic many-body theory and quantum Monte Carlo calculations. We also show new results on liquid 4He; the very rich dynamic behavior observed in a large momentum-energy domain challenges the current theoretical description of correlated bosons.

[1] H. Godfrin, M. Meschke, H.-J. Lauter, A. Sultan, H. Böhm, E. Krotscheck, M. Panholzer, Observation of a roton collective mode in a two-dimensional Fermi liquid, Nature, 483, 576-579 (2012)

[2] A. Sultan, M. Meschke, H.-J. Lauter, H. Godfrin, Static structure factor of two-dimensional liquid 3He adsorbed on graphite, J. of Low Temp. Phys. 169, 367-376 (2012)

• Rich Haley (Lancaster University): Probing the AB phase interface in superfluid 3He using quartz tuning forks (.pdf)

We present the results of our experimental study of the superfluid helium-3 A phase, B Phase, and the AB phase boundary between them, using quartz tuning fork resonators as mechanical probes. The transition between A phase and B phase is of first order, and the boundary between the two is arguably the most highly ordered interface to which we have experimental access. The order parameter maintains full coherence as it transforms smoothly from A phase on one side to B phase on the other over a distance of the order of a few coherence lengths. Our experiments take place at temperatures approaching 100 microkelvin in the pure condensate limit. We use shaped magnetic fields to induce the phase transition, stabilize the AB interface and control its motion. The properties of the interface and its motion through our experimental cell are inferred from the behaviour of quartz tuning fork resonators which project into the superfluid from the sidewalls of the cell. The damping of these resonators is used to measure the density of quasiparticle excitations. Variations in the damping are monitored as the interface is moved through the cell. Such variations may arise from several effects, for example heating, a change in the underlying order parameter of the surrounding superfluid phase, or the presence of defects in the order parameter texture. Our results are the first direct mechanical measurements of the boundary region that have been made in bulk superfluid.

• Kimitoshi Kono (Riken): Electron bubble transport under the free surface of superfluid 3He: chirality in 3He-A (.pdf)

Superfluid 3He-A is known as a p-wave chiral superfluid. The scattering of quasiparticles from a small object is predicted to be skew with respect to an anisotropy axis l, reflecting the chiral nature [1]. In this talk, we present our recent results of transport properties of electron bubbles trapped below the free surface of superfluid 3He. In particular, direct experimental evidence of the chirality in superfluid 3He-A will be presented [2]. The skew scattering of quasiparticles in 3He-A from an electron bubble results in bubble transport analogous to the Hall effect, where the anisotropy vector l plays the role of magnetic field. Under the experimental conditions, the effect is observed as an analogue of edge magnetoplasmon effect. After the analysis, we ascribe the observed signal to that from a single l domain covering over the whole detection area of 16x16mm2.

[1] R.H. Salmelin, M.M. Salomaa, and V.P. Mineev: Phys. Rev. Lett. 63, 868-871 (1989).

[2] H. Ikegami, Y. Tsutsumi, and K. Kono: Science 341, 59-62.

• Sorin Paraoanu (Aalto University): Analogue experiments in nanoelectronics

Superconducting quantum circuits offer an attractive toolbox for the simulation of effects predicted in quantum field theory but not yet confirmed experimentally. In this talk I will present our experiment [1] on the dynamical Casimir effect, a process in which the vacuum fluctuations of a field are transformed into real particles (typically photons) due to the action of an external modulation. By using an external magnetic field, we modulate the kinetic inductance per unit length of an array of SQUIDs. To measure the outgoing radiation, the array is coupled into a transmission line, via a low-dissipation (no-dielectric) capacitor realized with FIB (focused ion beam). This forms a cavity with quality factor Q = 50-100 and a resonant frequency tunable by magnetic field. We pump the device at 10.8 GHz and measure the spectrum and the correlations of the photons created by the dynamical Casimir effect at a frequency around 5.4 GHz.

I will mention certain further theoretical aspects of the modeling of this experiment, mostly the role of two-photon dissipative processes and the issue of backaction. Then I will discuss the connection between this experiment and other effects that rely on the instability of the quantum vacuum, namely the Hawking radiation, the Unruh effect, and the Schwinger effect.

[1] P. Lähteenmäki, G.S. Paraoanu, J. Hassel, P.J. Hakonen, Dynamical Casimir effect in a Josephson metamaterial, Proc. Natl. Acad. Sci. U.S.A., 110, 4234 (2013)

• John Saunders (Royal Holloway): Topological superfluids confined in nanoscale slab geometries

Nanofluidic samples of superfluid 3He provide a route to explore odd-parity topological superfluids and their surface, edge and defect-bound excitations under well controlled conditions. We have cooled superfluid 3He confined in a precisely defined nano-fabricated cavity to well below 1 mK for the first time. We fingerprint the order parameter by nuclear magnetic resonance, exploiting a SQUID NMR spectrometer of exquisite sensitivity. We demonstrate that dimensional confinement, at length scales comparable to the superfluid Cooper-pair diameter, has a profound influence on the superfluid order of 3He [1]. The chiral A-phase is stabilized at low pressures, in a cavity of height 650 nm. At higher pressures we observe 3He-B with a surface induced planar distortion. 3He-B is a time-reversal invariant topological superfluid, supporting gapless Majorana surface states. In the presence of the small symmetry breaking NMR static magnetic field we observe two possible B-phase states of the order parameter manifold, which can coexist as domains. Non-linear NMR on these states enables a measurement of the surface induced planar distortion [2], which determines the spectral weight of the surface excitations. The expected structure of the domain walls is such that, at the cavity surface, the line separating the two domains is predicted to host gapless states, protected by symmetry and topology. Increasing confinement should stabilize new p-wave superfluid states of matter, such as the quasi-2D gapped A phase. On the other hand, a cavity of height 1000 nm may stabilize a novel striped superfluid, with spatially modulated order parameter.

[1] L.V. Levitin, R.G. Bennett, A. Casey, B. Cowan, D. Drung. Th. Schurig, J.M. Parpia, Science 340, 841 (2013)

[2] L.V. Levitin, R.G. Bennett, E.V. Surovtsev, J.M. Parpia, B. Cowan, A. Casey, J. Saunders, submitted to Phys. Rev. Lett.

• Mihail Silaev (Physics of Microstructures, Nizhny Novgorod, and Aalto University): Localized fermionic states on vortices and interfaces in superfluid 3He-B

Localized fermions determine many physical properties of fully gapped superconductors and Fermi superfluids like 3He at low temperatures. Recently much interest was generated by proposals to study non-abelian statistics of Majorana fermions on vortices in chiral p wave superconductors and superfluids. Besides that bound fermions can appear at the interfaces between different topological media, e.g. different superfluid phases 3He-B and 3He-A. Surface bound states have been recently in the focus of intense research stimulated by the invention of topological superconductors.

