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arXiv:2502.14447 · Physical review. B./Physical review. B

Thermal conductance at the superradiant phase transition in the quantum Rabi model

Tsuyoshi Yamamoto, 康弘 都倉

Published May 29, 2025• 3 citations
arXivHTMLPDF

Abstract

The quantum Rabi model exhibits a superradiant phase transition when the coupling becomes strong, even though it involves only two components: a two-level atom and a single bosonic mode. This phase transition is referred to as a finite-component quantum phase transition, in contrast to conventional phase transitions in many-body systems. In this Letter, we investigate heat transport across an atom embedded in bosonic modes, modeled by the quantum Rabi model, between two thermal baths. We found a manifestation of the superradiant phase transition in the thermal conductance, which represents the linear response to a temperature bias. Our Letter can be helpful for the development of quantum heat devices utilizing controllable finite-component quantum phase transitions.

DOI
10.1103/physrevb.111.l201409

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The quantum Rabi model exhibits a superradiant phase transition when the coupling becomes strong, even though it involves only two components: a two-level atom and a single bosonic mode. This phase transition is referred to as a finite-component quantum phase transition, in contrast to conventional phase transitions in many-body systems. In this Letter, we investigate heat transport across an atom embedded in bosonic modes, modeled by the quantum Rabi model, between two thermal baths. We found a manifestation of the superradiant phase transition in the thermal conductance, which represents the linear response to a temperature bias. Our Letter can be helpful for the development of quantum heat devices utilizing controllable finite-component quantum phase transitions.
Abstract We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio η of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete Z 2 symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous U (1) symmetry. For a large enough but finite η , the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.
In the ultrastrong-coupling regime, the quantum Rabi model can exhibit quantum phase transition (QPT) when the ratio of the qubit transition frequency to the frequency of the cavity field approaches infinity. However, it is challenging to control the QPT in few-body systems because of the limited coupling strength and the A2{A}^{2}A2 term. Here, we propose a practical scheme to manipulate the QPT of quantum Rabi model in the strong-coupling regime. By applying a periodic frequency modulation to the two-level system in a quantum Rabi model in the strong-coupling regime, an anisotropic quantum Rabi model with ultrastrong and tunable coupling strengths for rotating and counterrotating terms is obtained. The ground state and excitation energy of this model, in terms of the modulation parameters, are studied. We find that the QPT of the quantum Rabi model can be observed in the strong-coupling regime and externally controlled by the modulation.
Physical systems close to a quantum phase transition exhibit a divergent susceptibility, suggesting that an arbitrarily high precision may be achieved by exploiting quantum critical systems as probes to estimate a physical parameter. However, such an improvement in sensitivity is counterbalanced by the closing of the energy gap, which implies a critical slowing down and an inevitable growth of the protocol duration. Here, we design different metrological protocols that exploit the superradiant phase transition of the quantum Rabi model, a finite-component system composed of a single two-level atom interacting with a single bosonic mode. We show that, in spite of the critical slowing down, critical quantum optical probes can achieve a quantum-enhanced time scaling of the sensitivity in frequency-estimation protocols.
Abstract Quantum thermalization and thermal entanglement in the open quantum Rabi model (QRM), in which a two‐level system and a single‐mode bosonic field are coupled to either two individual heat baths or a common heat bath, are studied. By treating the QRM as an effective multilevel system and deriving global quantum master equations in the eigenstate representation of the QRM, the physical conditions for quantum thermalization of the QRM is studied. It is found that, in the individual heat‐bath case, the QRM can only be thermalized when either the two heat baths have the same temperature or the QRM is only coupled to one of the two baths. In the common heat‐bath case, differently, the QRM can always be thermalized. Thermal entanglement of the QRM in both the resonant‐ and non‐resonant coupling cases is also studied. The logarithmic negativity for the thermal state of the QRM is obtained in a wide parameter space, ranging from the low‐ to high‐temperature limits, and from the weak‐ to deep‐strong‐coupling regimes. This work paves the way toward the study of quantum effects in nonequilibrium ultrastrongly‐coupled light‐matter systems.
Entanglement and quantum correlations between atoms are not usually considered key ingredients of the superradiant phase transition. Here we consider the Tavis-Cummings model, a solvable system of two-levels atoms, coupled with a single-mode quantized electromagnetic field. This system undergoes a superradiant phase transition, even in a finite-size framework, accompanied by a spontaneous symmetry breaking, and an infinite sequence of energy level crossings. We find approximated expressions for the ground state, its energy, and the position of the level crossings, valid in the limit of a very large number of photons with respect to that of the atoms. In that same limit, we find that the number of photons scales quadratically with the coupling strength, and linearly with the system size, providing a new insight into the superradiance phenomenon. Resorting to novel multipartite measures, we then demonstrate that this quantum phase transition is accompanied by a crossover in the quantum correlations and entanglement between the atoms (qubits). The latters therefore represent suited order parameters for this transition. Finally, we show that these properties of the quantum phase transition persist in the thermodynamic limit.
We demonstrate the existence of finite-component multicriticality in a qubit-boson model where biased qubits collectively coupled to a single-mode bosonic field. The interplay between biases and boson-qubit coupling produces a rich phase diagram which shows multiple superradiant phases and phase boundaries of different orders. In particular, multiple phases become indistinguishable in appropriate bias configurations, which is the signature of multicriticality. A series of universality classes characterizing these multicritical points are identified. Moreover, we present a trapped-ion realization with the potential to explore multicritical phenomena experimentally using a small number of ions. The results open a novel way to probe multicritical universality classes in experiments.