New symmetry in the Rabi model

Gardas, Bartłomiej; Dajka, Jerzy

doi:10.1088/1751-8113/46/26/265302

Cited by 25 publications

(34 citation statements)

References 36 publications

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“…These numerical observations suggest that the spectral compression dramatically enhances the effect of a reduced parity-flip symmetry breaking (so as to boost the early onset of near-degenerate energy levels), or else, that some hidden symmetry is at play for values of g for which the parity-flip symmetry is still manifestly broken. While we find this latter alternative to be rather unlikely, we should alert the reader that there are indeed claims that already the original quantum Rabi model has a hidden symmetry, with implications for its dynamics [56]. In any event, a further analysis of the compression of the spectrum for increasing γ, with the concurrent rapid emergence of near-degeneracy, seems to be called for.…”

Section: Spectral Structure Of the Quantum Rabi-stark Modelmentioning

confidence: 85%

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

Eckle

Johannesson

2017

J. Phys. A: Math. Theor.

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We consider a generalization of the quantum Rabi model where the twolevel system and the single-mode cavity oscillator are coupled by an additional Starklike term. By adapting a method recently introduced by Braak [Phys. Rev. Lett. 107, 100401 (2011)], we solve the model exactly. The low-lying spectrum in the experimentally relevant ultrastrong and deep strong regimes of the Rabi coupling is found to exhibit two striking features absent from the original quantum Rabi model: avoided level crossings for states of the same parity and an anomalously rapid onset of two-fold near-degenerate levels as the Rabi coupling increases.

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Section: Spectral Structure Of the Quantum Rabi-stark Modelmentioning

confidence: 85%

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

Eckle

Johannesson

2017

J. Phys. A: Math. Theor.

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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.

100

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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“…It turns out that the w n and z n satisfy the same relations (10) and (11) as f n and e n . Thus, w n = rf n , z n = re n , with some constant r. Now we assume the state |ψ to be the unique eigenvector of H sb belonging to energy E, i.e.…”

Section: G-functionsmentioning

confidence: 88%

“…G R (E) was then recovered with the simpler formalism of extended coherent states [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]. It is well known in quantum optics [21] that two-mode squeezed states are important since several devices produce correlated light at two frequencies.…”

Section: Introductionmentioning

confidence: 99%

Solution of the two-mode quantum Rabi model using extended squeezed states

Duan¹,

He²,

Braak³

et al. 2015

EPL

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The two-mode quantum Rabi model with bilinear coupling is studied using extended squeezed states. We derive G-functions for each Bargmann index q. They share a common structure with the G-function of the one-photon and two-photon quantum Rabi models. The regular spectrum is given by zeros of the G-function while the conditions for the presence of doubly degenerate (exceptional) eigenvalues are obtained in closed form through the lifting property. The simple singularity structure of the G-function allows to draw conclusions about the distribution of eigenvalues along the real axis and to understand the spectral collapse phenomenon when the coupling reaches a critical value.

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New symmetry in the Rabi model

Abstract: It is recognized that, apart from the total energy conservation, there is a nonlocal and a somewhat hidden symmetry in this model. Conditions for the existence of this observable, its form and its explicit construction are presented.

Cited by 25 publications

References 36 publications

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

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

Two-photon Rabi model: analytic solutions and spectral collapse

Solution of the two-mode quantum Rabi model using extended squeezed states

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