Hybrid Microwave-Cavity Heat Engine

We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum-dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functions even with moderate electronic relaxation and dephasing in the quantum dots. We provide detailed estimates for the electrical current and output power using realistic parameters.

Figure 1

Hybrid quantum heat engine. (a) Double quantum dots (yellow) coupled to each end of a microwave cavity (gray). External gates (green) are used to tune the quantum dots. The quantum dots are tunnel coupled to external electrodes. Heat flows from the hot electrodes (red) to the cold electrodes (blue) via the double quantum dots and the microwave cavity. (b) The hybridized levels of the quantum dots are in resonance with the cavity frequency ${\omega }_0$. Heat is transferred through processes, where electrons enter the excited state of the hot DQD and leave it via the ground state (arrows). With a finite mixing angle for the cold DQD [see Eq. (1)], electrons mainly enter the ground state from one lead and leave it from the excited state via the other lead. An electrical current is thereby induced in the cold conductor.

Figure 2

Thermoelectric performance. (a) Thermally induced current in DQD 2 as a function of the temperature ratio $T_2/T_1$ with different mixing angles ${\theta }_2$. Here, $k_B{T}_1=0.5\hslash {\omega }_0$ and $I_0=e\mathrm{\Gamma }/2$ with $\mathrm{\Gamma }={\mathrm{\Gamma }}_1={\mathrm{\Gamma }}_2$. Full numerics (continuous lines) compare well with Eq. (3) (dashed lines). (b) Power as a function of the applied voltage $V_2$. Temperatures are $k_B{T}_1=0.5\hslash {\omega }_0$ and $k_B{T}_2=0.1\hslash {\omega }_0$ and $P_0=\mathrm{\Gamma }{k}_B{T}_1$. Equation  (4) is shown with dashed lines. (c) Efficiency $\eta$ over the Carnot efficiency ${\eta }_C$ versus the applied voltage $V_2$. Same parameters as in panel (b). (d) Efficiency at maximum power as a function of the temperature ratio $T_2/T_1$. (e) Corresponding maximum power. (f) Optimized values of the voltage $V_2$ and the frequency ${\omega }_0$.

Figure 3

Influence of electronic dephasing and relaxation. Thermally induced current in DQD 2 as a function of the electronic relaxation and dephasing rates ${\mathrm{\Gamma }}_R$ and ${\mathrm{\Gamma }}_D$. Under optimal conditions, the current takes on the value $I_0=e\mathrm{\Gamma }/2$.