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arXiv:1004.2199

Nonlinear Quantum Optical Spring

Mohammad Javad Faghihi, Mohammad Kazem Tavassoly

Published Apr 13, 2010• 0 citations
arXivHTMLPDF

Abstract

The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of $ω$ to $ω\sqrt{1+μa^\dagger a}$ the mentioned idea can be established. In the present paper we generalize the approach of quantum optical spring (has been called by us as nonlinear quantum optical spring) with attention to the {\it dependence of frequency to the intensity of radiation field} that {\it naturally} observed in nonlinear coherent states. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters as particular quantum features will be revealed.

DOI
10.48550/arxiv.1004.2199

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The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of ωωω to ω1+μa†aω\sqrt{1+μa^\dagger a}ω1+μa†a​ the mentioned idea can be established. In the present paper we generalize the approach of quantum optical spring (has been called by us as nonlinear quantum optical spring) with attention to the {\it dependence of frequency to the intensity of radiation field} that {\it naturally} observed in nonlinear coherent states. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters as particular quantum features will be revealed.
The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of ω to the mentioned idea can be established. In the present paper, we generalize the approach of quantum optical spring with particular attention to the dependence of frequency to the intensity of radiation field that naturally observes in the nonlinear coherent states, from which we arrive at a physical system has been called by us as nonlinear quantum optical spring. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters, as particular quantum features, will be revealed.
We study the dynamics of the quantum optical spring, i.e., a spring whose spring constant undergoes discrete jumps depending on the quantum state of another system. We show the existence of revivals and fractional revivals in the quantum dynamics reminiscent of similar dynamical features in cavity QED. We recover in the semiclassical limit the results for an oscillator whose frequency undergoes a sudden change. The quantum optical spring is conceivable, for example, by a micromirror under the influence of radiation pressure by a field which is strictly quantum mechanical. Our work suggests that driven systems would in general exhibit a very different dynamics if the drive is replaced by a quantum source.
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The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q -function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.
In this paper, to study the effects of a nonlinear medium on the atom–field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as our nonlinear optical phenomena, and with the use of its algebra, we show that it can be considered as a deformed oscillator as well as a deformed su(2) algebra. Then we construct the associated two-mode nonlinear coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom–field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we study the effect of the nonlinear medium on the occupation probabilities of the atomic levels and consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider the photon distribution, correlation function, Mandel parameters of the field, von Neumann entropy, and also the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of the two modes is clarified.