Fate and origin of the quantum Otto heat engine based on the dissipative Dicke-Hubbard model

TL;DR

The paper studies a quantum Otto cycle where the working substance is a Dicke-Hubbard lattice, addressing how many-body collective effects, particularly superradiance, influence work extraction and efficiency. It develops a mean-field plus extended bosonic coherent state framework and a quantum dressed master equation to treat dissipation, enabling self-consistent steady states at different bath temperatures and a concrete four-stroke Otto protocol with heat and work expressions. Key findings show that high engine efficiency emerges in the weak-coupling regime ($\lambda<1$) and when the low- and high-temperature steady states lie within the same quantum phase (normal), with inter-cavity hopping $J$ and atom number $N$ tuning both the phase boundaries and performance. This work establishes a direct link between superradiant phase transitions and non-equilibrium quantum thermodynamics, offering actionable guidance for designing high-performance quantum Otto engines that exploit collective quantum phenomena.

Abstract

The Dicke-Hubbard model, describing an ensemble of interacting atoms in a cavity, provides a rich platform for exploring collective quantum phenomena. However, its potential for quantum thermodynamic applications remains largely uncharted. Here, we study a quantum Otto heat engine whose working substance is a system governed by the Dicke-Hubbard Hamiltonian. Through the research on steady-state superradiance phase transitions, it is demonstrated that the steady-state synergistic mechanism under high and low temperature environments is the reason for the emergence of high-performance heat engines. By analyzing the influences of atom-light coupling strength, inter-cavity hopping strength and atom number on the working modes of quantum Otto cycle, it is clarified that the effective working regions of each working mode. This work has established a close connection between superradiance phase transition and the quantum thermodynamic applications. It not only deepens our understanding of the energy conversion mechanism in non-equilibrium quantum thermodynamics but also lays a theoretical foundation for the future experimental design of high-performance quantum Otto heat engines.

Figures (6)

• Figure 1: Schematic representation of the four strokes of an Otto cycle for the realization of a heat machine based on the open DH model, as detailed in Section III. During the isochoric stroke the frequency of the working substance, as modelled by the DH Hamiltonian, is held fixed while interacting with a hot (cold) reservoir at temperature $T_{h}$ ($T_{c}$). Only heat is exchanged during this stroke. In the two quantum adiabatic strokes the working substance is isolated from the reservoir and has its frequency shifted, thus producing work. No heat is exchanged during this stroke. By controlling the parameters $\omega_{0}$, $\Delta$, $J$ and $\lambda$ of the model the machine can work as an engine, refrigerator, heater, or accelerator.
• Figure 2: Phase diagrams of the working modes of quantum Otto cycle in the $T_{h}$-$\lambda$ parameter space under different $T_{c}$. (a) $T_{c}=0.1$ (b) $T_{c}=0.2$, (c) $T_{c}=0.4$, and (d) $T_{c}=2$. The color code stands for heat engine (dark blue), refrigerator (light blue), heater (grass green), and accelerator (yellow). The other involved parameters are $N=8$, $J=0.01$, $\omega_{h} = 2\omega$, $\omega_{c} = \omega$, $\gamma_{c}=\gamma_{q}=10^{-4}$.
• Figure 3: (a)-(c): The efficiency of the quantum Otto heat engine. (a) $T_{c}=0.1$; (b) $T_{c}=0.2$; (c) $T_{c}=0.4$; (d) $T_{c}=2$. Other involved parameters are $N=8$, $J=0.01$, $\omega_{h} = 2\omega$, $\omega_{c} = \omega$, and $\gamma_{c}=\gamma_{q}=10^{-4}$.
• Figure 4: (a)-(b)The steady-state order parameter $|\psi|$ in $\lambda$-$J$ parameter space under temperature $T=0.1$ and $T=0.4$. (c) Phase diagrams of the working modes of quantum Otto cycle in the $\lambda$-$J$ parameter space with $T_c=0.1$ and $T_h=0.4$. (d) The efficiency of the quantum Otto heat engine. The other parameters are $N=4$, $\omega_{h} = 2\omega$, $\omega_{c} = \omega$, and $\gamma_{c}=\gamma_{q}=10^{-4}$.
• Figure 5: (a)-(b) The steady-state order parameter $|\psi|$ as the function of atom-light coupling strength $\lambda$ under different hopping strength $J$. The temperature is taken as (a) $T=0.1$, (b)$T=0.5$. (c)-(d) The efficiency $\eta$ and Work $W$ of the quantum heat engine as a function of the atom-light coupling strength $\lambda$ for different hopping strength $J$, keeping $T_c=0.1$ and $T_h=0.5$. The other system parameters are given by $N=8$, $\omega_{h} = 2\omega$, $\omega_{c} = \omega$, and $\gamma_{c}=\gamma_{q}=10^{-4}$.