Analytical eigenstates for the quantum Rabi model

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

doi:10.1088/1751-8113/46/41/415302

Cited by 149 publications

(188 citation statements)

References 61 publications

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“…G R (E) was then recovered within the extended coherent states approach, which avoids the mapping into the Bargmann space of analytic functions [7]. These results have stimulated extensive research in the QRM and related models [8,9,10,11,12,13,14,15,16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Two-photon Rabi model: analytic solutions and spectral collapse

Duan

Xie

Braak

et al. 2016

J. Phys. A: Math. Theor.

102

156

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Abstract. The two-photon quantum Rabi model with quadratic coupling is studied using extended squeezed states and we derive G-functions for Bargmann index q = 1/4 and 3/4. The simple singularity structure of the G-function allows to draw conclusions about the distribution of eigenvalues along the real axis. The previously found picture of the spectral collapse at critical coupling g c has to be modified regarding the low lying states, especially the ground state: We obtain a finite gap between ground state and the continuum of excited states at the collapse point. For large qubit splitting, also other low lying states may be separated from the continuum at g c . We have carried out a perturbative analysis allowing for explicit and simple formulae of the eigenstates. Interestingly, a vanishing of the gap between ground state and excited continuum at g c is obtained in each finite order of approximation. This demonstrates cleary the non-pertubative nature of the excitation gap. We corroborate these findings with a variational calculation for the ground state.

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Section: Introductionmentioning

confidence: 99%

Two-photon Rabi model: analytic solutions and spectral collapse

Duan

Xie

Braak

et al. 2016

J. Phys. A: Math. Theor.

102

156

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“…This labelling is used in figure 4, which shows the low-lying energy spectrum as a function of the coupling g. ¶ Note there is a typo in the figure 2 caption in Ref. [42]: G − (E, z) and G + (E, z) should be interchanged. Although the analytic solutions φ…”

Section: Energy Spectrummentioning

confidence: 99%

“…Therefore the energy spectrum of the quantum Rabi model can also be obtained with the Wronskian method [42,43]. Indeed, the above Wronskians can be written in terms of the confluent Heun functions.…”

Section: Energy Spectrummentioning

confidence: 99%

“…Subsequently this condition was reproduced via Bogoliubov transformation [41]. It was further found that the analytic solution for the quantum Rabi model can be given in terms of confluent Heun functions [42,43], with the well-known Judd isolated exact solutions [44] appearing naturally as ‡ For an early review of JC physics, the reader is referred to [7] (see also [8,9]). § One further regime is defined by the limit ω = 0, which is the relativistic Dirac regime [10].…”

Section: Introductionmentioning

confidence: 99%

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The quantum Rabi model: solution and dynamics

Xie

Zhong

Batchelor

et al. 2017

J. Phys. A: Math. Theor.

Self Cite

200

192

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Abstract. This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given.

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“…This could allow the DSC regime, which is hard to access experimentally in cavity QED, to be successfully simulated in other physical contexts. In spite of the vast research in this area and the relative simplicity of the Rabi model, its integrability has been proven just recently [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Mixed Rabi Jaynes–Cummings model of a three-level atom interacting with two quantized fields

Torosov¹,

Longhi²,

Valle³

2015

Optics Communications

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The quantum Rabi model describes the ultrastrong interaction of a two-level atom coupled to a single quantized bosonic mode. As compared to the Jaynes-Cummings model, in the Rabi model the absorption and emission processes do not need to satisfy energy conservation and the usual rotating wave approximation (RWA) breaks down. As a result, the atom-field dynamics in the Hilbert space splits into two independent parity chains, exhibiting a collapse-revival pattern and exact periodic dynamics in the limit of degenerate atomic levels. Here we introduce a mixed Rabi Jaynes-Cummings model by considering a three-level atom interacting with two quantized bosonic fields, in which the RWA is made for one transition (with a weak atom-field coupling) but not for the other one (with an ultrastrong atom-field coupling). As a result, we show that the field in the weak coupled atomic transition can be used as a tool to control the atom-field dynamics of the other (strong coupled) transition, thus realizing an effective two-level quantum Rabi model with a controllable field. In particular, a periodic temporal dynamics of the atom-field state can be realized by appropriate tuning of the weak control field, even for non-degenerate atomic levels. A photonic simulator of the mixed Rabi Jaynes-Cummings model, based on light transport in evanescently-coupled optical waveguide lattices, is also briefly discussed.

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Analytical eigenstates for the quantum Rabi model

Cited by 149 publications

References 61 publications

Two-photon Rabi model: analytic solutions and spectral collapse

Two-photon Rabi model: analytic solutions and spectral collapse

The quantum Rabi model: solution and dynamics

Mixed Rabi Jaynes–Cummings model of a three-level atom interacting with two quantized fields

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