Coherent feedback-enhanced asymmetry of thermal process in open quantum systems: Cavity optomechanics

TL;DR

The paper investigates how coherent feedback can enhance irreversibility in open quantum systems and demonstrates that, in the weak-coupling limit, the steady-state entropy production rate $\Pi_s$ is proportional to the quantum mutual information $\mathcal{I}$. Using a bipartite, linearly coupled, Gaussian steady-state model, the authors show that $\Pi_s$ can be controlled and increased via the feedback parameter, and they connect irreversibility to generated correlations and entanglement. The cavity optomechanics application (Fabry-Pérot cavity with a movable mirror) reveals that coherent feedback amplifies entropy production signatures associated with heating/cooling and strengthens correlations and entanglement, especially near resonance and with higher feedback reflectivity. These results suggest that irreversibility and quantum correlations are intertwined and can be jointly engineered for quantum thermal technologies.

Abstract

Entropy production is a fundamental concept in nonequilibrium thermodynamics, providing a direct measure of the irreversibility inherent in any physical process. In this work, we investigate in steady-state the enhancement of irreversibility employing coherent feedback loop. We evaluate the steady-state entropy production rate and quantum correlations by applying the quantum phase space formulation to calculate the entropy change. Our study reveals the essential contribution of coherent feedback in the thermal bath's input-noise operators, resulting in the system being driven far from thermal equilibrium. Our analysis shows that in the small-coupling limit, the entropy production rate is proportional to the quantum mutual information. We use for application the optomechanical system of Fabry-Pérot cavity, and show that the picks of the entropy production corresponding of the heating/cooling of movable mirror are improved. Therefore, we conclude that irreversibility and quantum correlations are not independent and must be analyzed jointly. The results demonstrate the possibility of enhancement of entropy production and pave the way for promising quantum thermal applications through coherent feedback loop.

Figures (9)

• Figure 1: Schematic of the system.
• Figure 2: Entropy production rate $\Pi_\text{s}/\omega_c$ and its two contributions $\mu_{\rm a}/\omega_c$ and $\mu_c/\omega_c$ against the ratio of the two frequencies for differents value of $\kappa_c$ with $\kappa_{\rm a}=\kappa_c=0.2\omega_c$ correspond to the Back curves, while $\kappa_{\rm a}=0.2\omega_c$ and $\kappa_c=0.5\omega_c$ correspond to the Red curves. In panels (a), (b), (c) when the reservoirs occupy their ground state $N_{\rm a}=N_c=0$. In panels (d), (e), (f) an imbalance in thermal excitations is considered, where $N_{\rm a}=0$ and $N_c=100$. We use parameters are $G=0.1\omega_c$$\tau=0.9$ and $\theta=\pi$.
• Figure 3: Entropy production rate $\Pi_\text{s}/\omega_c$ (a) and its two contributions $\mu_{\rm a}/\omega_c$ (b) and $\mu_c/\omega_c$ (c) against the ratio $N_{\rm a}/N_c$ for various value of $G$ with $G=0.05\omega_c$ correspond to the Back curves, while $G=0.2\omega_c$ correspond to the Red curves. The oscillators have the same frequency $\omega_{\rm a}=\omega_c$, $\kappa_{\rm a}=0.2\omega_c$ and $\kappa_{\rm c}=0.5\omega_c$, with $\tau=0.1$ and $\theta=\pi$.
• Figure 4: Entropy production rate $\Pi_\text{s}/\omega_c$ and its two contributions $\mu_{\rm a}/\omega_c$ and $\mu_c/\omega_c$ against the ratio of the two frequencies for differents value of $\kappa_c$ with $\kappa_{\rm a}=\kappa_c=0.2\omega_c$ correspond to the Back curves, while $\kappa_{\rm a}=0.2\omega_c$ and $\kappa_c=0.5\omega_c$ correspond to the Red curves. In panels (a)-(c) we use $G=10^{-2}\omega_c$ but in panels (d)-(f) we use $G=0.6\omega_c$. Other parameters are $N_{\rm a}=0$ and $N_c=10$, $\tau=0.9$ and $\theta=\pi$.
• Figure 5: Entropy production rate $\Pi_\text{s}/\omega_c$ and its two contributions $\mu_{\rm a}/\omega_c$ and $\mu_c/\omega_c$ against the reflectivity parameter $\tau$ for various value of $\kappa_c$ with $\kappa_{\rm a}=\kappa_c=0.2\omega_c$ correspond to the Back curves, while $\kappa_{\rm a}=0.2\omega_c$ and $\kappa_c=0.5\omega_c$ correspond to the Red curves. In panels (a), (b), (c) the reservoirs are in the ground state $N_{\rm a}=N_c=0$, while in panels (d), (e), (f) we considering an imbalance in thermal excitations $N_{\rm a}=0$ and $N_c=100$, with $\theta=\pi$ and $G=0.1\omega_c$.