Analytical method of spectra calculations in the Bargmann representation

Maciejewski, Andrzej J.; Przybylska, Maria; Stachowiak, Tomasz

doi:10.1016/j.physleta.2014.10.001

Cited by 56 publications

(75 citation statements)

References 31 publications

(61 reference statements)

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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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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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“…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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“…In paper [1] we proposed a general method which allows to determine spectra of quantum systems given in the Bargmann representation. This representation is very useful for systems with a Hilbert space which is a product of a finite and infinite-dimensional spaces.…”

Section: Introduction and Resultsmentioning

confidence: 99%

An exactly solvable system from quantum optics

Maciejewski

Przybylska²,

Stachowiak³

2015

Physics Letters A

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We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given.

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Analytical method of spectra calculations in the Bargmann representation

Cited by 56 publications

References 31 publications

Quantum Rabi–Stark model: solutions and exotic energy spectra

Quantum Rabi–Stark model: solutions and exotic energy spectra

Two-photon Rabi model: analytic solutions and spectral collapse

An exactly solvable system from quantum optics

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