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arXiv:2010.15113

From quantum Rabi model to Jaynes-Cummings model: symmetry-breaking quantum phase transitions, topological phase transitions and multicriticalities

Zu‐Jian Ying

Published Oct 28, 2020• 0 citations
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Abstract

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.

DOI
10.1002/qute.202270013,10.1002/qute.202100088

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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.
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.
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.
We systematically investigate the excited-state quantum phase transition (ESQPT) in the anisotropic quantum Rabi model, which interpolates between the quantum Rabi model with Z2{\mathbb{Z}}_{2}Z2​ symmetry and the Jaynes-Cummings model with U(1)\mathbb{U}(1)U(1) symmetry. We calculate the model energy spectra and density of states (DOS) with the cumulants in both analytical and numerical ways to describe the ESQPT by the singularities. In the Jaynes-Cummings limit, its continuous U(1)\mathbb{U}(1)U(1) symmetry presents different nonanalytic behaviors from the quantum Rabi model with the discrete Z2{\mathbb{Z}}_{2}Z2​ symmetry, and there exists a finite discontinuous jump at the critical energy. For the general anisotropy case with Z2{\mathbb{Z}}_{2}Z2​ symmetry, there are two types of ESQPTs characterized by the finite discontinuous jump and the logarithmic divergence in the DOS, respectively. Different from the ground-state quantum phase transition, the ESQPT of the anisotropic quantum Rabi model strongly depends on the anisotropy which leads to a discontinuity even though the Z2{\mathbb{Z}}_{2}Z2​ symmetry is still preserved.
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 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.
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.