Analytical energy spectrum for hybrid mechanical systems

Articles you may be interested inOn the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations Two-photon spectroscopy of the (n,3s) Rydberg transition in acetaldehyde: The torsional sequence This paper is concerned with the rigorous analytical determination of the spectrum of the two-photon and the two-mode quantum Rabi models. To reach this goal, we exploit the hidden symmetries in these models by means of the unitary and similarity transformations in addition to the Bargmann-Fock space description. In each case, the purely quantum mechanical problem of the Rabi model studied is reduced to solutions for differential equations. This eventually gives a third-order differential equation for each of these models, which is reduced to a second-order differential equation by additional transformations. The analytical expressions of the wave functions describing the energy levels are obtained in terms of the confluent hypergeometric functions. C 2014 AIP Publishing LLC. [http://dx.

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“…7,9,20,21,24,36, and 38 for some works). Specifically, the energy levels obtained in our paper may be compared to those obtained in Refs.…”

Section: Discussionmentioning

confidence: 99%

Full spectrum of the two-photon and the two-mode quantum Rabi models

Dossa

Avossevou

2014

Journal of Mathematical Physics

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“…The exceptional parts of the energy spectrum can be given from the conditions for truncation of the confluent Heun functions, and take the form [112] …”

Section: A Generalised Rabi Model Is the Asymmetric Quantum Rabi Modelmentioning

confidence: 99%

The quantum Rabi model: solution and dynamics

Xie

Zhong

Batchelor

et al. 2017

J. Phys. A: Math. Theor.

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199

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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“…Such results have prompted a number of theoretical studies on generalizations of the QRM, including multiqubit [48] and multimode [49] cases, as well as anisotropic couplings [50,51] and two-photon interactions [52][53][54][55]. In particular, two-photoncoupling models stand out for their highly counterintuitive spectral features.…”

Section: Introductionmentioning

confidence: 99%

Two-photon quantum Rabi model with superconducting circuits

Felicetti¹,

Rossatto²,

Rico³

et al. 2018

Phys. Rev. A

141

168

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We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong coupling regime and find that fundamental quantum optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield single-or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where twophoton interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multi-qubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.

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Analytical energy spectrum for hybrid mechanical systems

Cited by 54 publications

References 51 publications

Full spectrum of the two-photon and the two-mode quantum Rabi models

Full spectrum of the two-photon and the two-mode quantum Rabi models

The quantum Rabi model: solution and dynamics

Two-photon quantum Rabi model with superconducting circuits

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