A Canonical Description of the Fabry-pérot Cavity

Colegrave, R. K.; Abdalla, M. Sebawe

doi:10.1080/713820584

Cited by 91 publications

(50 citation statements)

References 6 publications

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“…We apply a canonical transformation in order to concentrate the time dependence in the function y = -thl/m [9,10,14]; then introducing the dimensionless variables Q and P,…”

Section: Mass-pulsation Description Of Single-mode Emission and Reabsmentioning

confidence: 99%

“…Since only the electric-dipole interaction occurs in equations (1.1), we have no direct interest in H. The simplest representation of a pulsating field mode is by means of a variablemass oscillator [5,[8][9][10][14][15][16]; from equations (3.5) the motion is then described by…”

Section: R K Colegrave and A Vahabpour-roudsarimentioning

confidence: 99%

“…We modify the mode description given by equations (1.1) by replacing the simple harmonic oscillators by time-dependent oscillators, which have been the subject of much study over the past decade [5][6][7][8][9][10][11][12][13]. In previous communications [14] it has been argued that, in order to take full account of the presence of the atoms, the mode parameters (and consequently the frequencies) in the field modes should vary with time. In this way account may be taken of fluctuations in the strength of the field, arising from exchanges of photons with the atoms.…”

Section: Introductionmentioning

confidence: 99%

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Periodic Fluctuations in a Fabry-Perot Cavity in Resonance with a Reservoir of Two-level Atoms

Colegrave

Vahabpour-Roudsari

1985

Optica Acta: International Journal of Optics

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The Maxwell equations for the field in a cavity are modified to include the effect of irradiation by a reservoir of two-level atoms. A canonical treatment of the time-dependent field modes leads to predictions of the changes in the electric and magnetic field intensities, and in the photon statistics, for sufficiently small times. Coherent states evolve to squeezed states. The frequency converter and possible resonance phenomena are discussed.

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“…We apply a canonical transformation in order to concentrate the time dependence in the function y = -thl/m [9,10,14]; then introducing the dimensionless variables Q and P,…”

Section: Mass-pulsation Description Of Single-mode Emission and Reabsmentioning

confidence: 99%

Section: R K Colegrave and A Vahabpour-roudsarimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Periodic Fluctuations in a Fabry-Perot Cavity in Resonance with a Reservoir of Two-level Atoms

Colegrave

Vahabpour-Roudsari

1985

Optica Acta: International Journal of Optics

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“…In the present communication we reconsider the problem of time-dependent harmonic oscillator which has been extensively studied in the mid of the last century, see for example [1][2][3][4][5][6][7][8][9][10][11][12]. The question which may arise why one comes back to study one of the old problem and try to resurrect it.…”

Section: Introductionmentioning

confidence: 96%

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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“…Tailored time-dependent perturbations are used to improve system performance [49] in high-resolution NMR spectroscopy, where versatile decoupling techniques are available to manipulate the overall spin Hamiltonian [16]. Colegrave and Abdalla studied quantum systems with a time-dependent mass to investigate the field intensities in a Fabry-Perot cavity [51]. They suggested possible applications to solid-state physics and quantum field theory [52].…”

Section: Introductionmentioning

confidence: 99%

Analytic controllability of time-dependent quantum control systems

Lan

Tarn

Chi

et al. 2005

Journal of Mathematical Physics

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Abstract-The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrödinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finitedimensional submanifold of the unit sphere in Hilbert spaceand thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrödinger control problem. The applicability of the resulting theorem is illustrated with selected examples.

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A Canonical Description of the Fabry-pérot Cavity

Cited by 91 publications

References 6 publications

Periodic Fluctuations in a Fabry-Perot Cavity in Resonance with a Reservoir of Two-level Atoms

Periodic Fluctuations in a Fabry-Perot Cavity in Resonance with a Reservoir of Two-level Atoms

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

Analytic controllability of time-dependent quantum control systems

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