With advanced fabrication techniques it is possible to make nanoscale electronic structures that have discrete energy levels. Such structures are called artificial atoms because of analogy with true atoms. Examples of such atoms are quantum dots in semiconductor heterostructures and Josephson-junction qubits. It is also possible to have artificial atoms interacting with each other. This is an artificial molecule in the sense that the electronic states are analogous to
the ones in a molecule. In this letter we present a different type of artificial molecule that, in addition to electronic states, also includes the analog of nuclear vibrations in a diatomic molecule. Some of the earlier experiments could be interpreted using this analogy, including qubits coupled to oscillators and qubits driven by an intense field. In our case the electronic states of the molecule are represented by a Josephson-junction qubit, and the nuclear separation corresponds to the magnetic flux in a loop containing the qubit and an LC oscillator. We probe the vibronic transitions, where both the electronic and vibrational states change simultaneously, and we find that they are analogous to true molecules. The vibronic transitions could be used for sideband cooling of the oscillator, and we see damping up to sidebands of order 10.
The potential energy of the artificial molecule. The total potentials (red) are formed as a sum of qubit energy (blue) and a harmonic vibrational potential. The six lowest energy eigenstates are shown for both electronic states. The bars represent the energy differences ΔE = hν corresponding to the drives of low and high frequency, νLF and νHF, respectively. The parameters are for the bias point (Φb, ng) = (0:60Φ0, 1.16) marked by a cross in Fig. 3a. b, A close-up at the lowest eigenstates together with wave functions (shaded). The strongest transitions according to the Franck-Condon principle are shown by arrows, and are labeled by the change of vibrational quanta k.
SEM micrographs and circuit diagram of the artificial molecule. a, General view showing top electrodes of the the oscillator capacitors (2 large pads) with capacitances 2C each. b, Enlargement of the white square area in a showing the 300 μm-long microstrip loop that forms the inductance L of the oscillator. c, Magnification of the white diamond in b showing the single Cooper pair transistor (SCPT) formed by two Josephson junctions with coupling energies EJ1 and EJ2 and the gate electrode. Also visible is a reference SCPT (lower left) which enables to estimate the resistances of the junctions in the sample. d, The circuit diagram shows the SCPT and the LC oscillator connected in parallel. The resistance R = 2.8 kΩ represents the AC-dissipation of the capacitors as well as of other parts of the circuit. The artificial molecule is biased by a gate voltage Vg and an external magnetic flux Φb. For measurement it is connected to a low frequency drive (LF) via a Z0 = 50 Ω transmission line and a coupling capacitor Cc = 7 pF. The high frequency drive (HF) is used to excite the vibronic transitions.
as a function of the bias point (Φb, ng). The color bar gives the scale for Γ. The dashed arch indicates the pure electronic transition δE/h = νHF = 22 GHz. The cross denotes the bias point of Fig. 1 where k = -2. The low frequency power PLF = -129 dBm. b, the same as a but at higher PLF = -123 dBm. c, A cut along ng = 1.27 as indicated by the horizontal lines in panels a and b. d, A cut along Φb = 0.56Φ0.
Simulated properties of the artificial molecule. a, The reflection amplitude Γ calculated as a function of the bias point in the flux-charge plane. The parameters correspond to the measurement plotted in Fig. 3a. b, The energy flow from the qubit to the resonator showing damping for lower sideband transitions (blue) and amplification for the upper sideband transitions (red). The power unit is PLF = -129 dBm.
Vibronic spectroscopy of an artificial molecule
David Gunnarsson, Jani Tuorila, Antti Paila, Jayanta Sarkar,
Erkki Thuneberg, Yuriy Makhlin, and Pertti Hakonen, Phys. Rev. Lett. 101, 256/8061-4 (2008).