Quantum thermal diode with additional control by auxiliary atomic states

TL;DR

This work analyzes a quantum thermal diode formed by two primary two-level atoms in contact with heat reservoirs, with the left atom additionally coupled to $N$ auxiliary two-level atoms. Using a global master equation, the authors show that the auxiliary atoms create $2^N$ independent subspaces and induce an effective left-atom frequency shift $\omega'_L$, enabling tunable heat rectification. They find that excited auxiliary states tend to weaken current and strengthen rectification when $\omega_L>\omega_R$, while ground-state auxiliary atoms have the opposite effect; a superposition state yields rectification controlled by the excited-state fraction $p_1$, with a critical value $p_c$. The rectification can be eliminated by appropriate coupling design, and the effects persist under weak auxiliary-dissipation, suggesting practical routes to controllable quantum thermal management, potentially in superconducting-qubit architectures.

Abstract

A quantum thermal diode, similar to an electronic diode, allows for unidirectional heat transmission. In this paper, we study a quantum thermal diode composed of two two-level atoms coupled to auxiliary two-level atoms. We find that the excited auxiliary atoms can weaken heat current and enhance the rectification effect, but the ground-state auxiliary atoms can enhance heat current and weaken the rectification effect. The more auxiliary atoms are coupled, the stronger the enhancing or weakening impact is. If the auxiliary atom is in a superposition state, we find that only the fraction that projects onto the excited state plays a significant role. In particular, if we properly design the coupling of the auxiliary atoms, the rectification effect can be eliminated. This provides the potential to control the heat current and the rectification performance by the states of the auxiliary atoms.

Figures (9)

• Figure 1: Schematic diagram of the quantum thermal diode. Quantum thermal diodes consist of two types of atoms: $L$ atoms and $R$ atoms. The $L$ atom is surrounded by auxiliary atoms, and the $L$ atom and the $R$ atom are connected to their respective heat reservoirs, temperature $T_L$ and $T_R$. The coupling strength between the L atom and the R atom is $g_{LR}$, while the coupling strength between the $L$ atom and the $a$th auxiliary atoms around it is $g_{La}$.
• Figure 2: The heat current $\dot{Q}_L$ varies with the temperature $T_L$. Here, $T_R=0.5$ is fixed. All solid lines represent the positive heat current, and dashed lines represent the reverse heat current by exchanging the temperatures $T_L$ and $T_R$. The red line indicates that the $L$ atom is not connected to any auxiliary atoms. In (a), (c), and (e), the auxiliary atoms are at excited states, and the color changes from cyan to magenta, indicating increasing auxiliary atom number $N$ from $1$ to $10$. In (b), (d), and (f), the auxiliary atoms are at ground states, and the color from brown to green indicates increasing the auxiliary atom number $N$ from $1$ to $10$. In (a) and (b), the inset shows the positive and reverse heat current over $T_L$ from $0.65$ to $0.7$. In (c) and (d), the inset shows the reverse heat current over $T_L$ from $0.8$ to $1$. In (e) and (f), the inset shows the positive heat current over $T_L$ from $0.8$ to $1$. In (a) and (b), $\omega_L=4$ and $\omega_R=4$, in (c) and (d), $\omega_L=4$ and $\omega_R=2$, in (e) and (f), $\omega_L=2$ and $\omega_R=4$. Other parameters are $\omega_a=2$, $g_{LR}=0.1$, $g_{La}=0.05$, $\gamma=0.001$.
• Figure 3: The heat current $\dot{Q}_L$ varies with time $t$. The purple solid line with inverted triangles, the blue dotted line with crosses, and the red dashed line with plus signs, correspond to the state $\left\vert\psi\right\rangle_0$. In contrast, the purple solid line with regular triangles, the blue dotted line with circles, and the red dashed line with squares, correspond to $\rho_0$. The inset shows the heat current over time $t$ from $7,800$ to $8,000$. The values of $\vert\alpha\vert^2$ and $p_1$ are given in the figure. Other parameters are $\omega_L=5$, $\omega_R=3$, $\omega_1=2$, $\gamma=0.001$, $g_{LR}=1$, $g_{L1}=0.5$, $T_L=2$, $T_R=1$.
• Figure 4: The rectification $\mathcal{R}$ as a function of the temperature $T_L$. The red line with plus signs indicates the absence of auxiliary atoms, while the solid line indicates the presence of auxiliary atoms. From bottom to top, $N$ goes from $1$ to $10$. In (a), the auxiliary atoms are all at excited states, and in (b), they are all at ground states. In this figure, $\omega_L=\omega_R=4$, $\omega_a=2$, $g_{LR}=0.2$, $g_{La}=0.05$, $\gamma=0.001$, $T_R=0.5$.
• Figure 5: The rectification $\mathcal{R}$ varies with the temperature $T_L$. The red solid line with plus signs indicates the absence of the auxiliary atoms, while the solid and dashed lines indicate the presence of the auxiliary atoms. The solid line represents all the excited auxiliary atoms, and the dashed line represents the ground-state auxiliary atoms. The color from cyan to magenta indicates an increase in the number of atoms $N$, from 1 to 10. Here we take $\omega_a=2$, $g_{LR}=0.1$, $g_{La}=0.05$, $\gamma=0.001$, $T_R=0.5$.