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arXiv:2311.11346 · Physical Review Research

Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model

Guitao Lyu, Korbinian Kottmann, Martin Bodo Plenio, Myung-Joong Hwang

Published Jul 17, 2024• 23 citations
arXivHTMLPDF

Abstract

We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counter-rotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033075

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Emergence of Rich Dissipative Phases in the Anisotropic Quantum Rabi Model Driven by the A2A^2A2 Term
The open anisotropic quantum Rabi model (QRM) is studied in this work, with an explicit A2A^2A2 term incorporated. It is shown that, in the presence of cavity loss, anisotropy allows the steady-state superradiant transition to occur even when the A2A^2A2 term prohibits the transition in the isotropic case. The A2A^2A2 term reshapes and enriches the known steady-state phase diagram of the open anisotropic QRM, leading to an asymmetric structure composed of normal, superradiant, and bistable phases. In particular, the nonequilibrium tricritical points are generally separated from the merger point of the two critical branches that bound the superradiant region. Isolated bistable regions also emerge, and the number and positions of tricritical points are reduced. Notably, the anomalous photon-number fluctuation scaling is associated with the merger of the two critical branches, rather than with the tricritical points. These results clarify the role of the A2A^2A2 term contribution in the steady-state structure of the open anisotropic QRM and provide a refined extension of the previously known dissipative phase diagram, offering a useful theoretical reference for future studies of related open light--matter systems.
We demonstrate that the open quantum Rabi model (QRM) exhibits a second-order dissipative phase transition (DPT) and propose a method to observe this transition with trapped ions. The interplay between the ultrastrong qubit-oscillator coupling and the oscillator damping brings the system into a steady state with a diverging number of excitations, in which a DPT is allowed to occur even with a finite number of system components. The universality class of the open QRM, modified from the closed QRM by a Markovian bath, is identified by finding critical exponents and scaling functions using the Keldysh functional integral approach. We propose to realize the open QRM with two trapped ions where the coherent coupling and the rate of dissipation can be individually controlled and adjusted over a wide range. Thanks to this controllability, our work opens a possibility to investigate potentially rich dynamics associated with a dissipative phase transition.
Quantum multicriticality not only has fundamental research significance but also can promote the development of emerging quantum technologies, owing to its rich phase transition mechanisms and quantum resources. While theoretical studies have predicted the multicritical phenomena in the light-matter systems, the experimental demonstration remains elusive for the challenges of achieving the system's ground or steady states in strong coupling regimes. Here, by implementing the quantum adiabatic algorithm and the dissipative-system variational quantum algorithm on nuclear magnetic resonance quantum simulator, we successfully demonstrate the tricritical phenomena both in the closed and open systems described by the two-axis Rabi model. The experimental results clearly show that, beyond the decoherence effect, dissipation leads to the emergence of a novel multicritical phenomenon: it splits the first-order phase transition line of the closed Rabi model, and doubles the tricritical point. Our work provides a feasible technique for engineering the open quantum systems and opens a new avenue for exploring nonequilibrium many-body physics.
Although the superradiant phase transition (SRPT) is prohibited in the paradigmatic quantum Rabi model due to the no-go theorem caused by the A2{\mathbf{A}}^{2}A2 term, we demonstrate two distinct types of SRPTs emerging from the normal phase in the anisotropic quantum Rabi model. A discontinuous phase transition between the two types of superradiant phases also emerges in the presence of a strong A2{\mathbf{A}}^{2}A2 term. Additionally, a rich phase diagram featuring a triple point, which connects first- and second-order phase transitions, is derived analytically and confirmed through numerical diagonalization at large effective system sizes. Finally, distinct critical behavior at the triple point is revealed and contrasted with that of a single continuous SRPT. This work may open a new avenue for observing SRPTs in their intrinsic form without altering the A2{\mathbf{A}}^{2}A2 term, while also offering a practical platform for exploring rich quantum phenomena.
Precise control of criticality in superradiant phase transitions is essential for quantum state engineering and the simulation of nonequilibrium phase transitions. Here, we investigate theoretically multicritical phenomena in a dissipative two-Rydberg-atom cavity--QED system. The intrinisic dipole--dipole interaction between the two Rydberg atoms restructures the energy-level landscape of the atomic subsystem, thereby significantly modifying the boundary of the continuous second-order superradiant phase transition, and shifting both the phase boundary and the multicritical point toward weaker atom--cavity strengths. For sufficiently strong dipole--dipole interactions, the continuous second-order phase transition and the multicritical point both disappear, leaving only a discontinuous first--order phase transition that enables the emergence of a superradiant phase even at arbitrarily weak atom--cavity coupling. This work is of fundamental interest for studying dissipative quantum phase transitions, with potential implications for quantum precision measurement and quantum sensing.