From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

Abstract

The ground state and excitation gap are studied for the anisotropic quantum Rabi model (QRM) which connects the fundamental QRM and the Jaynes-Cummings model (JCM). While conventionally the ground state has a second-order quantum phase transition in the low frequency limit, turning on finite frequencies sheds a novel light on the phase diagram to illuminate a fine structure of first-order transition series. It is found that the conventional quantum phase transition is accompanied with a hidden symmetry breaking, whereas the emerging series transitions are topological transitions without symmetry breaking. The topological structure of the wave function provides a novel universality classification in bridging the QRM and the JCM among the diversity that arises from finite frequencies. The aspect of topological transitions provides a renewed insight for the role of the counter-rotating interaction. Moreover, it is shown that the conventionally established tricritical point is actually a pentacritical or hexacritical point and following this multicritical point emerges a series of quadruple points. Besides the emerging multicriticality and reformed universality, the result demonstrates that a single-qubit system can even exhibit analogs of topological phase transitions which traditionally occur in condensed matter.

Hidden Single‐Qubit Topological Phase Transition without Gap Closing in Anisotropic Light‐Matter Interactions

“…Note that in the polaron picture the quantum phase transition at g 𝜆 c = 2 1+|𝜆| g s , with g s = √ 𝜔Ω∕2, essentially is a wave packet splitting from a Gaussian-like wave packet into two wave packets in the potential separation. [24,34] In the positive-𝜆 regime, comparing Equation (2) with its dual form indicates that g ′ z with a larger amplitude can generate a larger potential separation in x space than g ′ y in p space to bring the quantum phase transition, while the g ′ y term in x space and the g ′ z term in p space play little role for the quantum phase transition due to self-cancelation as the derivative of the Gaussian-like wave packet before the transition is an odd function. [34] Thus the positive-𝜆 regime is x-type in the sense that ⟨ x2 ⟩ is more dominant than ⟨p 2 ⟩, and vice versa, the negative-𝜆 regime is p-type.…”

“…[24,34] In the positive-𝜆 regime, comparing Equation (2) with its dual form indicates that g ′ z with a larger amplitude can generate a larger potential separation in x space than g ′ y in p space to bring the quantum phase transition, while the g ′ y term in x space and the g ′ z term in p space play little role for the quantum phase transition due to self-cancelation as the derivative of the Gaussian-like wave packet before the transition is an odd function. [34] Thus the positive-𝜆 regime is x-type in the sense that ⟨ x2 ⟩ is more dominant than ⟨p 2 ⟩, and vice versa, the negative-𝜆 regime is p-type. [31,34] Hereafter, unless specifically mentioned for the negative-𝜆 regime, we discuss in the x space for 𝜆 > 0, while the result is symmetrically available in the p space for 𝜆 > 0.…”

“…[27,31,34] The convenient model to study the role of the CRTs is the anisotropic QRM which connects the QRM and the JCM by continuously tuning the CRTs via the anisotropy of the coupling. [27,31,34] One of the most fascinating phenomena in enhancing the coupling is the possible onset of few-body phase transitions. [5,[23][24][25]31,33,34,65] When phase transitions traditionally lie in the thermodynamic limit in condensed matter, the QRM possesses a few-body quantum phase transition [23][24][25] in the low-frequency limit, that is, 𝜔∕Ω → 0 relatively to the atomic level splitting Ω, which replaces the thermodynamic limit in a finite system.…”

“…[27,31,34] One of the most fascinating phenomena in enhancing the coupling is the possible onset of few-body phase transitions. [5,[23][24][25]31,33,34,65] When phase transitions traditionally lie in the thermodynamic limit in condensed matter, the QRM possesses a few-body quantum phase transition [23][24][25] in the low-frequency limit, that is, 𝜔∕Ω → 0 relatively to the atomic level splitting Ω, which replaces the thermodynamic limit in a finite system. [31,43] On the other hand, it was also suggested that whether the transition should be termed quantum or not is a matter of taste by considering the negligible quantum fluctuations in the photon vacuum state.…”

“…[43] Moreover, a single-qubit system can even exhibit multicriticalities either with different patterns of symmetry breaking [33] or with the parity symmetry preserved. [34] Interestingly, a universality of criticality manifests itself in the scaling of critical exponents of the anisotropic QRM. [31] However, such a universality holds only under the condition of low-frequency limit, while at finite frequencies the universality breaks down and diversity, namely the quality to be diverse or different oppositely to universality, arises and dominates the physical properties.…”