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arXiv:2503.23654 · Advanced Quantum Technologies

Quantum Features of the Thermal Two‐Qubit Quantum Rabi Model in Ultra‐ and Deep‐Strong Regimes

Ciro Micheletti Diniz, Gabriella G. Damas, N. G. de Almeida, Celso J. Villas-Bôas, G. D. de Moraes Neto

Published Jun 11, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202500250

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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.
Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this work, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling.
Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this paper, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling. Published by the American Physical Society 2024
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 This research investigates the dynamics of entanglement and uncertainty‐induced nonlocality (UIN) in a spin‐1/2 Ising‐Heisenberg diamond chain subjected to local non‐Markovian decoherence channels. By examining amplitude damping (AD) and random telegraph noise (RTN) in both zero and finite temperature regimes, the study reveals nuanced distinctions in the degradation and revival of quantum correlations. The interplay between intrinsic spin couplings, thermal effects, and memory‐induced coherence backflow highlights the complex behavior of quantum resources under realistic noise conditions. Concurrence emerges as a sensitive marker of entanglement recovery in dephasing environments, while uncertainty‐induced nonlocality proves more resilient in high‐temperature or dissipative regimes. The analysis further demonstrates that moderate thermal activation and external magnetic fields can nontrivially enhance or suppress quantum features depending on system parameters. These findings offer a detailed perspective on the robustness and complementarity of different quantum correlation measures, providing guiding principles for the design of thermally stable and noise‐resilient quantum information protocols.
The ultrastrong and deep strong coupling regimes exhibit a variety of intriguing physical phenomena. In this work, we utilize the Hopfield model of a two-mode bosonic system, with each mode interacting with a heat reservoir, to research the behavior of quantum coherence. Our results indicate that a coupled oscillator system can exhibit significant quantum coherence in the ultrastrong and deep strong coupling regimes. In the ground state, the photon mode and the matter mode coherences are equal. The larger coherences that encompass the photon mode, the matter mode, and the overall system are achieved at lower optical frequencies and with increased coupling strengths. Notably, the beam splitter and phase rotation terms alone do not generate coherences for either total coherence or subsystem coherences; instead, the generation of quantum coherences originates from the one-mode and two-mode squeezing terms. When hot environments are present, the total coherence can be enhanced by the beam splitter and phase rotation terms, while it has no effect on subsystem coherences. Moreover, when the one-mode and two-mode squeezing terms and the beam splitter and phase rotation terms are considered together, the total coherence increases with stronger coupling. We also observe that lower frequencies maximize total coherence in the deep strong coupling regime. These results demonstrate that the ultrastrong coupling and deep strong coupling regimes give rise to characteristics of quantum coherences. This work provides valuable insights into the quantum coherence properties, particularly in the ultrastrong and deep strong coupling regimes between light and matter, and may have potential applications in quantum information processing.
Abstract Superconducting charge qubits represent a cutting-edge technology in the field of quantum computing, offering a promising platform for quantum processing. This study delves into the behaviors of thermal coherence and quantum correlations within a two-superconducting charge qubit system coupled by a fixed capacitance. Specifically, we investigate the effects of thermal noise on entanglement (measured by concurrence), nonclassical correlations (quantified by local quantum uncertainty), and quantum coherence (measured by correlated coherence) within the two-superconducting charge qubit capacitively coupled. Our analysis takes into account the interplay between the equilibrium temperature of the reservoir and various system parameters. Our findings demonstrate that an increase in temperature leads to a decrease in coherence and quantum correlations within the considered system. However, the behavior of these quantum resources is heavily dependent on the system parameters, and a careful selection of these parameters can help mitigate the negative effects of absolute temperature. Additionally, we observe that local quantum uncertainty and correlated coherence are more resilient than thermal entanglement to rising temperatures. These results provide insight into how a two-superconducting charge qubit system can be optimized for achieving quantum advantages.