Multifunctional quantum thermal device utilizing three qubits

Quantum thermal devices which can manage heat as their electronic analogs for the electronic currents have attracted increasing attention. Here a three-terminal quantum thermal device is designed by three coupling qubits interacting with three heat baths with different temperatures. Based on the steady-state behavior solved from the dynamics of this system, it is demonstrated that such a device integrates multiple interesting thermodynamic functions. It can serve as a heat current transistor to use the weak heat current at one terminal to effectively amplify the currents through the other two terminals, to continuously modulate them ranging in a large amplitude, and even to switch on or off the heat currents. It is also found that the three currents are not sensitive to the fluctuation of the temperature at the low-temperature terminal, so it can behave as a thermal stabilizer. In addition, we can utilize one terminal temperature to ideally turn off the heat current at any one terminal and to allow the heat currents through the other two terminals, so it can be used as a thermal valve. Finally, we illustrate that this thermal device can control the heat currents to flow unidirectionally, so it has the function of a thermal rectifier.

Figure 1

Three coupling qubits with the transition frequencies ${\omega }_L, {\omega }_M$, and ${\omega }_R$ are in contact with three separate baths at temperatures $T_L, T_M$, and $T_R$, where ${\omega }_L+{\omega }_M={\omega }_R$ means the resonant coupling.

Figure 2

(a) Three heat currents ${\dot{Q}}_{\mu }/{\omega }_R^2$ versus $T_M/{\omega }_R$ at the steady state. The solid red, dashed green, and dotted blue lines correspond to the heat currents ${\dot{Q}}_L/{\omega }_R^2, {\dot{Q}}_M/{\omega }_R^2$, and ${\dot{Q}}_R/{\omega }_R^2$, respectively. (b) The amplification factors ${\alpha }_{\mu }$ versus $T_M/{\omega }_R$ at the steady state. The solid red and dotted blue lines correspond to ${\alpha }_L$ and ${\alpha }_R$, respectively. Here ${\omega }_L=0.9{\omega }_R, {\omega }_M=0.1{\omega }_R, g=0.1{\omega }_M, {\gamma }_L={\gamma }_M={\gamma }_R=\gamma ={10}^{-4}{\omega }_R, T_L=0.2{\omega }_R$, and $T_R=0.02{\omega }_R$.

Figure 3

Three heat currents ${\dot{Q}}_{\mu }/{\omega }_R^2$ (a) versus $T_L/{\omega }_R$ and (b) versus $T_R/{\omega }_R$ at the steady state. The solid red, dashed green, and dotted blue lines correspond to the heat currents ${\dot{Q}}_L/{\omega }_R^2, {\dot{Q}}_M/{\omega }_R^2$, and ${\dot{Q}}_R/{\omega }_R^2$, respectively. Here ${\omega }_L=0.9{\omega }_R, {\omega }_M=0.1{\omega }_R, g=0.8{\omega }_M, {\gamma }_L={\gamma }_M={\gamma }_R=\gamma ={10}^{-4}{\omega }_R$. In addition, in panel (a) $T_R=0.12{\omega }_R, T_M=0.08{\omega }_R$, and in panel (b) $T_L=0.12{\omega }_R, T_M=0.08{\omega }_R$.

Figure 4

Three heat currents ${\dot{Q}}_{\mu }/{\omega }_R^2$ versus $T_M/{\omega }_R$ at the steady state. The solid red, dashed green, and dotted blue lines correspond to currents ${\dot{Q}}_L/{\omega }_R^2, {\dot{Q}}_M/{\omega }_R^2$, and ${\dot{Q}}_R/{\omega }_R^2$, respectively. Here we have ${\omega }_L=0.6{\omega }_R, {\omega }_M=0.4{\omega }_R, g=0.8{\omega }_M$ fixed. In panel (a) the spontaneous decay rate ${\gamma }_{\mu }\left({\omega }_{\mu l}\right)={\gamma }_{\mu }$ is chosen to be independent of frequency, as mentioned before, i.e., ${\gamma }_L={\gamma }_M={\gamma }_R=\gamma ={10}^{-4}{\omega }_R$, and $T_L=0.25{\omega }_R, T_R=0.2{\omega }_R$, while in panel (b) the Ohmic spectrum is applied [70], i.e., ${\gamma }_{\mu }\left({\omega }_{\mu l}\right)={\gamma }_{\mu }{\omega }_{\mu l}$, and ${\gamma }_{\mu }$ is constant as above. The temperatures are set as $T_L=0.45{\omega }_R, T_R=0.4{\omega }_R$. Obviously the valve function is also obtained at different critical temperature points.

Figure 5

(a) Three heat currents ${\dot{Q}}_{\mu }/{\omega }_R^2$ versus $\mathrm{\Delta }T/{\omega }_R=(T_R-T_M)/{\omega }_R$ with $g=0.8{\omega }_M$ and $T_L=0.18{\omega }_R$. (b) Heat current ${\dot{Q}}_R/{\omega }_R^2$ versus $\mathrm{\Delta }T/{\omega }_R=(T_R-T_M)/{\omega }_R$ for different coupling strength $g$ without the bath $L$. (c) The rectification factors $R_{RM}$ versus $\left|\mathrm{\Delta }T\right|/{\omega }_R=\left|(T_R-T_M)\right|/{\omega }_R$ corresponding to the cases in panel (b), and the inset is a close-up image over the range of $0.15<\left|\mathrm{\Delta }T\right|/{\omega }_R<0.2$. In all the cases the spontaneous decay rates ${\gamma }_L={\gamma }_M={\gamma }_R=\gamma ={10}^{-4}{\omega }_R, {\omega }_L=0.9{\omega }_R, {\omega }_M=0.1{\omega }_R$, and the average temperature $T_A=(T_R+T_M)/2=0.25{\omega }_R$ is fixed. The dotted blue, solid red, dashed green, and dot-dashed magenta lines correspond to $g=0.8{\omega }_M, g=0.4{\omega }_M, g=0.2{\omega }_M$, and $g=0.1{\omega }_M$ in panels (b) and (c), respectively.