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arXiv:2010.01379 · Physical Review A

Symmetry-breaking patterns, tricriticalities, and quadruple points in the quantum Rabi model with bias and nonlinear interaction

Zu‐Jian Ying

Published Jun 1, 2021• 31 citations
arXivHTMLPDF

Abstract

Quantum Rabi model (QRM) is fascinating not only because of its broad relevance but also due to its few-body quantum phase transition. In practice, both the bias and the nonlinear coupling in QRM are important controlling parameters in experimental setups. We study the interplay of the bias and the nonlinear interaction with the linear coupling in the ground state which exhibits various patterns of symmetry breaking and different orders of transitions. Several situations of tricriticalities are unveiled in the low-frequency limit and at finite frequencies. We find that the full quantum-mechanical effect leads to transitions, tricriticalities, quadruple points, and a fine structure of spontaneous symmetry breaking, which are much beyond the semiclassical picture. We clarify the underlying mechanisms by analyzing the energy competitions and the essential changeovers of the quantum states, which enables us to extract most analytic phase boundaries.

DOI
10.1103/physreva.103.063701

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Quantum Rabi model (QRM) is fascinating not only because of its broad relevance but also due to its few-body quantum phase transition. In practice, both the bias and the nonlinear coupling in QRM are important controlling parameters in experimental setups. We study the interplay of the bias and the nonlinear interaction with the linear coupling in the ground state which exhibits various patterns of symmetry breaking and different orders of transitions. Several situations of tricriticalities are unveiled in the low-frequency limit and at finite frequencies. We find that the full quantum-mechanical effect leads to transitions, tricriticalities, quadruple points, and a fine structure of spontaneous symmetry breaking, which are much beyond the semiclassical picture. We clarify the underlying mechanisms by analyzing the energy competitions and the essential changeovers of the quantum states, which enables us to extract most analytic phase boundaries.
Abstract The experimental advance on light–matter interaction into strong couplings has invalidated the Jaynes–Cummings model and brought the quantum Rabi model (QRM) to more relevance. The QRM only involves linear coupling via a single -photon process (SPP), while the nonlinear two -photon process (TPP) is weaker and conventionally neglected. However, we find a contrary trend that enhancing the linear coupling might not suppress the nonlinear effect more but backfire to trigger some collapse of linear characters. Indeed, in strong SPP couplings a tiny strength of the TPP may dramatically change properties of the system, like a symmetry spontaneous breaking. By extracting the ground-state phase diagram including both a SPP and TPP, we find the TPP in low frequency limit induces a quantum phase transition with continuity–discontinuity double faces, which split into two distinct transitions at finite frequencies and yields a triple point. Our analysis unveils a subtle SPP–TPP entanglement.
We study the ground state (GS) and excitation gap of anisotropic quantum Rabi model (QRM) which connects the fundamental QRM and the Jaynes-Cummings model (JCM). While the GS has a second-order quantum phase transition (QPT) in the low frequency limit, turning on finite frequencies we shed a novel light on the phase diagram to illuminate a fine structure of first-order transition series. We find the QPT 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. We show that the conventionally established triple point is actually a quintuple or sextuple point and following the penta-/hexa-criticality emerge a series of tetra-criticalities.
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.
The Rabi model plays a fundamental role in understanding light-matter interaction. It reduces to the Jaynes-Cummings model via the rotating-wave approximation, which is applicable only to the cases of near resonance and weak coupling. However, recent experimental breakthroughs in upgrading light-matter coupling order require understanding the physics of the full quantum Rabi model (QRM). Despite the fact that its integrability and energy spectra have been exactly obtained, the challenge to formulate an exact wave function in a general case still hinders physical exploration of the QRM. Here we unveil a ground-state phase diagram of the QRM, consisting of a quadpolaron and a bipolaron as well as their changeover in the weak-, strong-, and intermediate-coupling regimes, respectively. An unexpected overweighted antipolaron is revealed in the quadpolaron state, and a hidden scaling behavior relevant to symmetry breaking is found in the bipolaron state. An experimentally accessible parameter is proposed to test these states, which might provide novel insights into the nature of the light-matter interaction for all regimes of the coupling strengths.
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.
Abstract Phase transitions are both thermodynamically and quantum-mechanically ubiquitous in nature and laboratories, and their understanding remains one of the most active issues in modern physics and related disciplines. The Landau theory provides a general framework to describe phenomenologically phase transitions by introducing order parameters and associated symmetry breaking. This theory is also taken as a starting point to explore critical phenomena in connection with phase transitions in the renormalization group, which provides a complete theoretical description of behaviors close to critical points. In this context, the microscopic mechanism of phase transitions remains unclear. In this study, we explore the microscopic mechanism of the superradiant phase transition in the quantum Rabi model (QRM). First, we perform a diagonalization operation in an operator space to obtain three fundamental patterns, denoted as λ 1 , λ 2 , and λ 3 , involved in the QRM. Then, we explicitly analyze the energy evolutions of these patterns with increasing coupling strength. The observed characteristic behaviors reveal the microscopic mechanism of the superradiant phase transition as a consequence of competition between patterns due to different phase relations. In other words, with increasing coupling strength, the pattern λ 1 drives the phase transition, the pattern λ 2 exhibits a similar response speed but less energy compensation than the pattern λ 1 , and the pattern λ 3 exhibits a slow response speed but plays a key role in the balance between it and the pattern λ 1 , which stabilizes the new phase. This type of dissecting mechanism explains why and how the superradiant phase transition occurs in the QRM and paves the way for exploring the microscopic mechanism of phase transitions that occur frequently in nature.