A generalization of the quantum Rabi model: exact solution and spectral structure

Eckle, Hans-Peter; Johannesson, Henrik

doi:10.1088/1751-8121/aa785a

Cited by 56 publications

(58 citation statements)

References 56 publications

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“…The AQRM has been studied, for instance, numerically in the context of the process of physical bodies reaching thermal equilibrium through mutual interaction [38]. In recent works [16,58] on the AQRM and the quantum Rabi-Stark model (another generalization of the QRM) the respective authors have studied the degeneracies of the spectrum from different points of view than the present work.…”

Section: Introduction and Overviewmentioning

confidence: 93%

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model

Kimoto

Reyes-Bustos

Wakayama

2020

International Mathematics Research Notices

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The purpose of this paper is to study the exceptional eigenvalues of the asymmetric quantum Rabi models (AQRM), specifically, to determine the degeneracy of their eigenstates. Here, the Hamiltonian H ε Rabi of the AQRM is defined by adding the fluctuation term εσ x , with σ x being the Pauli matrix, to the Hamiltonian of the quantum Rabi model, breaking its Z 2 -symmetry. The spectrum of H ε Rabi contains a set of exceptional eigenvalues, considered to be remains of the eigenvalues of the uncoupled bosonic mode, which are further classified in two types: Juddian, associated with polynomial eigensolutions, and non-Juddian exceptional. We explicitly describe the constraint relations for allowing the model to have exceptional eigenvalues. By studying these relations we obtain the proof of the conjecture on constraint polynomials previously proposed by the third author. In fact, we prove that the spectrum of the AQRM possesses degeneracies if and only if the parameter ε is a half-integer. Moreover, we show that non-Juddian exceptional eigenvalues do not contribute any degeneracy and we characterize exceptional eigenvalues by representations of sl 2 . Upon these results, we draw the whole picture of the spectrum of the AQRM. Furthermore, generating functions of constraint polynomials from the viewpoint of confluent Heun equations are also discussed.

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Section: Introduction and Overviewmentioning

confidence: 93%

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model

Kimoto

Reyes-Bustos

Wakayama

2020

International Mathematics Research Notices

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“…Grimsmo and Parkins conjecture that the nonlinear coupling manipulated by the dispersive energy shift would possibly induce a new superradiant phase at this single atom level if U < −2ω [21]. Although the total Hamiltonian H 0 = H R + H N L has been studied by the Bargmann approach [24,29], no much attention has yet been paid to its possible novel and peculiar physical properties, to the best of our knowledge.…”

Section: Introductionmentioning

confidence: 99%

Quantum Rabi–Stark model: solutions and exotic energy spectra

Xie¹,

Duan²,

Chen³

2019

J. Phys. A: Math. Theor.

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The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived in a compact way, much simpler than previous ones obtained in the Bargmann representation. The zeros of transcendental functions reproduce completely the regular spectra. In terms of the explicit pole structure of these functions, two kinds of exceptional eigenvalues are obtained and distinguished in a transparent manner. Very interestingly, a first-order quantum phase transition indicated by level crossing of the ground state and the first excited state is induced by the positive nonlinear Starklike coupling, which is however absent in any previous isotropic quantum Rabi models. When the absolute value of the nonlinear coupling strength is equal to twice the cavity frequency, this model can be reduced to an effective quantum harmonic oscillator, and solutions are then obtained analytically. The spectra collapse phenomenon is observed at a critical coupling, while below this critical coupling, infinite discrete spectra accumulate into a finite energy from below.

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“…A few typical models are listed in Table 1 . Besides introducing the asymmetry from the bias, [ 3 ] as inspired by experimental setups nonlinear terms can be also added to interplay with the linear coupling, such as the two‐photon process, [ 10–12,60–63 ] the Stark‐like coupling, [ 11,12,64,65 ] and the A 2 term. [ 33 ] As one knows, the reduced symmetry from the JCM to the QRM leads to avoided crossings, [ 8 ] while the nonlinearity and the bias results in various patterns of symmetry breaking, different orders of transitions and a rich physics of tricriticalities and quadruple points.…”

Section: Paradigmatic Modelsmentioning

confidence: 99%

“…[ 95 ] In such a case, the spectral collapse occurs at a critical value of the coupling strength

g = g_{normalt} / 2

. [ 95,99 ] Other nonlinear process, such as quantum Rabi–Stark model, [ 64,100–103 ] can also cause spectrum collapse. [ 101,102 ] As extensions, bias two‐photon QRM [ 104 ] and multiphoton QRM [ 28,98,105,106 ] have also been explored.…”

Section: Quantum States In Polaron Picturementioning

confidence: 99%

Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

Liu

Ying

et al. 2021

Adv Quantum Tech

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The light–matter interaction not only is ubiquitous in nature but also can be simulated in various artificial systems. Besides the tunability of artificial quantum systems, the experimental access to the ultra‐strong and even deep‐strong couplings has brought a regime with novel phenomenology. Theoretically the finding of the integrability for the quantum Rabi model (QRM) has attracted tremendous attention to the study of the QRM and its extensions which are fundamental models of the light–matter interaction. With the continuing enhancements of coupling strengths, a most fascinating phenomenon of these light–matter models is that they can exhibit few‐body quantum phase transitions (QPTs), while a full understanding of these QPTs is a challenge. The polaron picture is a method capable of analyzing these fundamental models in the entire coupling regime and extracting the essential physics behind the QPTs. A review of its extensive applications on the fundamental light–matter models is presented, with discussions on the phase diagrams and QPT‐related features. The universality of critical exponent of the anisotropic QRM as well as the possibility of QPTs in A2 terms are also addressed.

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A generalization of the quantum Rabi model: exact solution and spectral structure

Cited by 56 publications

References 56 publications

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model

Quantum Rabi–Stark model: solutions and exotic energy spectra

Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

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