Bridging Quantum and Semi-Classical Thermodynamics in Cavity QED

Abstract

In cavity quantum electrodynamics (QED), photons leaving the cavity can be irreversibly lost or reused as a power source. This dichotomy is reflected in two different thermodynamic bookkeepings of the light field, both corresponding to valid thermodynamic frameworks. In this work, we formulate a rigorous semi-classical limit of cavity QED and show that the resulting thermodynamic description may qualitatively differ from that of the fully quantised model. We find that violations of the thermodynamic uncertainty relations are recovered in the semi-classical limit only by one of the two thermodynamic frameworks: the one which treats part of the photon flux as a power source. We illustrate our findings in a three-level system coupled to a driven cavity.

Figures (2)

• Figure 1: Sketch of the general results. The standard thermodynamic framework treats the coherent part of the output as waste, while the input-output framework (IO) as useful energy. The standard framework leads to predictions which are incompatible with the semi-classical model, while the IO-framework leads to compatible ones.
• Figure 2: (a) Sketch of the cavity-embedded three-level maser coupled to hot (H) and cold (C) baths. In (b,c) the hot-bath occupation $n_{\mathrm{H}}$ is varied (horizontal axis) at fixed $g/\kappa$. (b) Average heat currents and power. According to the IO-framework, the cavity-embedded maser operates as a heat engine, in agreement with its semi-classical version. (c) Thermodynamic uncertainties. Semi-classical TUR violations are observed, showing consistency of the IO-framework, and inconsistency of the standard framework. In (d,e) $n_{\mathrm{H}}$ is fixed and the coupling $g/\kappa$ is varied. We observe the breakdown of the semi-classical limit for (d) average heat currents, power, and (e) thermodynamic uncertainties. In (b--e), fixed parameters are $\mathcal{E}/\kappa = 1.5$, $g/\kappa = 0.025$, $\gamma_{\mathrm{H}}/\kappa = 0.1$, $\gamma_{\mathrm{C}}/\kappa = 2.0$, $\Omega/\kappa = \omega_2/\kappa = \omega_{\mathrm{d}}/\kappa = 3.5\times 10^3$, $\omega_3 = 3\omega_2$, $T/\kappa = 2\times 10^3$, $T_{\mathrm{C}} = T$, and $T_{\mathrm{H}}/\kappa \simeq 7.4 \times 10^4$. The cut-off for the cavity modes is $30$ levels.