The quantum Rabi model: solution and dynamics

Xie, Qing; Zhong, Honghua; Batchelor, Murray T.; Lee, Chaohong

doi:10.1088/1751-8121/aa5a65

Cited by 188 publications

(205 citation statements)

References 170 publications

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“…Transformation of this electronic-vibrational Hamiltonian into normal mode coordinates [31,37] shows that only the relative displacement mode, with creation operator D ( †) = (d ( †) 1 − d ( †) 2 )/ √ 2, couples to the excitonic system. The effective Hamiltonian for the prototype dimer takes the form of a generalised quantum Rabi model [38]:…”

Section: Comparison Of Original and Proposed Methodsmentioning

confidence: 99%

Perturbation approach for computing frequency- and time-resolved photon correlation functions

2018

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We propose an alternative formulation of the sensor method presented in [Phys. Rev. Lett 109, 183601 (2012)] for the calculation of frequency-filtered and time-resolved photon correlations. Our approach is based on an algebraic expansion of the joint steady state of quantum emitter and sensors with respect to the emitter-sensor coupling parameter . This allows us to express photon correlations in terms of the open quantum dynamics of the emitting system only and ensures that computation of correlations are independent on the choice of a small value of . Moreover, using time-dependent perturbation theory, we are able to express the frequency-and timeresolved second-order photon correlation as the addition of three components, each of which gives insight into the physical processes dominating the correlation at different time scales. We consider a bio-inspired vibronic dimer model to illustrate the agreement between the original formulation and our approach.

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Section: Comparison Of Original and Proposed Methodsmentioning

confidence: 99%

Perturbation approach for computing frequency- and time-resolved photon correlation functions

2018

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“…We also note that it is possible to equivalently redefine the G-function G ε (x; g, ∆) using the solutions of the system (2.3) (i.e. with the change of variable y = g+z 2g ), however, we use the definition given in §2.3 since it is standard in the literature, including e.g., [5,40,68].…”

Section: Rabimentioning

confidence: 99%

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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“…For instance, the interaction Hamiltonian for trapped ions is non-linear, thus allowing this system to be exploited in order to investigate the dynamics of various QRM generalizations [7,11]. For these reasons, the interest in the QRM and its variants has been rekindled, and a strong effort to construct their solutions and to clarify the relative dynamical properties is under way [12][13][14][15][16][17][18]. A major role in these new developments has been played by the analytic solutions of the QRM, found first in 2011 [15] and based on its representation in the Bargmann space of the holomorphic functions [19].…”

Section: Introductionmentioning

confidence: 99%

A continued fraction based approach for the Two-photon Quantum Rabi Model

Lupo

Napoli

Messina

et al. 2019

Sci Rep

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We study the Two Photon Quantum Rabi Model by way of its spectral functions and survival probabilities. This approach allows numerical precision with large truncation numbers, and thus exploration of the spectral collapse. We provide independent checks and calibration of the numerical results by studying an exactly solvable case and comparing the essential qualitative structure of the spectral functions. We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model.

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The quantum Rabi model: solution and dynamics

Cited by 188 publications

References 170 publications

Perturbation approach for computing frequency- and time-resolved photon correlation functions

Perturbation approach for computing frequency- and time-resolved photon correlation functions

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

A continued fraction based approach for the Two-photon Quantum Rabi Model

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