Squeezing light to get nonclassical work in quantum engines

TL;DR

The paper addresses whether nonclassical light, specifically squeezed states, can be harnessed to produce usable mechanical work in quantum engines absent a temperature gradient. It develops a Lindblad-based model with squeezing baths, demonstrates that the standard quantum-work measure $W_{\text{Al}}$ fails to capture extractable work due to two-photon leakage (captured by $\Delta W$), and promotes expansion-work $W_{\text{exp}}$ as the correct observable. A squeezing Otto engine is designed with isochoric squeezing strokes at fixed temperature, and its thermodynamic performance is analyzed numerically, revealing a nontrivial interplay between squeezing strength and thermal occupancy, including an optimal $\bar n^*(r_2)$ and a bound $\eta=\varepsilon\eta_{\text{Otto}}$ with $\varepsilon<1$ due to internal energy expenditure to maintain squeezing. The results establish a thermodynamically consistent framework for nonclassical work extraction from squeezing and point to feasible experimental implementations in optical, microwave, and hybrid optomechanical platforms. The work highlights how quantum resources can enable work extraction beyond classical limits while remaining compatible with the first and second laws, and it delineates practical paths to realize isothermal, squeezing-driven engines.

Abstract

Light can be squeezed by reducing the quantum uncertainty of the electric field for some phases. We show how to use this purely quantum effect to extract net mechanical work from radiation pressure in a simple quantum photon engine. Along the way, we demonstrate that the standard definition of work in quantum systems does not capture the extractable mechanical work, as it does not reflect the energy leaked to these quantum degrees of freedom. We use these results to design an Otto engine able to produce mechanical work from squeezing baths, in the absence of a thermal gradient. Interestingly, while work extraction from squeezing generally improves for low temperatures, there exists a nontrivial squeezing-dependent temperature for which work production is maximal, demonstrating the complex interplay between thermal and squeezing effects.

Figures (4)

• Figure 1: Sketch of the squeezing Otto engine. A single-mode cavity of section ${\cal S}$ and length $L_1$ is initially prepared in a squeezed thermal state with average photon number $\bar{n}$ and squeezing amplitude $r_1$ (top panel). The cavity is first compressed to length $L_2<L_1$ (stroke 1), then squeezed to $r_2\ne r_1$ (stroke 2). Next, we expand back to $L_1$ at constant squeezing $r_2$ (stroke 3), and it is finally brought back to the initial state by contact with a squeezing bath at $r_1$ (stroke 4).
• Figure 2: Difference between Alicki's work definition and the observed expansion work, $\Delta W (t)= \tilde{W}_{\text{Al}}(t) - W_{\text{exp}}(t)$, resulting from internal two-photon processes in the squeezed system, for different values of the squeezing amplitude $r$ (with $\varphi=0$). The parameters for this expansion protocol are $L_0 = 1$, $v = 2.5 \times 10^{-3}$, $\bar{n}=10$, $t_f = 1000$, $\gamma = 0.01$, and units are such that $\hbar=k_{\mathrm{B}}=1$.
• Figure 3: (a) Energy balance for a squeezing Otto engine. Top panel shows the expansion work $W_\text{exp}$, middle panel displays the heat $Q$ exchanged with the squeezing baths, and the bottom panel shows the energy $\Delta W$ leaked to internal degrees of freedom to maintain squeezing. Consistency with the first law of thermodynamics is fulfilled in all cases. The squeezing amplitudes are $r_1 = 0.1$ and $r_2 = 10$, for different values of the bath average photon number $\bar{n}$. (b) Time evolution of the total energy during an Otto cycle. Panel (c) shows the energy as a function of the frequency $\omega(t)$ for these cycles, while panel (d) displays the pressure-volume diagrams for the same cases. The parameters used in the cycle simulation are: $\omega_0 = 2\pi, \tau = 1000, \gamma = 0.01, L_0 = 10, |v|=0.005$, and units are such that $\hbar=k_{\mathrm{B}}=1$.
• Figure 4: Expansion work for an Otto cycle as a function of the high-squeezing amplitude $r_2$, for different values of $\bar{n}$, and fixed $r_1=0.1$. Note the crossing of curves for intermediate squeezing $r_2$, and the large-$r_2$ saturation. This reveals a nontrivial interplay between squeezing and thermal effects which can be harnessed for optimal work output. Inset: Optimal excitation number $\bar{n}^*(r_2)$ maximizing work output as a function of $r_2$. Simulation parameters as in Fig. \ref{['fig:cycles']}.