An important property of shot noise is that it is typically proportional to the average current. This property may be taken advantage of by using an adiabatic cyclostationary drive that modulates the noise by a few first harmonics of the base frequency.
We have analyzed theoretically a setup (see the figure on the right) where a time-dependent current consisting of a DC bias and two sinusoidal harmonics, is driven through a sample. The down-converted noise power spectrum is found to vary depending on the local-oscillator phase of the mixer. The theory of this phase-dependent noise suggests that the cyclostationary drive can be used to improve the sensitivity of a radio-frequency single electron transistor (RF-SET) by a small fraction.
In addition, we have shown that this scheme can be used to measure the shot noise accurately even in nonlinear high-impedance samples.
The modulation setup. Current i(t) =I0 + I1sin(ωt) + I2cos(2ωt) + n(t) flows through the sample. Output current is y(t) = i(t) x D(t), where D(t) = D0 sin(ωt + φ0). When the sample exhibits current-dependent shot noise, the down-converted noise power spectrum varies depending on the local-oscillator phase of the mixer.
An arbitrary nonlinear I-V curve illustrating the problem of the noise measurements. Regions A and B have different impedances and the amplifier noise contribution to the total noise is different at these points. In 2v0 modulation, the sample is dc biased (marked by circles) and a signal I2cos(s2v0td) is added (marked with dotted lines). By measuring the noise in both quadratures by varying mixer phase f, one may extract the shot noise contribution to the total noise.
Measurement schemes considered in this paper. Each contain an input I filtered through a band-pass filter (denoted with BP, corresponding to the function HBP). In the DC mixing scheme, analogous to that utilized in B. Reulet et al., Phys. Rev. Lett. 91, 196601 (2003), the stationarily driven and band-pass filtered input is mixed twice with itself, low-pass filtered sdenoted with LP, corresponding to the function HLPm) and averaged. The “AC mixing scheme” is a modification of the DC scheme, including a cyclostationary driving of the measured system, and mixing with an extra function fstd=cos(nω0(t+t0), synchronized with the driving and with a controlled phase shift t0. In the “AC statistics scheme,” the statistics of the output is measured and the driven and filtered signal is mixed only with fstd.
Cyclostationary measurement of low-frequency odd moments of current fluctuations
T.T. Heikkilä and L. Roschier
Phys. Rev. B 71, 085316 (2005)
Cyclostationary shot noise in mesoscopic measurements