Driving Quantum Heat Engines Beyond Classical Limits through Multilevel Coherence

Abstract

Quantum coherence provides a controllable thermodynamic resource that can raise or lower the effective temperature of a cavity mode, enabling efficiency tuning in quantum heat engines. Here, we derive analytic expressions for the effective engine temperature, demonstrating the enhanced temperature tunability achievable via $N$-level ground-state coherence. We further unify ground- and excited-state coherence within a single analytic framework, revealing their interplay as a mechanism for thermodynamic control. Such quantum resources serve as tunable parameters that enable switching between heating, cooling, and cancellation regimes, driving the effective temperature from near-zero to divergence. Ultimately, our framework connects and generalizes previous models of quantum heat engines, and we identify rubidium atoms as a promising candidate for experimentally realizing these coherence-assisted effects.

Figures (4)

• Figure 1: (a) Quantum heat engine schematic. Radiation pressure from a thermally excited cavity field drives a piston. Atoms that thermalize with either a hot bath at temperature $T_\mathrm{h}$ (explicitly shown) or a cold bath at temperature $T_\mathrm{c}$ (omitted for simplicity) enter the cavity, thereby controlling the effective temperature of the engine’s working medium. (b) Carnot cycle as an idealized thermodynamic cycle performed by a heat engine, illustrated on a $T$–$S$ (temperature–entropy) diagram. The cycle takes place between a hot bath at $T_\mathrm{h}$ and a cold bath at $T_\mathrm{c}$.
• Figure 2: Atomic configurations considered in this work. (a) Coherence among $N$ nearly degenerate ground states. (b) Four-level system with coherence between the two ground states and between the two excited states.
• Figure 3: Quantum efficiency $\eta_\mathrm{Q}$ versus $N$. (a) Blue dashed, green solid and red dash-dotted curves corresponds to $\chi = -0.01$, $\chi = -0.03$, and $\chi = -0.05$, respectively (with $\bar{n}_\mathrm{eq} = 0.5$). (b) Blue dashed, green solid and red dash-dotted curves corresponds to $\chi = 0.2$, $\chi = 0.6$, and $\chi = 1$, respectively (with $\bar{n}_\mathrm{eq} = 5$).
• Figure 4: (a) Effective cavity temperature normalized to the bath temperature, $T_\mathrm{Q}/T_\mathrm{bath}$, versus ground-state ($\epsilon_g$, blue) or excited-state ($\epsilon_e$, red) coherence. Negative $\epsilon_g$ or positive $\epsilon_e$ raises the effective temperature (heating), whereas positive $\epsilon_g$ or negative $\epsilon_e$ lowers it (cooling). (b) Combined effect of ground- and excited-state coherence in the four-level configuration. Colors show $T_\mathrm{Q}/T_\mathrm{bath}$: red $>$ 1 (heating), blue $<$ 1 (cooling). In both panels, $\bar{n}=5$.