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Physica Scripta

Parametric Excitation of Photon-added Coherent States

V. V. Dodonov, Marcelo A. Marchiolli, Ya. A. Korennoy, Vladimir I. Man’ko, Y A Moukhin

Published Nov 1, 1998• 7 citations
Publisher

Abstract

We study the evolution of the photon-added coherent state | α, m ⟩ (introduced by Agarwal and Tara [Phys. Rev. A43, 492 (1991)]) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. We give explicit expressions for the photon distribution function, mean values and variances of the quadrature components and of the photon number, the Wigner and Q -functions, etc. We show that the parametric excitation leads to strong oscillations of the photon (phonon) distribution function and changes the subpoissonian photon statistics to the superpoissonian one. Besides, it enables to achieve a larger squeezing coefficient than in the usual squeezed states.

DOI
10.1088/0031-8949/58/5/008

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We study the evolution of the photon-added coherent state | α, m ⟩ (introduced by Agarwal and Tara [Phys. Rev. A43, 492 (1991)]) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. We give explicit expressions for the photon distribution function, mean values and variances of the quadrature components and of the photon number, the Wigner and Q -functions, etc. We show that the parametric excitation leads to strong oscillations of the photon (phonon) distribution function and changes the subpoissonian photon statistics to the superpoissonian one. Besides, it enables to achieve a larger squeezing coefficient than in the usual squeezed states.
We study the dynamical squeezing of the photon-added coherent state (PACS) due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. Explicit expressions for the time dependence of various functions characterizing the quantum state, such as the photon distribution, the Wigner function, the mean values and variances of the quadrature components and of the photon number, show that the dynamically squeezed PACS possesses a larger squeezing coefficient than the usual squeezed states. The dynamical squeezing is accompanied by a change of the sub-Poissonian photon statistics to the super-Poissonian one.
Photon distribution function, means and dispersions are found explicitly for the nonclassical state of light which is created from the photon--added coherent state ∣α,m⟩\vert α,m \rangle∣α,m⟩ due to a time--dependence of the frequency of the electromagnetic field oscillator. Generating function for factorial momenta is obtained. The Wigner function and Q--function are constructed explicitly for the excited photon--added coherent state of light. Influence of added photons on known oscillations of photon distribution function for squeezed light is demonstrated. oscillator are considered.
Quantum statistical properties of general superpositions of coherent states of the type Nα,βα+eiξβ have been studied. Formulas for fluctuations (variances) of the coordinate and momentum quadratures and fluctuations of the number of photons in these states are obtained. The amplitude Nα,βnαeiφ+eiξnβeiφ,φ=φα=φβ and phase Nα,βneiφα+eiξneiφβ,n=nα=nβ superpositions of coherent states are considered separately. In the case of amplitude superpositions, a field under certain conditions occurs in a quadrature-squeezed state. At the same time, the photon distribution in the case of amplitude superpositions is always super-Poissonian. In the case of phase superpositions, a field under certain conditions occurs in quadrature-squeezed states for small average numbers of photons. For certain parameters of coherent states, the photon statistics in phase superpositions is sub-Poissonian. Using amplitude superpositions, it is possible to generate a microscopic electromagnetic field with the average photon number below or on the order of unity, as well as mesoscopic and even macroscopic fields with arbitrary large average photon numbers, characterized by significant quadrature squeezing. Using phase superpositions, it is possible to create under certain conditions the electromagnetic field states with sub-Poissonian statistics (squeezed distribution of photon numbers) for an arbitrary large average photon number. Expressions for a ‘strict’ coordinate–momentum uncertainty relation (Cauchy inequality) are obtained and analysed in cases of general, amplitude and phase superpositions of coherent states.
We construct a new type of photon-added squeezed coherent state generated by repeatedly operating the bosonic creation operator on a new type of squeezed coherent state [Fan H Y and Xiao M 1996 Phys. Lett. A 220 81]. We find that its normalization factor is related to single-variable Hermite polynomials. Furthermore, we investigate its statistical properties, such as Mandel’s Q parameter, photon-number distribution, and Wigner function. The nonclassicality is displayed in terms of the intense oscillation of photon-number distribution and the negativity of the Wigner function.
We construct a new type of photon-added squeezed coherent state generated by repeatedly operating the bosonic creation operator on a new type of squeezed coherent state [Fan H Y and Xiao M 1996 Phys. Lett . A 220 81 ]. We find that its normalization factor is related to single-variable Hermite polynomials. Furthermore, we investigate its statistical properties, such as Mandel's Q parameter, photon-number distribution, and Wigner function. The nonclassicality is displayed in terms of the intense oscillation of photon-number distribution and the negativity of the Wigner function.
In this paper, we introduce a modified class of correlated coherent states. These states are realized during the consideration of a new model which represents the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a cavity. By using the transition amplitude we have managed to establish the relationship between the usual coherent states and the modified states. The phenomenon of squeezing and the variances of the photon number sum and difference are discussed. It has been shown that the mean photon number controls the value of the correlation. Furthermore, our discussion on the quasi-probability distribution functions (the Wigner and Q-functions) shows that both functions are sensitive to the change in the ratio of the field modes as well as the coupling parameter λ1.