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arXiv:2310.19595 · Physical Review Research

Thermodynamic limit in the two-qubit quantum Rabi model with spin-spin coupling

Roberto Grimaudo, G. Falci, ANTONINO MESSINA, Elisabetta Paladino, Alessandro Sergi, E. Solano, Davide Valenti

Published Dec 20, 2024• 8 citations
arXivHTMLPDF

Abstract

The occurrence of a second-order superradiant quantum phase transition is brought to light in a quantum system consisting of two interacting qubits coupled to the same quantized field mode. We introduce an appropriate thermodynamic limit for the integrable two-qubit quantum Rabi model with spin-spin interaction. Namely, this limit is determined by the infinite ratios of the spin-spin and the spin-mode couplings to the mode frequency, regardless of the spin-to-mode frequency ratios. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043298

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The occurrence of a second-order superradiant quantum phase transition is brought to light in a quantum system consisting of two interacting qubits coupled to the same quantized field mode. We introduce an appropriate thermodynamic limit for the integrable two-qubit quantum Rabi model with spin-spin interaction. Namely, this limit is determined by the infinite ratios of the spin-spin and the spin-mode couplings to the mode frequency, regardless of the spin-to-mode frequency ratios. Published by the American Physical Society 2024
The second-order quantum phase transition and quench dynamics in the two-mode Rabi model are investigated. We propose a diagonalization approach of jointly using a beam-splitter operator and a squeezed operator for each effective low-energy Hamiltonian when the ratio of the qubit transition frequency to the oscillator frequency approximates infinity. Eigenenergy and eigenstate of the normal and superradiant phases in the system are analytically derived, demonstrating the second-order quantum phase transition at a critical point. This critical point means that the requirement of coupling strength between the qubit and two oscillators is largely loosened by joint effect of two modes when compared with the standard Rabi model. The universal scaling between residual energy and quench time from ${\ensuremath{\tau}}^{\ensuremath{-}\frac{1}{3}}$ to ${\ensuremath{\tau}}^{\ensuremath{-}2}$ is confirmed.
We investigate the dissipative phase transitions of the anisotropic quantum Rabi model with cavity decay and demonstrate that large spin fluctuations persist in the stationary state, having important consequences on the phase diagram and the critical properties. In the second-order phase transition to the superradiant phase, there is a significant suppression of the order parameter and the appearance of nonuniversal factors, which directly reflect the spin populations. Furthermore, upon entering a parameter regime where mean-field theory predicts a tricritical phase, we find a first-order phase transition due to the unexpected collapse of superradiance. An accurate and physically transparent description going beyond mean-field theory is established by combining exact numerical simulations, the cumulant expansion, and analytical approximations based on reduced master equations and an effective equilibrium theory. Our findings, compared to the conventional thermodynamic limit of the Dicke model, indicate a general tendency of forming extreme nonequilibrium states in the single-spin system, thus have broad implications for dissipative phase transitions of few-body systems. Published by the American Physical Society 2024
A two-interacting-qubit quantum Rabi-like model with vanishing transverse fields on the qubit pair is studied. Independently of the coupling regime, this model can be exactly and unitarily reduced to two independent single-spin quantum Rabi models, where the spin-spin coupling plays the role of the transverse field. This transformation and the analytical treatment of the single-spin quantum Rabi model provide the key to prove the integrability of our model. The existence of different first-order quantum phase transitions, characterized by discontinuous two-spin magnetization, mean photon number, and concurrence, is brought to light.
The existence of zero-dimensional superradiant quantum phase transitions seems inconsistent with conventional statistical physics. This work clarifies this apparent inconsistency. We demonstrate the corresponding effective field theories and finite-temperature properties of light-matter interacting systems, and show how this zero-dimensional quantum phase transition occurs. We first focus on the Rabi model, which is a minimum model that hosts a superradiant quantum phase transition. With the path-integral method, we derive the imaginary-time action of the photon degrees of freedom. We also define a dynamical critical exponent as the rescaling between the temperature and the photon frequency, and perform dimensional analysis to the effective action. The dynamical critical exponent shows that the effective theory of the Rabi model is a free scalar field, where a true second-order quantum phase transition emerges. These results are also verified by numerical simulations of imaginary-time correlation functions of the order parameter. Furthermore, we also generalize this method to the Dicke model. Our results make the zero-dimensional superradiant quantum phase transition compatible with conventional statistical physics, and pave the way to understand it in the perspective of effective field theories. Published by the American Physical Society 2024
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.
The controllability of current quantum technologies allows one to implement spin-boson models where two-photon couplings are the dominating terms of light-matter interaction. In this case, when the coupling strength becomes comparable with the characteristic frequencies, a spectral collapse can take place, i.e., the discrete system spectrum can collapse into a continuous band. Here, we analyze the thermodynamic limit of the two-photon Dicke model, which describes the interaction of an ensemble of qubits with a single bosonic mode. We find that there exists a parameter regime where two-photon interactions induce a superradiant phase transition, before the spectral collapse occurs. Furthermore, we extend the mean-field analysis by considering second-order quantum fluctuation terms, in order to analyze the low-energy spectrum and compare the critical behavior with the one-photon case.