In this talk we discuss characteristic properties of fermion spectra for different types of vortices in 3He-B. Due to the removed spin degeneracy singly quantized vortices in 3He-B have two anomalous branches crossing the Fermi level. In particular the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of fermionic zero modes. In the double-core vortices which appear in 3He-B at low pressure the manifold of zero energy states forms a highly anisotropic Fermi surface emerging inside vortex cores. We find a Lifshitz transition of the Fermi surface as a function of the momentum projection on the vortex axis and discuss its influence on the double-core vortex rotation dynamics.

• Peter Skyba (Institute of Experimental Physics, SAS, Kosice): Spin wave analogue of event horizon in superfluid 3He-B

We report on the theoretical model and the experimental results of the first experiment made in a limit of absolute zero temperature (~ 650 µK) studying the black/white hole horizon analogues using a completely new and pure physical system based on the spin superfluidity in superfluid 3He-B. The surface spin precession waves propagating on the background of the spin flow between two Bose-Einstein condensates of magnons in form of homogeneously precessing domains were used as an experimental tool simulating the properties of the black/white horizon. It is shown that at certain experimental conditions, confirmed by theoretical model, one can form a white hole horizon inside channel, which blocks propagation of the spin-precession waves between condensates. Once the white hole horizon is formed, there is an effect observed that the energy of excited spin precession waves is higher than the energy of the waves excited before horizon was formed.

• Edouard Sonin (Hebrew University): Transverse force on a vortex in superfluids without Galilean invariance (.ppt)

The talk addresses vortex dynamics in superfluids without Galilean invariance. Well-known examples of such superfluids are superfluids on lattices: the Josephson-junction array and the Bose-Hubbard model. The latter is usually used for the description of the cold-atom BEC in an optical lattice. The analysis is done within the continuous approximation. The continuous approximation restores translational invariance absent in the original lattice model, but the theory is not Galilean invariant. As a result, the calculation of the two transverse forces on the vortex, the Magnus Lorentz forces, requires the analysis of two balances, for the true momentum of particles in the lattice (Magnus force) and for the quasimomentum (Lorentz force), similar to that in the Bloch theory of particles in a periodic potential. While the developed theory yields the same Lorentz force, which was well known before, a new general expression for the Magnus force is obtained. The theory demonstrates how a small Magnus force emerges in the Josephson-junction array if the particle-hole symmetry is broken. The continuous approximation for the Bose-Hubbard model close to the superfluid-insulator transition is developed, which is used for calculation of the Magnus force. The theory shows that there is an area in the phase diagram for the Bose-Hubbard model, where the Magnus force has an inverse sign with respect to that expected from the sign of the velocity circulation.

• Viktor Tsepelin (Lancaster University): Studies of superfluid 4He using vibrating resonators (.pptx)

We present studies of superfluid 4He using a variety of mechanical oscillators; tuning forks, vibrating wires, and vibrating grids. The resonant frequency and the velocity determine the fluid drag force on the resonator. At low oscillation velocities the fluid drag force is proportional to the velocity and is dominated by the viscous normal fluid component below 100kHz and by sound emission at higher frequencies. At high oscillation velocities the flow becomes turbulent and the drag force becomes roughly proportional to the square of the oscillation velocity. We find that the critical velocity for superfluid turbulence is consistent with a square root dependence on the frequency for a wide range of oscillators. We also discuss measurements of the superfluid drag and the statistical properties of the transition from pure potential flow to turbulence at low temperatures.

• Paul Walmsley (Manchester University): Emission of small vortex loops due to reconnections in superfluid 4He in the zero temperature limit

We show that small vortex rings are emitted by reconnection events in superfluid 4He. In one experiment, binary collisions between unidirectional vortex rings produces secondary loops of both smaller and larger radii. The density of rings that had not interacted is capped at a critical value due to avalanche-like pile-ups. In another experiment, we observed the emission of small vortex rings with large mean free path from within dense vortex tangles. This process was found to only occur at temperatures below 0.7 K, providing insight into the quantum regime of superfluid turbulence where small-scale vortex structures are expected due to the fractalization of vortex tangles at low temperatures. At temperatures below 0.2 K, the condensation of 3He impurity atoms onto vortex cores was found to partially suppress the rate of ring emission.

(1) MIT bag model of hadrons, which is reproduced in magnon BEC confined in a textural trap. When the number of magnons increases, their zero point energy expels the texture, and the trap gradually transforms to a box with walls almost impenetrable for magnons. The resulting texture-free cavity filled by the magnon condensate wave function becomes the bosonic analog of the MIT bag, in which a hadron is seen as a cavity in the QCD vacuum, where the free quarks are confined in the ground or excited state.

(2) Higgs bosons - the amplitude modes, which have been experimentally investigated in condensed matter for many years, and now serve for the prediction of extra Higgs bosons. In He-B, the broken symmetry gives rise to 4 Goldstone modes and 14 Higgs modes. Based on the properties of the spectrum of these modes, Nambu suggested a general sum rule, which relates the masses of Higgs bosons to the masses of fermions. If this rule is applicable to the Standard Model, then one may expect that the observed Higgs boson with a mass of 125 GeV has a partner - another Higgs boson with mass 325 GeV. There is some evidence for such a particle.

(3) Majorana fermions, which exist in bulk 3He-A and on the boundaries, interfaces and inside the vortex cores in both phases.

• Vladislav Zavyalov (Aalto University): Probing vortex cores with trapped magnon condensates in 3He-B

Trapped Bose-Einstein condensates of magnon quasiparticles in 3He-B proved to be a convenient and sensitive tool for studying various 3He properties, such as the spatial distribution (or texture) of the order parameter or the relaxation processes in the zero temperature limit. In this work we investigate the influence of quantized vortices on the condensate. In a rotating sample filled with straight vortex lines we have observed a change in the trapping potential for the magnon condensate as well as an increase in the condensate relaxation rate. We attribute the additional relaxation to the dissipation of energy in a subsystem of fermionic quasiparticles bound to vortex cores. These core-bound fermions are coupled with the magnon condensate via oscillations of the vortex cores which are non-axisymmetric at low temperature. The relaxation rate of the condensate as a function of applied magnetic field displays a complicated pattern of peaks which in addition depends on temperature. We discuss whether this effect can be attributed to the 'minigap' structure of the energy spectrum of the core-bound fermions. Such spectra have been predicted by Caroli, de Gennes and Matricon in 1964 but have never been experimentally observed.

