Noise properties of two single-electron transistors coupled by a nanomechanical resonator

We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrically large enhancements of the low-frequency current noise. These noise properties can be understood in terms of the effects on the SET currents of fluctuations in the state of a resonator in thermal equilibrium that persist for times of the order of the resonator damping time.

Figure 1

Schematic circuit diagram for the two-SET resonator system. The central box represents the resonator and the outer boxes represent the two SET islands containing $N_1$ and $N_2$ electrons.

Figure 2

(Color online) Current noise through one of two SETs coupled to a resonator plotted as a function of the coupling strength, $\kappa$. The approximate expression for the current noise [Eq. (22)] and the noise of a SET coupled to a resonator whose state is controlled solely by a coupling to an external bath with fixed or variable damping are also shown for comparison. For each plot we have set $ϵ=0.1$ and $V_1=V_2$.

Figure 3

(Color online) The zero-frequency component of the cross-correlation power spectrum, plotted as a function of $\kappa$ and $v_d$, with $ϵ=0.1$.

Figure 4

(Color online) A comparison of the cross correlation between the two leads, and the autocorrelation minus the constant term $[S_{I_1{I}_1}^{-}\left(0\right)∕\left(2e{I}_0\right)]$ plotted as a function of $\kappa$ with $ϵ=0.1$ and $v_d=0$. Also plotted is the cross correlation without back-action.