Autonomous Quantum Heat Engine Enabled by Molecular Optomechanics and Hysteresis Switching

TL;DR

This work proposes an autonomous molecular quantum heat engine by integrating a hysteretic molecular switch with molecular optomechanics inside a plasmonic cavity. By reducing the coupled cavity modes to a single normal mode and allowing the switch to provide automatic feedback, the system operates without external driving, enabling self-sustained cycles that couple heat flows from hot and cold reservoirs to work performed on the molecular switch. The analysis covers both classical and quantum regimes, revealing how quantum tunneling, correlations, and nonclassical cavity statistics modify output power, operational parameter ranges, and plasmon statistics. The results show distinct quantum signatures, such as enhanced steady-state power beyond the classical limit and measurable correlation power, indicating a rich platform for exploring autonomous quantum AMMs with nonclassical light–matter dynamics.

Abstract

By integrating molecular optomechanics with molecular switches, we propose a scheme for a molecular quantum heat engine that operates autonomously through hysteretic feedback without external driving or modulation. Through a comparative analysis conducted within both semiclassical and fully quantum frameworks, we reveal the influence of quantum properties embedded within the autonomous control elements on the operational efficiency and performance of this advanced molecular machine.

Figures (6)

• Figure 1: (Color online) (a) Autonomous molecular heat engine with a molecular switch in a plasmonic cavity (gold spheres), coupled via dispersive and dissipative optomechanics. (b) The effective potential of the hysteretic molecular switch, where radiation pressure triggers the transition between states. (c) Heat engine's working cycle, featuring a hysteresis loop in the molecular reaction coordinate $x$, driven by radiation pressure proportional to plasmon number $n_{\rm a}$. The parameters are $\theta=\hbar\omega_{\rm m}x_0^{-1}, L=x_0, \beta=2\hbar\omega_{\rm m}$, where $x_0=\sqrt{\hbar/2m\omega_{\rm m}}$ represents the vacuum fluctuation of the reaction coordinate.
• Figure 2: (Color online) (a) Phase trajectories (black lines) in $(n_{\rm a},x)$ phase space for cases A, B, C. The hollow/solid dots mark initial/final states and the blue arrows are streamlines $(\dot{n}_{\rm a},\dot{x})$. The contour plots show the engine power $P$ (b) and working cycle period $T$ (c) as functions of $g_\kappa$ and $\beta$. The system parameters are $\kappa_{0}=0.05\omega_{\rm m}$, $\gamma=0.5\omega_{\rm m}$, $n_{\rm c}=0$, $n_{\rm h}=4$, $g_\omega=-\omega_{\rm m}x_0^{-1}$, and $\omega_{\rm a}=100\omega_{\rm m}$.
• Figure 3: (Color online) (a) Quasi-probability density $\tilde{\mathcal{Q}}(r,x)$ for cases corresponding to points A, B, and C in (b), respectively, with white arrows indicating the quasi-probability flows. The contour plots illustrate (b) the steady-state engine power and (c) the contribution from quantum correlation, within the framework of a quantum switch, where the dashed line outlines the boundary separating the classical operational domain. The parameters utilized are identical to those in Fig. \ref{['fig classical']}, and $n_{\rm th}=0$.
• Figure 4: (a) Wigner function of the cavity mode for four selected points indicated in (b). (b) Second-order field correlation $g^{(2)}(0)$ of the cavity mode as a function of optomechanical couplings $g_\omega$ and $g_\kappa$, with $g^{(2)}(0)=1$ indicated by a dashed line. All parameters as in Fig. \ref{['fig classical']}, except for $\beta=4\hbar\omega_{\rm m}$.
• Figure S1: (color online) (a) Frequency comparison of bared modes $A, B$ (dashed lines) and normal modes $a, b$ (solid lines) as functions of the molecular reaction coordinate $x$. (b) Comparison of exact (solid lines) and approximated (dashed lines) dissipation rates. The parameters are defined as $\omega_A = 10^2g$, $\omega_B = 10^3g$, $g_A = -g x_0^{-1}$, and $g_B = -20g x_0^{-1}$, where $x_0=\sqrt{\hbar/2m\omega_m}$ represents the vacuum fluctuation of the reaction coordinate.