Thursday 12 September

Measurement & devices – JRA4

Chair Christian Enss <enss(at)kip.uni-heidelberg.de>

• Joern Beyer (PTB, Berlin): SQUID sensors for precision measurements at low temperatures

We have developed SQUID sensors for precision measurements at mK temperatures and below. Applications of these sensors range from the readout of low-temperature detectors and NEMS devices to susceptometry and thermometry. The presentation will discuss circuit concepts, such as transformer-coupled signal input, SQUID cascades and on-chip flux-locked loop, as well as the sensors noise and dynamic performance.

• Andrew Casey (Royal Holloway): NMR with SQUID detection

Nuclear Magnetic Resonance, NMR, has proved to be an invaluable tool in identifying the order parameter of superfluid 3He [1]. The temperature dependence of the Larmor frequency, the lineshape and the non-linear response to tip-angle all provide rich information on the state of the system. Experimentally there has been an increased effort to extract information about ever smaller volumes of space or features within a sample, e.g. nanofluidic confinement, phase boundaries, domain walls, vortices, effects of texture or other topological defects. To measure these features it has been necessary to increase the sensitivity of the NMR spectrometers used for these studies. One solution to this has been to use DC SQUIDs as amplifiers in the spectrometer, exploiting their sensitivity to magnetic flux [2].

In this talk I will describe the operation and performance of such a SQUID based NMR spectrometer in both a tuned and broadband configuration. We have demonstrated the coupling of these SQUIDs to receiver coils with a few 100 micron diameter, allowing the possibility for studies of features with a size on the order of the dipole healing length ~ 10 µm. PTB, Berlin, have designed and fabricated a new generation of novel SQUID current sensing devices with output current feedback, OCF, which allows operation at higher frequencies > 100 MHz. We have used these devices to measure the nuclear quadruple resonance response (NQR) of sodium chlorate at 30 MHz cooled to 10 mK on a cryogen-free dilution refrigerator. The bandwidth was previously limited by propagation delays to the room temperature control electronics which for our nuclear demagnetisation cryostats imposed a practical limit of a few MHz. This increased bandwidth should enable SQUIDs to be used in a wider range of applications in the future.

[1] A.J. Leggett Ann. of Phys. 85, 11 (1974)

[2] L.V. Levitin et al., Appl. Phys. Lett.91, 262507 (2007)

• Eddy Collin (Institut Néel, CNRS, Grenoble): Energy dissipation in nano-electro-mechanical devices at mK temperatures (.ppt)
E. Collin, M. Defoort, K.J. Lulla, C. Blanc, and O. Bourgeois

Micro- and nanomechanical devices (MEMS and NEMS) are under intense investigation because of their promising instrumental applications and their implications in fundamental issues of physics. These devices are ultra-sensitive mass and force detectors; they can be used in their linear or nonlinear regimes to implement various signal processing schemes. In a more fundamental realm, they can be thought of as probes for non-Newtonian deviations to gravity at small scales, for refined studies of the Casimir force, and for the study of quantum fluids. Moreover, nanoresonators themselves cooled to their quantum ground state tackle problems that have been around in quantum mechanics since the beginning, with the possibility of controlling a mechanical collective macroscopic degree of freedom at the quantum level. Having high quality devices is desirable in many of these ﬁelds. However, it is well known that the quality factor Q of mechanical structures becomes worse as their size is reduced. Different groups using different devices and materials have conducted experiments in the millikelvin range addressing the issue of energy dissipation in nanomechanical structures. All the results are understood in the framework of the Anderson-Philips Two-Level-System (TLS) model. However, there is no consensus on the quantitative findings: the origin of the low Q factor still remains a puzzle. In this talk I will quickly review the literature, and present our own findings which clearly prove that the electronic degree of freedom of the metallic coatings plays a crucial role in energy dissipation. When the metal in use becomes superconducting, low-Q devices at 4.2 K can reach quality factors of the order of a million at 20 mK.

Amorphous dielectrics are non-equilibrium quantum systems whose low temperature properties are governed by atomic tunneling systems. Many aspects are well described within the phenomenological standard tunneling model. Via their elastic and electric dipole moments tunneling systems interact mutually and with external fields. The dynamics of tunneling systems can be investigated by polarization echo experiments. Here the echo amplitude is measured as a function of the delay time between the two excitation pulses. Different dephasing mechanisms contribute to the decay of the echo amplitude. In amorphous dielectrics at very low temperatures the dominating dephasing mechanism is spectral diffusion, which is the interaction of resonant tunneling systems with non-resonant thermally fluctuating ones.

We have performed such echo decay measurements with an improved setup allowing us to observe echoes at very long delay times where the echo has decayed five orders of magnitude from its original amplitude. The data obtained in this way allows a precision test of the model of spectral diffusion and the distribution of parameters of the tunneling systems given by the standard tunneling model. We will show experimental results from measurements on BK7 and will discuss them in the framework of spectral diffusion and the standard tunneling model.

• Aviad Frydman (Bar Ilan University): The electron glass in semiconductors
Aviad Frydman, Julien Delahaye and Thierry Grenet

The electric conductivity in many highly disordered electronic systems is subject to strong electronic interactions, exhibits glassy phenomena such as slow relaxation to equilibrium, memory effects and aging. Since the glassy behavior is attributed to conduction electrons, such systems have been termed the “electron glass”. So far electron glass properties have been seen only in highly disordered metals or metal-like materials exhibiting hopping transport and having charge carrier densities larger than n = 10^{20} cm-3. No clear signs for memory effects or slow relaxations after a rapid cool-down have been observed in semiconductors. It has been proposed that an electron glass requires a hopping system characterized by a large number of charge carriers within a localization length. A standard semiconductor has a relatively small charge carrier density. Hence, in order to fulfill the above requirement one would need a relatively high doping degree in order to increase the localization length at very low temperatures, so that transport in the semiconductor is dominated by hopping conductivity. In the framework of the Microkelvin project we explore the electron glass phenomena in silicon and diamond samples at ultra-low temperatures in an attempt to detect electron glass behavior in doped semiconductors. The results and their implications will be discussed.

• Sean Giblin (University of Cardiff): Frustrating ways to emergent behaviour
Sean Giblin and Carley Paulsen

Spin ice materials are known to demonstrate emergent behaviour in the form of quasiparticles which can be described as magnetic monopoles. I will discuss the basic phenomena of spin ice and demonstrate that the magnetic charge like excitations can be controlled by carefully controlling experimental phase space at very low temperatures. The behaviour we have observed strongly suggests monopole properties can be controlled. However, this will be discussed in the context of other work which considers the effect of defects in the samples.

