Maxwell's demon based on a single qubit

We propose and analyze Maxwell's demon based on a single qubit with avoided level crossing. Its operation cycle consists of adiabatic drive to the point of minimum energy separation, measurement of the qubit state, and conditional feedback. We show that the heat extracted from the bath at temperature $T$ can ideally approach the Landauer limit of $k_{B}Tln2$ per cycle even in the quantum regime. Practical demon efficiency is limited by the interplay of Landau-Zener transitions and coupling to the bath. We suggest that an experimental demonstration of the demon is fully feasible using one of the standard superconducting qubits.

Figure 1

The scheme and operation cycle of the qubit demon.

Figure 2

$\langle Q\rangle$ as a function of the rate $v=\hslash \dot{q}/\mathrm{\Delta }{E}_A$ in a quasistatic $A\to X$ ramp. The horizontal arrow points to the result of fully adiabatic evolution based on Eq. (1). The solid black line is the full numerical solution of the master equation (4). The blue dots are based on the stochastic quantum trajectory simulations. The parameters are $\epsilon =0.1,\beta \mathrm{\Delta }{E}_A=10$, and $g^2={10}^{-3}$.

Figure 3

Population of the excited state at the end of the return sweep $X\to A$ based on the master equation (4) (symbols), together with the analytical approximation of $|b_f{|}^2+p_{\uparrow }$ (lines) for the parameter values $\epsilon =0.1,\beta \mathrm{\Delta }{E}_A=10,g^2={10}^{-3}$ (upper line and symbols), and $g^2=0$ (lower line and symbols).

Figure 4

Results of stochastic quantum trajectory simulations over $N$ cycles of demon operation. In (a) the quasistatic ramp rate $v$ (with $v_R=1.25\times {10}^{-3}$) and in (b) the return ramp rate $v_R$ (with $v=1\times {10}^{-6}$) are varied as indicated by the numbers with arrows. The top (red) line in both (a) and (b) shows the result when the demon is not active, whereas the bottom (blue) line shows the result of elusive ideal cycles. The horizontal dashed line shows the break-even result.

Figure 5

Results on $Q$ (black line) and $W$ (red line) of stochastic quantum trajectory simulations over $N$ cycles of demon operation. The quasistatic ramp has the rate $v=1\times {10}^{-6}$, and the return ramp rate $v_R$ is varied as indicated by the numbers with arrows. The bottom (blue) line shows the result of elusive ideal cycles. The horizontal dashed line shows the break-even result. The other parameters in the simulation are $\epsilon =0.1,\beta \mathrm{\Delta }{E}_A=10$, and $g^2={10}^{-3}$. Since temperature is rather low, the system happens to start in the ground state in all three presented examples, and therefore $W$ either coincides with $Q$ or exceeds it by $\mathrm{\Delta }{E}_A$ everywhere.