Boosting Thermodynamic Efficiency with Quantum Coherence of Phaseonium Atoms

Abstract

We present a realistic implementation of a quantum engine powered by a phaseonium gas of coherently prepared three-level atoms -- where quantum coherence acts as a thermodynamic resource. Using a collision model framework for phaseonium-cavity interactions and cavity optomechanics, we construct a full engine cycle based on two non-thermal reservoirs, each characterized by coherence-induced effective temperatures. This configuration enhances the efficiency of a simple optomechanical engine operating beyond standard thermal paradigms. We further address scalability by coupling a second cavity in cascade configuration, where the same phaseonium gas drives both cycles. Our results demonstrate the operational viability of coherence-driven quantum engines and their potential for future thermodynamic applications.

Figures (5)

• Figure 1: Quantum heat engine architecture. (a) The working medium consists of a single-mode optical cavity with a movable end mirror, allowing the cavity length to vary from $x_1$ to $x_1 + L$ under the influence of radiation pressure. The cavity interacts with a stream of three-level atoms in $\Lambda$ configuration, characterized by partial coherence in the ground-state subspace and represented by the density matrix $\lambda$. These atoms serve as a tunable quantum reservoir. (b) Thermodynamic Otto cycle plotted in the entropy--temperature (S--T) plane. The movable mirror is attached to a piston to transfer useful work on the outside environment. Isochoric strokes correspond to energy exchange with phaseonium atoms, while isentropic strokes are driven by mirror displacement. Adjusting the coherence phase $\phi$ of phaseonium atoms changes the thermalization temperature in the isochoric transformations, enhancing efficiency $\eta_\phi$ of the engine with respect to one working with classical thermal baths, $\eta_{\text{cl}}$. (c) Cascade setup: two identical cavities, each with a piston, are sequentially traversed by the same atomic beam, enabling heating or cooling via a shared phaseonium reservoir. The atomic flux is tuned so only one ancilla is in each cavity at a time.
• Figure 2: Ratio between the temperature carried by phaseonium atoms $T_\phi$ and that of diagonal $\Lambda$ atoms $T_{cl}$. The classical temperature $T$ is defined only for $\alpha<\sqrt{1/3}$, while phaseonium temperature $T_\phi$ is defined for $\alpha<\sqrt{(1-\sin\phi)/(3-\sin\phi)}$, limited by the dashed black line represented in the plot. For $\phi=k\pi$ and $k\in\mathbb{Z}_0$, along the dash-dotted grey lines, the two temperatures are the same.
• Figure 3: Ratio between the QE efficiency $\eta$ and the efficiency of an ideal Curzon-Ahlborn engine $\eta^\text{CA}$ working at the respective classical temperature, for different quantum baths. Hot and cold quantum baths are kept to temperature $T_\phi^h=4.8K$ and $T_\phi^c=0.024K$ respectively. As the hot phaseonium atoms' phase $\phi_H$ get closer to $\pi/2$ and the cold atoms' phase $\phi_C$ goes to $3/2\pi$, the efficiency of the quantum engine rises from almost $30\%\,\eta^\text{CA}$ up to $300\%\,\eta^\text{CA}$.
• Figure 4: Regime dynamics of two cavities $S_1$ and $S_2$ during one thermodynamical cycle. The hot isochore stroke is not long enough to make the second cavity thermalize, so the two cycles are not equal. In particular, the second cavity performs a smaller cycle, represented with a dashed gray line. Hot phaseonium atoms' coherence phase is set to $\phi_H=0.84\pi$, while for cold atoms $\phi_C=\pi/40$. Mutual information shared during expansion is approximately $0.008$. The top panel shows the standard Energy-Frequency diagram, typical for an Otto cycle, while the two bottom ones show the dynamics of Frequency and Energy in time. Red and blue bars highlight the heating and cooling processes, respectively.
• Figure 5: Comparison of the different definitions of work outputs---$W^m$ and $W^\text{Al}$---and heat absorbed in the hot isochore stroke, for increasing shared mutual information. Mutual information increases by giving less time to the cavities to thermalize: this means less heat absorbed and consequently less work done. The coherence phase of hot and cold phaseonium baths are set to $0.681\pi$ and $1.525\pi$, respectively.