Quantum thermal rectification via state-dependent two-photon dissipation

TL;DR

We address quantum heat transport through a harmonic oscillator coupled to two thermal baths via both single-photon and two-photon processes. Using a Born–Markov–secular GKSL framework with rates $\gamma_\alpha$ and $\Gamma_\alpha$ and Bose factors $\bar{n}_\alpha$ and $\bar{m}_\alpha$, we show that rectification arises from (i) a state-dependent two-photon emission blockade at low $T_L$ when the cold bath dominates (reducing transitions with $n\ge 2$), and (ii) asymmetric scaling of higher-order moments at higher $T$ biased by nonlinear dissipation. We derive analytic currents in limiting cases (purely linear, purely nonlinear, and hybrid) and demonstrate that rectification strengthens with the order of the multiphoton process, including a three-photon extension. An experimentally feasible scheme using an auxiliary two-level system to realize effective two-photon dissipation is proposed, along with reservoir-engineering techniques to selectively suppress single- or two-photon channels. These results illuminate how nonlinear dissipation enables directional heat transfer in quantum systems and point to practical routes for nanoscale thermal diodes.

Abstract

Controlling heat flow at the quantum level is essential for the development of next-generation thermal devices. We investigate thermal rectification in a quantum harmonic oscillator coupled to two thermal baths via both single-photon (linear) and two-photon (nonlinear) exchange processes. At low temperatures, rectification arises from a state-dependent suppression of two-photon emission: when the cold bath dominates, it drives the oscillator into low-occupancy states, inhibiting emission and creating a thermal bottleneck. At higher temperatures, rectification is governed by the asymmetric scaling of higher-order moments associated with two-photon absorption and emission. We systematically explore various bath coupling configurations and identify the conditions under which nonlinear dissipation leads to directional heat flow. Furthermore, we propose an implementation scheme based on coupling an auxiliary two-level system to the oscillator, enabling effective two-photon dissipation. These results contribute to the understanding of quantum heat transport in the presence of nonlinear dissipation and may support future efforts in nanoscale thermal rectification design.

Figures (9)

• Figure 1: Schematic representation of the model studied in this work. A quantum harmonic oscillator of frequency $\omega$ is coupled to two thermal baths at temperatures $T_L$ and $T_R$. Each bath can induce both single-photon and two-photon transitions in the oscillator. The red (left) and blue (right) arrows represent dissipative processes associated with the left and right baths, respectively. Single-photon exchanges allow transitions between adjacent energy levels, while two-photon exchanges involve jumps between levels separated by two quanta.
• Figure 2: Heat flow and thermal rectification in the presence of two-photon dissipation. (Top panel) Steady-state heat current $\mathcal{J}_R$ as a function of temperature $T$. In the black dashed curve, $T_L = 2$ is fixed while $T_R$ is varied; in the green solid curve, $T_R = 2$ is fixed while $T_L$ is varied. The circular markers (red and green) indicate full numerical calculations using the master equation given in Eq. (\ref{['eq:fullmaster']}) for $\gamma_\alpha = 0$. (Bottom panel) The thermal rectification coefficient $\mathcal{R}$ as a function of $T$. The blue solid and orange dashed lines compare analytical and numerical results for $\Gamma_R = 0.001$. The black dash-dotted line corresponds to the analytical result for $\Gamma_R = 0.01$. Parameters used: $\omega = 1$, $\Gamma_L = 0.1$.
• Figure 3: Steady-state heat current $\mathcal{J}_R$ flowing from the right bath, plotted as a function of its temperature $T_R$, with the left bath temperature held fixed at $T_L = 0.25$. The figure compares numerical results (circles) with analytical results (solid green line). Parameters: $\omega = 1$, $\gamma_R = 0.4$, $\gamma_L = 0.4$, $\Gamma_L = 0.01$, and Fock space dimension = 50.
• Figure 4: Heat current and rectification for $\Gamma_R = 0$. The forward configuration corresponds to fixed left bath temperature $T_L = 2$ and varying $T_R$, while the reverse configuration interchanges the temperatures. Top: Steady-state heat current $\mathcal{J}_R$ flowing into the right bath as a function of $T_R$, evaluated for two values of the two-photon dissipation rate: $\Gamma_L = 0.001$ (solid and dashed green curves) and $\Gamma_L = 0.1$ (dotted and dash-dotted red curves). Solid and dotted lines represent the forward configuration, while dashed and dash-dotted lines represent the reverse configuration. Bottom: Corresponding rectification coefficient quantifying the asymmetry of heat transport under temperature exchange. System parameters: oscillator frequency $\omega = 1.0$, and one-photon dissipation rates $\gamma_L = \gamma_R = 0.5$.
• Figure 5: Steady-state heat current $\mathcal{J}_R$ (top) and corresponding rectification coefficient $\mathcal{R}$ (bottom) as a function of temperature $T$. The forward bias configuration corresponds to the case where the left bath is fixed ($T_L = 2.0$) while $T_R$ is varied; in the reverse bias configuration, $T_R = 2.0$ is fixed and $T_L$ is varied. The left bath is coupled to the harmonic oscillator via both single- and two-photon processes, with $\gamma_L = 0.2$ and $\Gamma_L = 0.1$, while the right bath supports both dissipation channels with $\gamma_R = 0.2$ and varying two-photon coupling strength $\Gamma_R = 0.001, \text{and}\, 0.01$. Solid and dotted lines show forward bias configurations, while dashed and dash-dotted lines represent the reverse configuration. Increasing $\Gamma_R$ enhances the nonlinear response of the right bath, leading to a pronounced asymmetry in the heat current under temperature exchange and resulting in higher rectification.