• Pertti Hakonen (Aalto University): Josephson junction amplifiers near the quantum limit

There is a strong need for robust quantum limited amplifiers at microwave frequencies. Lately, parametric amplifiers based on pumped nonlinear reactance have been considered for this purpose. An important class of these devices is formed by reflection amplifiers with negative impedance elements. Negative dynamical resistances are well known in semiconductor electronics, and can be used as amplifiers and oscillators. This possibility has not been widely studied in low temperature systems, although such phenomena are readily found in systems based on Josephson junctions and also microelectromechanical systems. In this talk, I will review two classes of parametric devices that we have been investigating in the Low Temperature Laboratory in collaboration with VTT.

We have developed a concept for the low-noise, wide-band microwave reflection-amplifier which utilizes the intrinsic negative resistance of a single Josephson junction. In our first generation amplifiers, the negative resistance of the shunted single junction is singled out on the amplification band using a band stop filter. A gain of 30 dB at 2.8 GHz was measured over a band width of 1 MHz, and the noise temperature was found to be within a factor of three from the quantum limit (½ $\hbar \omega$). Since the regular Langevin analysis is insufficient with frequency-dependent dissipation, we have resorted to numerical simulations using the fundamental AC and DC Josephson relations. According to the simulations, the device relies heavily on noise compression, accomplished via diminishing down mixing and increasing up mixing when enough power gain is available.

In the second class of amplifiers, we have operated parametric devices in which pumped metamaterial made of arrays of SQUIDs is placed in a coplanar transmission line cavity with a high quality factor. As such systems can be quickly tuned, they allow for the creation of two-photon microwave states and the observation of elusive phenomena such as the dynamic Casimir effect. Under flux-pumping at double frequency, these devices provide a gain up to 25 dB and a noise temperature of ~ 200 mK at 5 GHz. At detuned pumping conditions, we have analyzed two-mode correlations, which indicate strong increase of dissipation with increasing pump power. Dissipation, presumably in the silicon nitride dielectric, limits the achieved squeezing of the two mode correlations in the dynamic Casimir pair production.

• Klaus Hasselbach (Institut Néel, CNRS, Grenoble): Magnetic imaging with NanoSQUID microscopy

We present the scanning NanoSQUID microscope built in Grenoble and show results obtained through vortex imaging in pnictide superconductors, BaFeNiAs. We were able to obtain directly the dependence of the absolute value of the penetration depth on the electron doping.

We also present new types of NanoSQUIDs with improved sensitivity allowing fast readout down to the lowest temperatures, ideally suited for integration in present and future NanoSQUID microscopes.

In collaboration with P. Castellazzi, Z.S. Wang, D. Hykel, D. Hazra, J.R. Kirtley.

• Sebastian Kempf (Universität Heidelberg): Microcalorimeters with inductively read out paramagnetic and superconducting temperature sensors

The excellent energy resolution and the intrinsically dissipationless nature of operation are only two out of many properties that make microcalorimeters with paramagnetic or superconducting temperature sensors particularly attractive candidates for a variety of applications. In many cases, the temperature sensor has tight thermal contact to a suitable particle absorber and is inductively coupled to a superconducting pickup coil, thus making the inductance of this coil temperature dependent. The inductance change following the absorption of an energetic particle is read out by SQUIDs and is a high-resolution measure of the temperature change of the detector and therefore of the absorbed energy. After an introduction to the basics including design, optimization, fabrication and readout of the detectors, we summarize the present status of the detector development, discuss readout techniques for detector arrays and highlight some applications in which the detectors are either actively being used or are currently being developed for.

• Rüdiger Klingeler (Universität Heidelberg): Probing low-energy excitations in unconventional superconductors and quantum magnets by specific heat

Low-temperature specific heat is applied to the study of low-energy excitations in correlated electron systems with small or vanishing gaps. In Fe-based superconductors the symmetry of the superconducting gap is still under discussion. While most Fe-based superconductors exhibit s+- symmetry, our recent studies on K1−xNaxFe2As2 single crystals imply large T^2 contributions to the specific heat at low temperature. The strength and field dependence of this contribution provides evidence of d-wave superconductivity on almost all Fermi-surface sheets and enables to quantify the gap amplitude. Another prominent example where low-energy excitations show up are frustrated quantum magnets in the vicinity of a critical point. Again, thermodynamic studies on Li2ZrCuO4 and Li2CuO2 show signatures of short range helical/AFM correlations, a linear-in-T contribution to the specific heat at low temperatures and indicate a strongly enhanced gamma value.

• Tjerk Oosterkamp (Leiden Universiteit): MRI-AFM at mK temperatures and the prospects of scanning probe experiments at sub-mK temperatures

Magnetic Resonance Imaging by Atomic Force Microscopy (MRI-AFM) combines the non-destructive subsurface sensitivity and elemental specificity of an MRI scanner with the high spatial resolution of an Atomic Force Microscope. It relies on the detection of a small number of spins by a soft, magnetically tipped cantilever. In order to minimize thermomechanical noise of the cantilever and to increase spin polarization, MRFM is carried out at ultralow temperatures. Therefore, we developed a SQUID-based detection technique, which avoids cantilever heating. Among others, we demonstrate the manipulation and detection of electron spins on a silicon surface at temperatures as low as 30 mK. Our experiments are done in a pulse-tube dilution refrigerator (dry fridge), and care has been taken to reduce vibrations. We present STM-data, taken at milliKelvin temperatures, with atomic resolution even when the pulse tube is running. We will discuss future prospects for scanning probe microscopy experiments at even lower temperatures.

• Andreas Reiser (Universität Heidelberg): A microkelvin magnetic flux noise thermometer

Due to its non-driven nature, noise thermometry instrinsically is the method of choice when minimal heat input during the temperature measurement is required. Our noise thermometer, experimentally characterized for temperatures between 45 µK and 0.8 K, is a magnetic Johnson noise thermometer. Here the noise source is a cold-worked high purity copper cylinder, 5 mm in diameter and 20 mm long. The magnetic flux fluctuations generated by the electrons' Brownian motion is measured inductively with two dc-SQUID magnetometers at the same time. Cross-correlation of these two channels leads to a reduction of parasitic noise by more than one order of magnitude which allows measuring the tiny noise powers at microklevin temperatures.

