Transport and Nonreciprocity in Monitored Quantum Devices: An Exact Study

We study noninteracting fermionic systems undergoing continuous monitoring and driven by biased reservoirs. Averaging over the measurement outcomes, we derive exact formulas for the particle and heat flows in the system. We show that these currents feature competing elastic and inelastic components, which depend nontrivially on the monitoring strength $\gamma$. We highlight that monitor-induced inelastic processes lead to nonreciprocal currents, allowing one to extract work from measurements without active feedback control. We illustrate our formalism with two distinct monitoring schemes providing measurement-induced power or cooling. Optimal performances are found for values of the monitoring strength $\gamma$, which are hard to address with perturbative approaches.

Figure 1

(a) Monitored level of energy ${ϵ}_d$, coupled to left and right reservoirs with asymmetric hybridization functions ${\mathrm{\Gamma }}_L(\omega )\ne {\mathrm{\Gamma }}_R(\omega )$. The level occupation is measured with strength $\gamma$, providing the inelastic mechanism promoting particles from energy ${\omega }_1$ to ${\omega }_2$ and inducing a current against the bias (arrows). The blue-shaded areas correspond to the Fermi distributions of the reservoirs. For all plots, we use the two-filter model discussed in the main text, with ${ϵ}_R=1.48t=-{ϵ}_L$, $\mathrm{\Delta }=0.55t$, which maximizes the unbiased particle current at ${\mu }_{L,R}=T_{L,R}=0$. (b) Peaked structure of the unbiased particle current as function of the measurement strength $\gamma$ for varying ${ϵ}_d$. Inset: the unbiased current decays for increasing temperatures ($\gamma =1$). (c) Differential conductance $G$ as a function of the chemical potential $\mu$ at $T=0$ for increasing $\gamma$. The measurement suppresses the resonance associated with the single level and favors those from the filters, as highlighted by arrows. (d) Electric power as function of a symmetric bias ${\mu }_R-{\mu }_L$ around $\mu =0$, for different values of $\gamma$. Dashed lines correspond to linear response calculations.

Figure 2

(a) Two-level system under continuous monitoring of its cross-correlations, coupled to a left (hot) and right (cold) reservoir. For applications, we consider the same filters as in Fig. 1, aligned with the levels ${ϵ}_{L/R}$. (b) Parameter region where a reservoir at temperature $T_R=t$ can be cooled by measurement $\mathrm{\Delta }=0.5t$ and varying $\gamma$. The range of parameters where quantum measurement cooling is possible reduces with increasing $\gamma$. The black dot corresponds to ${ϵ}_L=10t$ and ${ϵ}_R=3t$, used in (c) and (d). (c) Heat flowing into the right reservoirs for increasing temperature bias $T_L>T_R$. QmC occurs in the colored region below some critical temperature bias. (d) Parametric plot of the coefficient of performance (COP) of QmC. Curves are obtained by varying the measurement strength $\gamma$.