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.
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.
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 Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological classification provides another type of universality essentially different from the critical universality. Both classes of universalities can be present in a single‐qubit system with light‐matter interactions, as exhibiting generally in the fundamental quantum Rabi model with anisotropy not only for linear coupling but also for nonlinear Stark coupling (NSC). In low frequencies different levels of scaling relations are extracted, holding for anisotropic or/and NSCs, locally or globally. At finite frequencies such a critical universality breaks down and diversity is dominant. However, common topological feature of the ground state can be extracted from the node number, which yields a topological class of universality amidst the critical diversity. Both conventional and unconventional topological transitions emerge, with their meeting, which never occurs in linear interaction, enabled by the nonlinear coupling to form topological quadruple points which are found to be spin‐invariant points. Sensitivity analysis indicates that the NSC can be another applicable approach to manipulate topological transitions in addition to coupling anisotropy.
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 Light‐matter interactions provide an ideal testground for interplay of critical phenomena, topological transitions, quantum metrology, and non‐Hermitian physics with high controllability and tunability. The present work considers two fundamental non‐Hermitian Jaynes‐Cummings models in light‐matter interactions that possess real energy spectra in parity‐time (PT) symmetry and anti‐PT symmetry. The quantum Fisher information is shown to be critical around the transitions at the exceptional points and exhibit a super universality, with respect to different parameters, all energy levels, both models, symmetric phases, and symmetry‐broken phases, which guarantees a universally high measurement precision in quantum metrology. In particular, the transitions are found to be both symmetry‐breaking Landau‐class transitions (LCTs) and symmetry‐protected topological‐class transitions (TCTs), thus realizing a simultaneous occurrence of critical LCTs and TCTs that are conventionally incompatible due to contrary symmetry requirements. Besides establishing a paradigmatic case to break the incompatibility of the LCTs and the TCTs in non‐Hermitian systems, the both availabilities of the sensitive critical feature and the robust topological feature can also provide more potential for designing quantum devices or sensors.
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 symmetry and the Jaynes-Cummings model with 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) symmetry presents different nonanalytic behaviors from the quantum Rabi model with the discrete Z2 symmetry, and there exists a finite discontinuous jump at the critical energy. For the general anisotropy case with 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 symmetry is still preserved.
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.