Friday 13 September

Microkelvin grant review

Chair Matti Krusius <mkrusius(at)neuro.hut.fi>

• Microkelvin: views from the EU Project Office – Project Officer Maria Douka
• Report on management (NA1) & transnational access (NA2) – Coordinator Matti Krusius
• Report on knowledge & technology transfer (NA3) – Activity leader Peter Skyba
• Strengthening European research (NA4) – Activity leader Henri Godfrin
• Opening the microkelvin regime to nanoscience (JRA1) – Activity leader George Pickett
• Ultra-low-temperature nanorefrigeration (JRA2) – Activity leader Jukka Pekola
• Attacking fundamental physics questions with microkelvin condensed matter experiments (JRA3) – Activity leader Henri Godfrin
• Novel methods & devices for ultra-low-temperature measurement (JRA4) – Activity leader Chiristian Enss
• Microkelvin: views from the Advisory Board
• Microkelvin: observations from the Referees
• Microkelvin future: further possibilities within EU Horizon 2020 – Project Officer Maria Douka
• General Assembly: discussion about continuation & election of working group

Workshop finish Friday at 16:00

Posters

• Samuli Autti (Aalto University): Spontaneous formation of the magnon Q-ball in superfluid 3He-B
S. Autti, V.V. Dmitriev, V.B. Eltsov, P.J. Heikkinen, and V.V. Zavjalov

Long-living coherent magnetic states can be created by NMR techniques in 3He-B. These states can be described in terms of Bose-Einstein condensation of magnon quasiparticles. At temperatures below 0.2 Tc the magnon condensate can be formed in a pre-defined potential trap, created in an external magnetic field and inhomogeneous texture of the 3He-B order parameter [1,2]. Unlike Bose-Einstein condensates of cold atoms, the magnon BEC in 3He-B is able to modify its trapping potential since the order-parameter texture depends on the magnon density. This property makes the magnon condensate analogous to a so-called Q-ball [3]. A Q-ball in field theories is a soliton of self-localized charge in the scalar field with attractive interaction. In the case of the magnon BEC in 3He-B, the magnon number plays the role of the charge and the spin-orbit interaction provides the self-localization. We have observed that a condensate with a large enough number of magnons moves from the pre-existing trap to another location forming a new potential trap. This trap exists only while the condensate is localized inside it and thus displays the soliton nature of a "true" Q-ball. We have also observed two coexisting spatially separated magnon condensates in their self-supported original traps.

[1]. S. Autti et al., Phys. Rev. Lett. 108, 145303 (2012).

[2]. S. Autti et al., JETP Lett., 95, 611 (2012).

[3]. Yu. M. Bunkov, G. E. Volovik, Phys. Rev. Lett. 98, 265302 (2007).

• Andrew Casey (Royal Holloway): Demonstration of NMR signals from microcoils coupled to low inductance SQUIDs

A very small, planar pickup coil - a microcoil, is being developed to act as a local probe in the study of superfluid 3He confined in a thin film. As features such as domain boundaries could be present, it is of interest to develop a pickup coil with an increased spatial resolution to detect spins from various positions within the nanofluidic cell. The microcoils have an internal square loop size of 400 μm x 400 μm and were fabricated using lithographic techniques at PTB Berlin. This poster describes the design and performance of initial (single layer) and improved (triple layer) designs of the microcoils, using a 3He gas sample.

• Daniel Cox (Aalto University): Electron-phonon coupling in suspended graphene
Antti Laitinen, Mika Oksanen, Daniel Cox, Pertti Hakonen

The voltage biased electron system of a graphene monolayer will attain a quasi-equilibrium state where the Joule heat flows from electrons to the supporting substrate both via electronic heat diffusion and through inelastic scattering with the phonons of the graphene lattice. Heat flow from the electron system as a function of the electron temperature is characterized by a specific power law [1] given by $P = \Sigma \, ({T_e}^\delta - {T_p}^\delta)$, where Te is the electron temperature, Tp the phonon temperature, ∑ the coupling constant and δ a characteristic exponent.

We have employed shot noise thermometry in combination with ac conductance measurement for the determination of the electron-phonon coupling in high quality suspended graphene monolayers. The substrate, acting as a thermal bath, was kept at 50 mK using a dilution refrigerator while the electrons in our two-terminal graphene devices were heated up to Te = 100 - 600 K by Joule heating. In the regime Te > 200 K, we found that the electron-phonon coupling became the most important thermal relaxation channel with only minor contributions by the electronic heat diffusion along the current leads. Moreover, the chemical potential of the sample was varied using a back gate in our experiments.

At Te < 100 K, we observe power-law behavior characteristic to electronic diffusion with an exponent δ ≈ 1.5 - 2.0. Around Te = 200 K, there is a transition to a region with enhanced thermal relaxation. When Te > 200 K, we observe power-law dependence, δ ≈ 3 - 5, and the coupling constant increases as ∑ ~ μ2, which indicates a crucial role of two-phonon scattering events, reminiscent to the supercollision events analyzed by J. Song et al [2].

[1] J.K. Viljas, T.T. Heikkilä, Phys. Rev. B 81, 24504 (2010)

[2] J.C.W. Song, M.Y. Reizer, L.S. Levitov, Phys. Rev. Lett. 109, 106602 (2012)

• Martial Defoort (Institut Néel, CNRS, Grenoble): Modal decomposition in goalpost micro/nano electro-mechanical devices
M. Defoort, E. Collin, K.J. Lulla, C. Blanc, J. Guidi, S. Dufresnes, O. Bourgeois, and H. Godfrin

We have studied the first three symmetric out-of-plane ﬂexural resonance modes of a goalpost silicon micro-mechanical device. The fabrication process and ﬁrst ﬂexural mode have been described in earlier work. Measurements have been performed at 4.2 K in vacuum, demonstrating high Q and good linear properties. Numerical simulations have been realized to ﬁt the resonance frequencies and produce the mode shapes. These mode shapes are complex, since they involve distortions of two coupled orthogonal bars. Nonetheless, analytic expressions have been developed to reproduce these numerical results, with no free parameters. Owing to their generality they are extremely helpful, in particular to identify the parameters which may limit the performances of the device. The overall agreement is very good, and has been veriﬁed also on our nano-mechanical version of the device.

• Simone Gasparinetti (Aalto University): Cooper-pair pumping: experimental progress and perspective

In Cooper-pair pumps a net transfer of charge results from the cyclic manipulation of a macroscopically coherent quantum object. Cooper-pair pumps can be used to observe geometric phases and their interference, to realize quantum pumping using superpositions of charge states, and to investigate the interplay between decoherence and a periodic drive. They have also been considered as a candidate for quantum metrology.

In our recent experiments, we demonstrate quantized Cooper-pair pumping down to the level of a single pair. We study the crossover between adiabatic and nonadiabatic regimes and provide a characterization of Landau-Zener transitons in our pump. Finally, by operating the pump in a different way, we observe signatures of pure quantum pumping in our device.

[1] M. Möttönen, J.J. Vartiainen, J.P. Pekola, Phys Rev Lett 100, 177201 (2008).

