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Journal of Modern Optics

Statistical Properties of a New Squeezed Operator Model

M. Sebawe Abdalla

Published Apr 1, 1992• 11 citations
Publisher

Abstract

We introduce a new squeezed operator which is a combination of the two-mode squeezed operator and the two single photon squeezed operator. Here we study the effects of this operator on the photon number sum and difference. The squeezing in the frequency converter model has been examined, and statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q-function). An application to the parametric amplifier is given.

DOI
10.1080/09500349214550781

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We introduce a new squeezed operator which is a combination of the two-mode squeezed operator and the two single photon squeezed operator. Here we study the effects of this operator on the photon number sum and difference. The squeezing in the frequency converter model has been examined, and statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q-function). An application to the parametric amplifier is given.
In this paper we introduce a new squeeze operator which is a combination of the two single photon squeezing operator and two mode correlated operator. We construct the general coherent-state wave function, and study the effects of this operator on the photon number sum and difference. We find in absence of the squeezing parameters λ1 and λ2 both the sum and the difference are conserved by the two mode correlated operator. The squeezing phenomenon is discussed, and the minimum uncertainty state is found for small value of the squeezing parameter λ. Besides the Glauber second order correlation function, the statistical investigations are carried out for the quasi-probability distribution functions (P-representation, Wigner function and Q-function). The discussion related to the phase space distribution function is given, and the matrix elements of the density operator are calculated. The photocount distribution is also considered.
The statistical properties of the time evolution operator for the Hamiltonian describing the simultaneous non-degenerate parametric amplifier, and mixing of two modes in the rotator frame is considered. Here we study the effects of this operator on the photon number sum and difference. The Glauber second-order correlation function is calculated, and the squeezing related to the frequency converter and the parametric amplifier has been discussed. The statistical investigations for the quasiprobability distribution functions are carried out.
Photon statistics and phase properties of two-mode squeezed number states are studied. It is shown that photon number distribution and Pegg-Barnett phase distribution for such states have similar (N + 1)-peak structure for nonzero value of the difference in the number of photons between modes. Exact analytical formulas for phase distributions based on different phase approaches are derived. The Pegg-Barnett phase distribution and the phase quasiprobability distribution associated with the Wigner function are close to each other, while the phase quasiprobability distribution associated with the Q function carries less phase information.
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.