Quantum heat transport in nonequilibrium anisotropic Dicke model

Abstract: Nonequilibrium heat transport and quantum thermodynamics in light-matter interacting systems have received increasing attention. Quantum thermal devices, e.g., heat valve and head diode, have been realized. Recently, it has been discovered that the anisotropic light-matter interactions can greatly modify the eigenvalues and eigenvectors of hybrid quantum systems, leading to nontrivial quantum phase transitions, quantum metrology, and nonclassicality of photons. To explore the influences of anisotropic light-matter interactions on quantum transport, we investigate heat flow in the nonequilibrium anisotropic Dicke model. In this model, an ensemble of qubits collectively interacts with an anisotropic photon field. Each component interacts with bosonic thermal reservoirs. Quantum dressed master equation (DME) is included to properly study dissipative dynamics of the anisotropic Dicke model. Within the eigenbasis of the reduced anisotropic Dicke system, strong qubit-photon couplings can be properly handled. Our results demonstrate that anisotropic qubit-photon interactions are crucial for modulating steady-state heat flow. In particular, it is found that under strong coupling the heat flow is dramatically suppressed by a large anisotropic qubit-photon factor. While under moderate coupling, the anisotropic qubit-photon interactions enhance the heat flow. Moreover, the increase in the number of qubits amplifies the flow characteristics, with the peaks increasing and the valleys decreasing. Besides, we derive two analytical expressions of heat flows in thermodynamic limit approximation with limiting anisotropic factors. These heat currents exhibit the cotunneling heat transport pictures. They also serve as the upper boundaries for the heat flows in the finite-size anisotropic Dicke model. We also analyze the thermal rectification effect in the anisotropic Dicke model.

• The paper demonstrates that anisotropic interactions can either suppress or enhance quantum heat transport in the Dicke model depending on the coupling regime.
• The study employs a quantum dressed-state master equation to capture strong and ultrastrong coupling effects and to derive analytic bounds in both finite-size and thermodynamic limits.
• The work reveals that significant anisotropy and temperature bias yield pronounced thermal rectification, suggesting practical applications as a quantum heat diode.

Quantum Heat Transport in the Nonequilibrium Anisotropic Dicke Model

Introduction

This paper presents a rigorous study of heat transport in the nonequilibrium anisotropic Dicke model, focusing on the interplay between photon-qubit anisotropy, coupling strength, and steady-state thermal currents in open quantum systems. The work extends the current understanding of quantum thermodynamics in cavity and circuit QED by analyzing the role of anisotropic interactions beyond isotropic or purely rotating wave approximations. Utilizing a quantum dressed-state master equation (DME) approach, the authors address regimes of strong and ultrastrong coupling, where standard perturbative or secular approximations fail, and connect finite-size results with analytic expressions derived in the thermodynamic limit.

Theoretical Formulation

The system comprises a collective ensemble of qubits (spins) coupled to a single-mode photon field, with both subsystems individually coupled to their own thermal reservoirs. The Hamiltonian incorporates an anisotropic light-matter interaction term, parameterized by an anisotropy coefficient $y$ that interpolates between the standard Dicke limit ($y=1$) and a maximally anisotropic case ($y=0$). Through the Holstein-Primakoff transformation and subsequent mapping to coupled bosonic modes, the model admits tractable analyses in both finite-$N_s$ and thermodynamic ($N_s\to\infty$) regimes. The authors consider both rotating and counter-rotating contributions, highlighting the breakdown of standard JC or RWA descriptions in the ultrastrong and deep strong coupling limits.

The dissipative dynamics are captured via the DME, constructed in the system's dressed eigenbasis. This formulation accommodates strong coupling and nontrivial bath-induced transitions, utilizing an Ohmic spectral density to model photon and qubit dissipation channels. The general expression for steady-state heat current, derived from the microscopic transition rates, provides a foundation for analyzing both symmetric and rectified (nonreciprocal) thermal transport.

Results: Steady-State Heat Flow

Numerical and analytical investigations reveal a non-monotonic dependence of the steady-state heat flux on photon-qubit coupling strength and the anisotropy parameter $y$. At weak coupling, heat flow is largely insensitive to anisotropy, dominated by the rotating-wave channel. With increasing coupling strength, counter-rotating contributions induce pronounced suppression of the heat current, a direct consequence of multiphoton scattering and reduced coherence in energy exchange pathways.

An explicit finding is that strong anisotropy ($y \to 1$) in the strong coupling regime dramatically suppresses heat flow, while in the moderate coupling regime, anisotropy enhances thermal transport relative to the isotropic case. The role of system size is also emphasized: increasing the number of qubits amplifies both the peaks and valleys of the heat flow, exacerbating the sensitivity to system parameters. Analytic expressions for the heat current in the thermodynamic limit are derived for $y=0$ and $y=1$, establishing cotunneling-like transport mechanisms and providing rigorous upper bounds for finite-size systems.

Results: Thermal Rectification

The study of rectification shows that the anisotropic Dicke model can act as a tunable quantum thermal diode. The thermal rectification factor, quantifying nonreciprocity under temperature bias reversal, increases monotonically with reservoir temperature difference and anisotropy. At both weak and moderate coupling, local maxima of the rectification factor are observed, while strong coupling induces regions where heat flow reciprocity is restored ($R \to 0$). The authors demonstrate that large anisotropy, significant temperature bias, and nonweak photon-qubit coupling are necessary to realize pronounced thermal rectification ($y=1$0), with system size further enhancing this effect.

Implications and Future Directions

The results provide comprehensive insights into the tunability of quantum heat transport via anisotropy and coupling engineering in hybrid light-matter QED systems. From a practical standpoint, the identification of regimes supporting controllable amplification or suppression of thermal currents and the realization of giant thermal rectification have direct relevance for quantum thermal management and device engineering, such as in thermal valves and quantum heat diodes.

Theoretically, the analytic bounds supplied in the thermodynamic limit serve as benchmarks for future studies, and the cotunneling-based interpretation of heat currents suggests new routes for optimizing heat transport in nontrivial quantum states. These findings motivate further exploration of non-Markovian effects, structured reservoirs, and dynamical modulation of anisotropy or coupling for tailored nonequilibrium thermal phenomena.

Conclusion

This paper establishes the central importance of anisotropic light-matter interaction in nonequilibrium heat transport within the Dicke model, demonstrating both strong suppression and enhancement effects dependent on coupling regime and anisotropy. The DME formalism provides a robust framework for treating open-system quantum thermodynamics in the strong-coupling regime, and the analytic thermodynamic limit results offer predictive upper bounds for quantum heat currents. Thermal rectification is shown to be highly tunable, suggesting immediate applications in quantum thermal devices. The work substantially augments the theoretical foundation for quantum thermodynamics in hybrid systems and indicates promising directions for device-oriented and fundamental investigations of quantum thermal transport.