[2] S. Gasparinetti, P. Solinas, J.P. Pekola, Phys Rev Lett 107, 207002 (2011)

[3] S. Gasparinetti, P. Solinas, Y. Yoon, J.P. Pekola, Phys Rev B 86, 060502(R) (2012)

[4] S. Gasparinetti, I. Kamleitner, Phys Rev B 86, 224510 (2012)

The LUMINEU project aims at developing a pilot double b decay experiment using scintillating bolometers based on ZnMoO4 crystals enriched in 100Mo. In the next months, regular deliveries of large-mass ZnMoO4 crystals are expected from the Nikolaev Institute of Inorganic Chemistry (Novosibirsk, Russia). It is therefore crucial for the LUMINEU program to test systematically and in real time these samples in terms of their bolometric properties, light yield and internal radioactive contamination. In this paper we describe an above-ground cryogenic facility based on a dilution refrigerator coupled to a pulse-tube cooler capable performing these measurements. A 23.8 g ZnMoO4 crystal was fully characterised in this setup. We show also that macro-bolometers can be operated with high signal-to-noise ratio in liquid-free dilution refrigerators.

Waves on the surface of a fluid in a gravitational field are among the most ubiquitous phenomena in nature. We report the first observation of gravity waves on the surface of superfluid 3He-B at temperatures below 0.2 Tc in the ballistic regime of quasiparticle motion [1]. At higher temperatures gravity waves are damped by the large viscosity of the normal component, and only third sound waves in a thin film have been observed. We excite the waves by vibrating a vertical cylindrical container filled partially with 3He-B. The oscillating free surface is coupled to a magnon Bose-Einstein condensate in a magneto-textural trap [2]. In the magnon BEC the magnetization of 3He precesses with coherent phase and common frequency, which is determined by the trapping potential. The oscillating surface modifies the shape of the trap and modulates the frequency. By measuring the precession frequency of the magnetization we have identified the two lowest surface wave modes of our system. Our measurements show that the damping of the waves decreases with temperature linearly with the density of the normal component and extrapolates to a finite value at zero temperature. We have also observed an enhancement of the relaxation rate of the trapped magnon condensate when the surface waves modulate the trap, whereas a similar modulation of the trap with the magnetic field does not affect the relaxation. We discuss the possibility that both the finite damping at T = 0 and the enhanced magnon relaxation could be related to surface-bound Majorana states expected to exist at the free surface of the topological superfluid 3He-B.

[1] V.B. Eltsov et al., arXiv:1302.0764

[2] S. Autti et al., Phys. Rev. Lett. 108, 145303 (2012)

According to current understanding Kelvin waves have a significant role in the energy dissipation of quantum turbulence in the zero temperature limit. The identification of a helical distortion on a straight vortex or a vortex ring is straightforward. In more complicated situations, such as Kelvin waves on a curved vortex or in case of a vortex tangle, it becomes a challenging task. Here we review the methods used to identify Kelvin waves within the vortex filament model. We test their suitability by using vortex configurations with known Kelvin spectra. We find that none of the methods is accurate enough, such that the verification of the theoretically predicted spectrum is not possible.

We report on experimental studies of dynamic nuclear polarization (DNP) and relaxation of 31P donors in natural silicon. After the pioneering work of Feher [1] the recent interest towards this system has been raised by the proposal of Kane [2] to utilize impurity atoms for quantum computing. The samples were studied in strong magnetic fields and temperatures below 1 K. At these conditions the donor electron spins are fully polarized and the relaxation times of electrons and nuclei are very long. Pumping the allowed electron spin transitions of the sample with very low RF power (<1 μW) efficiently creates DNP of 31P and 29Si. Pumping the forbidden transition of 29Si (solid effect) creates narrow peaks in the ESR spectrum, which correspond to polarization of 29Si in certain resolved lattice sites around the donors.

[1] G. Feher, Phys. Rev. 114, 1219 (1959)

[2] B.E. Kane, Nature, 393, 133 (1998)

We present experimental progress toward ultrasensitive microwave power measurements using the superconductor proximity effect in a superconductor/normal-metal/superconductor (SNS) circuit. In our devices three aluminium leads directly contact a gold-palladium nanowire with a small volume ([100 nm]^3) in order to form long (700 nm) and short (300 nm) SNS junctions on the same nanowire. To calibrate the power sensor, we use the long junction as a local dc heater of the electronic system while simultaneously measuring the switching current probability distribution in the short junction. First results show resolution of the switching current statistics down to local dc heating powers of 1 fW at bath temperatures < 50 mK. Operated as a bolometer, the resulting noise equivalent power (NEP) is ~100 aW/sqrt(Hz) when ramping the current bias over 10 ms. By employing an RF measurement scheme and by further reducing heat capacity and thermal conductance of the nanowire, we aim to reach a NEP sufficient for detection of individual photons in the microwave regime.

• Matti Manninen (Aalto University): Surface Waves in normal and superfluid 3He and 4He

We have studied surface waves in 3He both in the normal and superfluid phases. The waves were excited mechanically and detected capacitively with an interdigital capacitor. In superfluid 3He the waves were observable only at temperatures below 0.2 mK and in normal 3He above 50 mK. The geometry of the helium sample volume was complex and many different surface wave resonance modes were excited. In normal 3He fewer resonances were observed than in superfluid 3He.

One of the challenges of the modern research on the dynamics of quantized vortices is the identiﬁcation of dissipation mechanisms in superﬂuids with almost no normal component. It is generally believed that an essential part of the dissipation is the energy cascade of Kelvin waves, helical excitations on vortex lines, which transfer the kinetic energy from macroscopic scales larger than the inter-vortex distance to small scales where microscopic dissipation mechanisms like quasiparticle emission by vortex cores terminate the cascade. So far the experimental veriﬁcation of this picture is missing.

We have studied the librating motion of a cylindrical sample of superﬂuid 3He-B, that is rotation of the sample around its axis with a periodically modulated angular velocity, in the temperature range 0.14 – 0.20 Tc. The modulation excites inertial waves in the liquid and Kelvin waves on vortex lines as seen from the decrease of vortex polarization. The polarization is determined from its inﬂuence on the order-parameter texture, probed with Bose-Einstein condensates of magnon quasiparticles. When the modulation of rotation velocity is stopped, the energy stored in the inertial waves is dissipated and the vortex polarization is restored. By calibrating the energy using the known free energy diﬀerence in solid-body rotation at diﬀerent velocities we can extract the dissipation rate per vortex line in absolute units. We present dissipation measurements as a function of temperature, pressure, and rotation velocity, and discuss the relation of our results to the picture of the Kelvin-wave cascade.

