Thermodynamic decoupling in the deep-strong coupling regime

TL;DR

This work addresses energy transport in the deep-strong coupling (DSC) regime, where light–matter coupling exceeds bare frequencies, by deriving a thermodynamically consistent global master equation for a two-bath Hopfield model. The central result is that the steady-state heat current vanishes as the coupling enters the DSC ($g/\omega_{c,b}>1$), signaling thermodynamic decoupling caused by a growing population of virtual photons in the ground state. The authors provide closed-form expressions for the polariton decay rates $\Gamma_x$ and $\Gamma_y$, show the breakdown of the Purcell effect, and connect the vanishing heat current to the nonlocal observable physics of vacuum fluctuations. These findings have implications for quantum thermotronics, offering a pathway to control heat transport in strongly coupled photonic–matter devices, and they highlight the role of virtual photons in nonequilibrium energy flux.

Abstract

In the deep-strong coupling (DSC) regime, the interaction between light and matter exceeds their bare frequencies, leading to an effective decoupling. Theoretical and experimental evidence for this behavior has relied solely on measurements of local observables at equilibrium. However, such a local approach is insufficient to accurately describe energy fluxes in critical and nonequilibrium phenomena. Here, we use a two-terminal quantum junction to derive a thermodynamically consistent global master equation. We demonstrate that the associated heat current, a key nonlocal observable in any quantum thermal machine, also approaches zero in this extreme coupling scenario, underscoring the role of virtual photons in the vacuum ground state. Our results indicate that the decoupling is a more general feature of the DSC regime, with implications for quantum thermotronics.

Figures (4)

• Figure 1: Schematic representation of a thermal junction model. The central system (enclosed by the dashed green rectangle) consists of two coupled quantum oscillators with bare frequencies, $\omega_{c}^{}$ and $\omega_{b}^{}$. Each oscillator is weakly and locally coupled to a thermal bath—modeled as a collection of quantum harmonic oscillators—at temperatures $T_L^{}>T_R^{}$. The coupling strength between the central subsystems, $g$, may operate in the ultrastrong coupling or deep-strong coupling regime.
• Figure 2: Decay rates $\Gamma_{\!x,y}$ of the upper (cyan solid line) and lower (black solid line) polariton as a function of normalized coupling $g/\omega_c^{}$, and $\omega_b^{}=0.97\omega_c$. See Sec. \ref{['PurcellEffect']} for details.
• Figure 3: Steady-state heat current [Eq. (\ref{['HeatCurrent']}) and Eq. (\ref{['LME_RWA']})] as a function of normalized coupling $g/\omega_c^{}$ at resonant (dashed line) and nonresonant (solid line) conditions, see Sec. \ref{['Heat-current']} for details.
• Figure 4: Virtual photons population, $\langle a_L^\dagger a_L^{}\rangle_{{\rm SS}}^{}=f_2^2+f_4^2$, both out of resonance (orange solid line) and in resonance (cyan solid line) conditions. Depending on the normalized coupling ($g/\omega_c^{}$): from 0.01(weak) to 0.5(ultra-strong), the virtual photons contribution is well approximated by $(g/\omega_c)^2$ (black dashed line). Conversely, when we are over 2(deep-strong) the contribution is $\propto g/\omega_c^{}$ (blue dashed line), see Eq. (\ref{['virtualphotonsdeep']}). From 0.5 (USC) until 2 (DSC), the behavior can be captured by $g^2/\omega^2+g/\omega$ (magenta dashed line), see Eq. (\ref{['virtualphotonsinter']}).