Squeezing evolution with non-dissipative<i>SU</i>(1,1) systems

El-Orany, Faisal A. A.; Hassan, S. S.; Abdalla, M. Sebawe

doi:10.1088/1464-4266/5/5/004

Cited by 15 publications

(15 citation statements)

References 37 publications

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“…whereρ M andρ I are the statistical-mixture and interference parts whose exact forms are given in [17]. As we mentioned above that for the single-mode cat states the origin of the occurrence of the nonclassical effects is in the quantum interference between the components of the states.…”

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confidence: 99%

“…For instance, coherent states are close to classical states, however, even (odd) coherent states exhibit significant squeezing (sub-Poissonian statistics) and their photon number distributions provide oscillatory behavior. It is worth reminding that the evolution of the Schrödinger-cat states with the single-mode JCM has been treated in [18,19,20,21].…”

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confidence: 99%

“…For the sake of simplicity in (21) we restrict the calculation to the case φ = 0 . Also one can easily…”

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confidence: 99%

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Quantum phase properties of two-mode Jaynes–Cummings model for Schrödinger-cat states: interference and entanglement

El-Orany

Mahran

Wahiddin

et al. 2004

Optics Communications

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In this paper we investigate the quantum phase properties for the coherent superposition states (Schrödinger-cat states) for two-mode multiphoton Jaynes-Cummings model in the framework of the Pegg-Barnett formalism. We also demonstrate the behavior of the Wigner (W ) function at the phase space origin. We obtain many interesting results such as there is a clear relationship between the revival-collapse phenomenon occurring in the atomic inversion (as well as in the evolution of the W function) and the behavior of the phase distribution of both the single-mode and two-mode cases. Furthermore, we find that the phase variances of the single-mode case can exhibit revival-collapse phenomenon about the long-time behavior.We show that such behavior occurs for interaction time several times smaller than that of the single-mode Jaynes-Cummings model.

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confidence: 99%

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confidence: 99%

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Quantum phase properties of two-mode Jaynes–Cummings model for Schrödinger-cat states: interference and entanglement

El-Orany

Mahran

Wahiddin

et al. 2004

Optics Communications

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“…The linear dissipative processes in quantum optical systems can be also studied with SU(1, 1) Lie algebra in the framework of the Liouville space formulation [46,47]. Furthermore, beam splitters [48][49][50] interferometers [51], and linear directional couplers [52,53] are successfully described by SU (2) Lie algebra. In these studies the Baker-Campbell-Hausdorff formulas are useful, where in many cases the quantities to be calculated are exponential functions of the generators of the Lie algebras.…”

Section: Application Of Su(1 1) Casimir Operatormentioning

confidence: 99%

An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

Abdalla

Al-Ismael

2009

Int J Theor Phys

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In this paper we introduce the modified time-dependent damped harmonic oscillator. An exact solution of the wave function for both Schrödinger picture and coherent state representation are given. The linear and quadratic invariants are also discussed and the corresponding eigenvalues and eigenfunctions are calculated. The Hamiltonian is transformed to SU(1, 1) Lie algebra and an application to the generalized coherent state is discussed. It has been shown that when the system is under critical damping case the maximum squeezing is observed in the first quadrature F x . However, for the overcritical damping case the maximum squeezing occurs in the second quadrature F y . Also it has been shown that the system for both cases is sensitive to the variation in the coherent state phase.

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“…As studies with driven two-level systems (having only bound states) show [13][14][15][16], the qualitative properties of the HHG spectra can be calculated analytically us-ing traditional quantum optical notions like e.g., dressed states. An appropriately generalized version of the Jaynes-Cummings-Paul model has also been used to describe high-field, multiphoton processes [17][18][19]. Although a strong analogy can be drawn between the dynamics of a driven two-level system and the three-step model [20], for the realistic description of HHG in gas samples (with the obvious involvement of continuum states), the latter one became more widely used.…”

Section: Introductionmentioning

confidence: 99%

Quantum-optical model for the dynamics of high-order-harmonic generation

et al. 2016

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Abstract. Time-dependent nonequilibrium Green's functions (TDNEGF) are shown to provide a flexible, effective tool for the description of quantum mechanical single particle scattering on a spatially localized, time-dependent potential. Focusing on numerical methods, arbitrary space and time dependence of the potential can be treated, provided it is zero before an initial time instant. In this case, appropriate version of the Dyson and Keldysh equations lead to a transparent description with clear physical interpretation. The interaction of a short laser pulse and an electron propagating initially in free space is discussed as an example.

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Squeezing evolution with non-dissipativeSU(1,1) systems

Cited by 15 publications

References 37 publications

Quantum phase properties of two-mode Jaynes–Cummings model for Schrödinger-cat states: interference and entanglement

Quantum phase properties of two-mode Jaynes–Cummings model for Schrödinger-cat states: interference and entanglement

An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

Quantum-optical model for the dynamics of high-order-harmonic generation

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