The conditions for Fabry-Pérot resonances in rectangular graphene sheets with nonperfect contacts were recently analyzed by Gunlycke and White [1] who showed that, under certain conditions evenly spaced groups of resonances, separated by ΔE ~ hvF/2L, can emerge. These collective resonances originate owing to simultaneous participation of modes in nonequivalent channels that are facilitated by transversely quantized states with small energy separation. Such collective resonances should not be confused with the ordinary two-channel Fabry- Pérot resonances observed in single-wall carbon nanotubes.

We report the analysis of Fabry-Pérot type interferences in high-mobility suspended graphene using both shot noise and conductance measurements. Differential conductance shows definite Fabry-Pérot patterns emerging, by taking the derivative of the conductance the visibility is improved. The Fourier transform of the data shows three sets of peaks which are identified as resonances of 1) clean suspended part bordered by pn junctions, 2) full length of the sample with scattering from the contacts, and 3) width of the sample. The Fabry-Pérot pattern is also visible in our shot noise measurements. Their analysis reveals again three sets of Fourier peaks, which nearly coincide with those obtained from our conductance measurements. A correlation analysis between conductance and shot noise indicates rather weak correlation. This analysis demonstrates that the observed Fabry-Pérot pattern originates from more than two channels in contrast to interference phenomena in single walled carbon nanotubes.

[1] D. Gunlycke and C. T. White, Appl. Phys. Lett. 93, 122106 (2008)

In general, it is impossible to observe shot noise in macroscopic resistors but in small mesoscopic systems this is feasible at low temperatures. The criterion for seeing shot noise is the small size of the sample; the scale has to be below the electron–phonon scattering length of the material at the measuring temperature. Fano factor and cross correlations tell about the type of noise in the sample as well as about the physical phenomena behind the fluctuations. An interesting type of cross correlation measurement in a four port diffusive system is the determination of the Hanbury-Brown–Twiss (HBT) exchange correction factor in a manner proposed by Blanter and Büttiker [1]. The correction factor can be used to characterize the geometry of the sample; the resulting factor differs in sign depending on whether the sample forms effectively a diffusive cross or box structure.

In this work we present the measured shot noise relations of a thin-film copper cross in the cold and hot electron regimes. In the analysis of the experimental data the theoretically expected slope relations given by [2] in various configurations were found to match the data quite well. The exchange correction factor ΔS = |SC| - |SA| - |SB| is defined by subtraction of the cross correlation slopes in voltage following the original definitions by Blanter & Büttiker and Shukhorukov & Loss [1,2]. Theoretically, based on Pauli Virtanen’s simulation according to general principles of [2] it can be seen that in the cold regime ΔS = 0 whereas in the hot-electron regime ΔS < 0 should be clearly evident, and indeed this is the case in our measurements.

[1] Ya.M. Blanter, M. Büttiker, Phys Rev B 56,2127 (1997)

[2] E.V. Shukhorukov, D. Loss, Phys Rev B 59, 13054 (1999)

• Tetiana Romanova (Institute for Low Temperature and Structure Research, Polish Academy of Sciences, Wrocław): Heat transfer in CO-N2 solid solution

T.V. Romanova, P. Stachowiak, A. Jeżowski, W. Trzebiatowski

The dependences of thermal conductivity on temperature for pure carbon monoxide and solid solution of carbon monoxide-nitrogen for different concentrations of nitrogen in the temperature range 1.5 – 40 K are presented. The CO-N2 solution is a unique object for investigation, due to the absence of mass mismatch. The solution allows us to investigate the interaction of phonons with impurities directly, without isotopic effect. The obtained dependences of the thermal conductivity on temperature show a typical behavior for a dielectric crystal. This dependence is determined by the mechanisms of phonon scattering. The contribution of the various mechanisms of phonon scattering to the thermal conductivity of CO-N2 solid solution at different concentrations was calculated. The crystals with higher concentration of nitrogen admixture exhibit lower thermal conductivity. The excess thermal resistivity is calculated. Some discussion of the results is given.

• John Saunders (Royal Holloway): Superfluidity of 3He confined in slab geometry

Nanofluidic samples of superfluid 3He provide a route to explore odd-parity topological superfluids and their surface, edge and defect-bound excitations under well controlled conditions. We have cooled superfluid 3He confined in a precisely defined nano-fabricated cavity to well below 1 mK for the first time. We fingerprint the order parameter by nuclear magnetic resonance, exploiting a SQUID NMR spectrometer of exquisite sensitivity. We demonstrate that dimensional confinement, at length scales comparable to the superfluid Cooper-pair diameter, has a profound influence on the superfluid order of 3He [1]. The chiral A-phase is stabilized at low pressures, in a cavity of height 650 nm. At higher pressures we observe 3He-B with a surface induced planar distortion. 3He-B is a time-reversal invariant topological superfluid, supporting gapless Majorana surface states. In the presence of the small symmetry breaking NMR static magnetic field we observe two possible B-phase states of the order parameter manifold, which can coexist as domains. Non-linear NMR on these states enables a measurement of the surface induced planar distortion [2], which determines the spectral weight of the surface excitations. The expected structure of the domain walls is such that, at the cavity surface, the line separating the two domains is predicted to host gapless states, protected by symmetry and topology. Increasing confinement should stabilize new p-wave superfluid states of matter, such as the quasi-2D gapped A phase. On the other hand, a cavity of height 1000 nm may stabilize a novel striped superfluid, with spatially modulated order parameter.

[1] L.V. Levitin, R.G. Bennett, A. Casey, B. Cowan, D. Drung. Th. Schurig, J.M. Parpia, Science 340, 841 (2013)

[2] L.V. Levitin, R.G. Bennett, E.V. Surovtsev, J.M. Parpia, B. Cowan, A.Casey, J. Saunders, submitted to Phys. Rev. Lett.

• Aya Shibahara (Royal Holloway): A microkelvin cryogen-free platform

We report the experimental demonstration of the feasibility of reaching temperatures below 1 mK using cryogen-free technology. Our prototype system comprises an adiabatic nuclear demagnetisation stage, based on hyperfine-enhanced nuclear magnetic cooling, integrated with a commercial cryogen-free dilution refrigerator and 8 T superconducting magnet. Thermometry was provided by a current-sensing noise thermometer. The minimum temperature achieved at the experimental platform was 600 μK. The platform remained below 1 mK in excess of 24 hours, indicating a total residual heat-leak into the experimental stage of 5 nW. This work opens the way to widening the accessibility of temperatures in the microkelvin regime, of potential importance in areas from the application of strongly correlated electron states in nanodevices to quantum computing.

