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.
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.
Abstract The quantum thermalization of the Jaynes–Cummings (JC) model in both equilibrium and non‐equilibrium open‐system cases is studied, in which the two subsystems, a two‐level system and a single‐mode bosonic field, are in contact with either two individual heat baths or a common heat bath. It is found that in the individual heat‐bath case, the JC model can only be thermalized when either the two heat baths have the same temperature or the coupling of the JC system to one of the two baths is turned off. In the common heat‐bath case, the JC system can be thermalized irrespective of the bath temperature and the system–bath coupling strengths. The thermal entanglement in this system is also studied. A counterintuitive phenomenon of vanishing thermal entanglement in the JC system is found and proved.
We study analytically the quantum thermalization of two coupled two-level systems (TLSs), which are connected with either two independent heat baths (IHBs) or a common heat bath (CHB). We understand the quantum thermalization in eigenstate and bare-state representations when the coupling between the two TLSs is stronger and weaker than the TLS-bath couplings, respectively. In the IHB case, we find that, when the two IHBs have the same temperatures, the two coupled TLSs in eigenstate representation can be thermalized with the same temperature as those of the IHBs. However, in the case of two IHBs at different temperatures, just when the energy detuning between the two TLSs satisfies a special condition, the two coupled TLSs in eigenstate representation can be thermalized with an immediate temperature between those of the two IHBs. In bare-state representation, we find a counterintuitive phenomenon that, under some conditions, the temperature of the TLS connected with the high-temperature bath is lower than that of the other TLS, which is connected with the low-temperature bath. In the CHB case, the coupled TLSs in eigenstate representation can be thermalized with the same temperature as that of the CHB in nonresonant cases. In bare-state representation, the TLS with a larger energy separation can be thermalized to a thermal equilibrium with a lower temperature. In the resonant case, we find a phenomenon of antithermalization. We also study the steady-state entanglement between the two TLSs in both the IHB and CHB cases.
Abstract Quantum correlations and non‐classical states are indispensable resources for advancing quantum technologies, and their resilience at finite temperatures is crucial for practical experimental implementations. The two‐qubit quantum Rabi model (2QQRM), a natural extension of the quantum Rabi model, describes two qubits coupled to a single bosonic mode and is extensively studied in cavity quantum electrodynamics, superconducting circuits, and quantum information science. In this work, the persistence of quantum correlations and non‐classical states in the 2QQRM at thermal equilibrium is investigated, focusing on the ultrastrong and deep strong coupling regimes. Through a systematic analysis of quantumness quantifiers, the emergence of long‐lived quantum correlations is demonstrated, even in the presence of thermal noise. Notably, striking phenomena arising from the interplay between detuning and deep strong‐coupling are uncovered: in the high‐frequency limit, where the qubit energy exceeds the cavity‐mode energy, quantum criticality emerges, leading to a high degree of photon squeezing. In contrast, the opposite regime is characterized by robust qubit–qubit quantum correlations. Importantly, it is shown that both dispersive regimes exhibit quantum features that are remarkably robust to parameter fluctuations, making them advantageous for maintaining quantum coherence. These results highlight the exceptional resilience of quantum resources in the 2QQRM and provide valuable insights for developing quantum technologies operating under realistic, finite‐temperature conditions.
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.
Providing the microscopic behavior of a thermalization process has always been an intriguing issue. There are several models of thermalization, which often require interaction of the system under consideration with the microscopic constituents of the macroscopic heat bath. With the aim to simulate such a thermalization process, here we look at the thermalization of a two-level quantum system under the action of a Markovian master equation corresponding to memory-less action of a heat bath, kept at a certain temperature, using a single-qubit ancilla. A two-qubit interaction Hamiltonian ( H th , say) is then designed —with a single-qubit thermal state as the initial state of the ancilla— which gives rise to thermalization of the system qubit in the infinite time limit. Further, we study the general form of Hamiltonian, of which ours is a special case, and look for the conditions for thermalization to occur. We also derive a Lindblad-type non-Markovian master equation for the system dynamics under the general form of system-ancilla Hamiltonian.
In this paper, the density matrix is obtained using the non-Markovian master equation method for a system consisting of two-qubit modeling with the Heisenberg XXZ chain, which involves the Dzyaloshinskii–Moriya interaction and is exposed to the bosonic baths. Also, using the proposed formula for calculating the specific heat through the density matrix of the open quantum system, the specific heat is calculated. The quantum entanglement behavior with time and coupling constant is investigated. It is observed that the specific heat at low temperatures becomes negative when the system is exposed to the environment. The time behavior of quantum entanglement for this model showed that the entanglement decreases to zero with increasing time.