Noninvasive and nonadiabatic quantum Maxwell demon

Abstract

A quantum mechanical Maxwell demon is proposed in a quantum dot setting. The demon avoids continuous-measurement induced decoherence by exploiting an undetailed charge detector. The control of coherent tunneling via Landau-Zener-Stückelberg-Majorana driving allows for efficient feedback operations with no work invested. The local violation of the second law achieves simultaneous power generation and cooling. We discuss the response current fluctuations, and the demon backaction deriving from failures, finding optimal performance in the nonadiabatic regime.

Figures (9)

• Figure 1: Three steps of the demon operation inducing transport through a DQD coupled to reservoirs L and R: detection (of whether there is a particle in the DQD), operation (perform a voltage pulse that exchanges the energies of the left and right dot levels), and reset. The demon measures the total charge, $N$, continuously and activates feedback operations when $N$ changes. $\Omega$ is the avoided crossing splitting.
• Figure 2: (a) Average particle current through the DQD as a function of the applied electrochemical potential bias and the speed of the energy ramp, with cuts along the marked dotted lines plotted in the lateral panels, with $\Gamma=\Omega/\hbar$, $T_l = T_r = 0.75\Omega/k_{\rm B}$, $\varepsilon_0 = -0.5\Omega$, $\mu_r = 0$, $\Delta = 6\Omega$. The dashed line in the $\Delta\mu=0$ panel plots $[\tau_d+1/\Gamma f^0(1-f^0)]^{-1}$. (b) Histograms of the time-averaged current $I_\gamma\equiv\langle I^\gamma(t)\rangle_t$ of $10^6$ trajectories computed during a time $t_{run}=10^5\hbar/\Omega$ for three different speeds marked by colored symbols in the main panel in (a): $\Delta_\varepsilon/\tau_d=(0.1,0.65,0.8,1.1,1.75)\Omega^2/\hbar$ and $\Delta\mu=0$. We fix the splitting at the avoided crossing, $\Omega\sim\unit[1]{meV}$
• Figure 3: Thermodynamic currents: heat from terminal (a) $L$ and (b) $R$, (c) generated power and (d) work performed by the demon, as functions of the electrochemical potential difference and the driving speed. The dotted line in (a) marks the values of $\mu_L^*$ defined in the text. (e) Cuts of the other panels for fixed $\Delta\mu=-0.22\Omega^2/\hbar$. The grey line represents the left hand side of Eq. \ref{['eq:1law']}. The right panel shows a zoom of the adiabatic region marked by a dotted square. Same parameters of Fig. \ref{['fig:current']}.
• Figure 4: (a) Entropy production in the system reservoirs as a function of the applied electrochemical potential bias and the speed of the energy ramp. Side panels show cuts along the marked dotted lines with corresponding colors. Parameters as in Fig. \ref{['fig:current']}. (b) Histograms of the time-averaged entropy production rates, $\dot{S}_s^\gamma=\langle\dot{S}_s^\gamma(t)\rangle_t$ of $10^6$ trajectories computed during a time $t_{run}=10^4\hbar/\Omega$ at the conditions marked by the corresponding symbols in (a): $\Delta_\varepsilon/\tau_d=(0.25,0.36)\Omega^2/\hbar$ and $\Delta\mu=-2.26\Omega$ (yellow and orange), and $\Delta_\varepsilon/\tau_d=(0.1,0.65)\Omega^2/\hbar$ and $\Delta\mu=0$ (red and violet curves).
• Figure S1: Occupation probability of the right dot after going through the avoided crossing at a speed $\Delta_\varepsilon/\tau_d$, for $\varepsilon_0=-0.5\Omega$ and $\Delta_\varepsilon=6\Omega$, for three different temperatures of the reservoirs, $k_\text{B}T=(10^{-3},0.75,2)\Omega$, and $\Delta\mu=0$. The lower temperature curves are almost identical. The inset zooms in the adiabatic regime.