• Aya Shibahara (Royal Holloway): Fast current sensing noise thermometry for dilution refrigerator temperatures

We have developed a fast, precise current sensing noise thermometer based on a 1.290 Ω platinum tungsten resistor. The thermometer has been optimised for speed, taking advantage of the improvements in SQUID noise and bandwidth. We measure a 1 % precision in just 100 ms, independent of temperature.

Damping in macroscopic mechanical resonators can generally be described by a linear damping force. Present-day advances in nanofabrication, however, have made it possible to explore damping in systems with one or more atomic-scale dimensions. Recently, damping in graphene mechanical resonators was found to depend non-linearly on the amplitude of motion in measurements using frequency-modulated mixing techniques [1]. The drawback of such mixing techniques is that it is hard to know the amplitude of motion for quantitative analysis. In this work, we have employed capacitive detection methods, in which the graphene mechanical resonator, positioned on top of a counter-electrode, acts as part of an electrical cavity (LC) resonator. In our measurements, the change in the resonator capacitance can be calculated quite accurately, which allows a precise determination of the amplitude of vibrational motion [2]. At large vibration amplitudes, we observe both softening and hardening Duffing behavior on different single layer graphene resonators. These effects are typically caused by nonlinear external potentials and geometric effects, and can be modeled by a force that is proportional to the cube of the resonator displacement x3. At large amplitudes, we also observe the effect of nonlinear damping (force proportional to x2•dx/dt). From the response amplitude curve, it is difficult to distinguish between linear and nonlinear damping, but when we look at the responsivity (amplitude divided by driving force) of the resonator, we can clearly see a decrease for large amplitudes. As linear damping does not cause any change in responsivity, we can use this to determine the strength of nonlinear damping in our resonators.

[1] A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, Nature Nanotech 6, 339 (2011)

[2] X. Song, M. Oksanen, M. Sillanpää, H. Craighead, J. Parpia, P. Hakonen, Nano Lett. 12, 198 (2012)

• Juho Rysti (Aalto University): Melting pressure of saturated helium mixture

We have measured the melting pressure of a concentration saturated helium mixture from 10 mK to 450 mK. The hcp-bcc transition in the crystal structure is clearly observed.

• Sergey Vasiliev and Jarno Järvinen (Turku University): Magnetic resonance of atomic hydrogen and deuterium in solid H2 and D2 matrices below 1 K (.pptx)

Hydrogen and deuterium solids at low temperatures represent a special class of quantum crystals, where due to the large zero point oscillations and light mass, the effects of quantum tunneling play an important role. The behavior of atomic impurities in these crystals attracted the attention of researchers because of the possibility of reaching collective quantum phenomena related with Bose-Einstein Condensation (BEC) or the so-called supersolid behavior. This may happen at high enough densities of atomic hydrogen. In our recent work we succeeded in reaching record high densities of atoms 4^19 cm-3. This has been done by implementing a novel method of in-situ dissociation of H2 or D2 molecules by low temperature (<1 K) RF discharge. H and D are the simplest atomic systems where magnetic resonance methods may be utilized for the characterization of the sample properties. Having non-zero proton and electron spins they provide a large variety of possibilities for NMR, ESR and double resonance methods. Our experiments are performed in a strong magnetic field of 4.6 T, so that electron spins are fully polarized below 1 K. This simplifies the dynamic nuclear polarization (DNP) and offers several ways of measuring relaxation of allowed and forbidden magnetic resonance transitions.

In this work we present the first ESR study of H/D-impurities stabilized in solid H2 and D2 matrices below 1 K. We demonstrate that the chemical reactions of isotopic exchange play an important role and help in reaching even higher densities of atomic hydrogen. We found that the quantum isotopic exchange reactions D+H2=H+HD, D+HD=H+D2 proceed with sufficiently high rate even at temperatures below 1 K and effectively convert atomic deuterium into hydrogen. It turned out that H densities after such conversion reached record high densities of 8^19 cm-3, twice higher than ever before. At such densities the effects of the dipole-dipole interactions between atoms lead to substantial homogeneous broadening of the ESR lines with the line widths exceeding 10 Gauss. High, nearly 100 % nuclear polarization of H was created by means of solid- and Overhauser effects within one hour of irradiation by <1 µW of mm-wave power. Pumping the second line of D (center of ESR spectrum) we created simultaneously positive DNP of D and negative DNP of H. We discuss possible explanations of this effect, the nuclear polarization transfer between H and D, or strong exchange effects between clusters of H atoms.

• Maciej Zgirski (Institute of Physics, Polish Academy of Sciences, Warsaw): How to measure magnetic field by flipping a coin? Switching measurements of DC-SQUIDs

The SQUID (Superconducting Quantum Interference Device) is the most sensitive known sensor of magnetic flux. It is built of two Josephson Junctions embedded in a superconducting loop. Such a loop is capable of supporting a supercurrent up to a critical value Ic which periodically varies with the magnetic field. Above Ic a finite voltage develops across a SQUID. Its value is also magnetic field-dependent what provides a means for magnetic flux-to-voltage conversion. Traditionally the SQUID is current-biased above the critical current and the resulting voltage across the SQUID is measured by lock-in techniques [1]. The method requires shunting resistors which increases the complexity of sensor fabrication.

Recently there is a new trend in SQUID magnetometry [2]: nanometer-sized SQUID loops defined with e-beam lithography are tested for switching current – a current at which the SQUID switches to a finite voltage state due to thermal fluctuations. We present the new measuring protocol which involves probing a SQUID with a series of current pulses. The switching for a current pulse of given duration exhibits stochastic character: the SQUID may switch with probability p or not switch with probability 1-p. Hence it resembles a coin for which a “heads and tails” experiment is performed. However, unlike in a fair coin experiment our “coin” probabilities p can be set with the magnetic flux &phi threading the SQUID loop, p = p(&phi). The number of switchings n for N probing pulses is governed by the binomial distribution. The width of the distribution compared against p(&phi) gives the ultimate resolution of the pulse technique for DC-SQUID magnetometry.

In the future we are planning to apply this technique for magnetization measurements of clusters and nanowires.

[1] SQUID Handbook, edited by J. Clarke and A. Braginski (2004)

[2] W. Wernsdorfer, Supercond. Sci. Technol. 22, 064013 (2009)

General information

The workshop will host oral and poster sessions. Participation is expected to be around 70 persons. Presentations by visiting Microkelvin Users are particularly encouraged. Currently the programme is under construction. Please, contact the appropriate chairman and the coordinator Matti Krusius [mkrusius(at)neuro.hut.fi] about presentations and participation.

Information about the Microkelvin Collaboration (EU grant no. 228464 under FP7 research infrastructures) is available starting from the address [link].