Solution to the Landau–Zener problem via Susskind–Glogower operators

Rodríguez-Lara, B. M.; Rodríguez-Méndez, D.; Moya‐Cessa, H.

doi:10.1016/j.physleta.2011.08.051

Cited by 6 publications

(3 citation statements)

References 32 publications

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“…where the detuning between the qubit and cavity field frequency is given by δ ω ω = − c 0 . We can follow a right unitary approach [61][62][63] and rewrite this Hamiltonian in the form,…”

Section: Hybrid Qubit-optomechanical Modelmentioning

confidence: 99%

Operator approach to quantum optomechanics

2015

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We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be either solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.PACS numbers: 37.90.+j,42.50.-p, 42.65.-k Operator approach to quantum optomechanics

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Section: Hybrid Qubit-optomechanical Modelmentioning

confidence: 99%

Operator approach to quantum optomechanics

2015

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“…where the parameter δ = ω q − ω is the detuning between the two-level atom and field frequencies. We can follow a right unitary approach [17,18] to decompose this Hamiltonian into the following product,Ĥ…”

Section: Right Unitary Decompositionmentioning

confidence: 99%

Ultracold two-level atom in a quadratic potential

Soto‐Eguibar

Zúñiga-Segundo²,

Rodríguez-Lara

et al. 2015

Optics Communications

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We use a right unitary decomposition to study an ultracold two-level atom interacting with a quantum field. We show that such a right unitary approach simplifies the numerical evolution for arbitrary position-dependent atom-field couplings. In particular, we provide a closed form, analytic time evolution operator for atom-field couplings with quadratic dependence on the position of the atom.Comment: 11 pages, 2 figue

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“…This solution involves the Bethe ansatz method. The general Hamiltonian (2) can also be solved by extending our right unitary approach to the quantum Landau-Zener problem for a single two-level system presented in [27], which delivers an evolution operator with the form…”

Section: The Modelmentioning

confidence: 99%

The exact solution of generalized Dicke models via Susskind–Glogower operators

Rodríguez-Lara¹,

Moya‐Cessa²

2013

J. Phys. A: Math. Theor.

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Abstract. We show a right unitary transformation approach based on SusskindGlogower operators that diagonalizes a generalized Dicke Hamiltonian in the field basis and delivers a tridiagonal Hamiltonian in the Dicke basis. This tridiagonal Hamiltonian is diagonalized by a set of orthogonal polynomials satisfying a three-term recurrence relation. Our result is used to deliver a closed form, analytic time evolution for the case of a Jaynes-Cummings-Kerr model and to study the time evolution of the population inversion, reduced field entropy, and Husimi's Q-function of the field for ensembles of interacting two-level systems under a Dicke-Kerr model.

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Solution to the Landau–Zener problem via Susskind–Glogower operators

Cited by 6 publications

References 32 publications

Operator approach to quantum optomechanics

Operator approach to quantum optomechanics

Ultracold two-level atom in a quadratic potential

The exact solution of generalized Dicke models via Susskind–Glogower operators

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