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Physical Review A

Photocount distribution of two-mode squeezed states

M. Artoni, U. P. Ortiz, Joseph L. Birman

Published Apr 1, 1991• 20 citations
Publisher

Abstract

We derive a closed-form expression for the number probability distribution of a ``generic'' two-mode field in a two-mode squeezed state. We discuss its dependence on the average particle number in the two modes and on the amount of squeezing. We show that the distribution exhibits oscillations for particle numbers appropriately greater than the average, similar to the one-mode case, although the conditions under which such an oscillatory behavior occurs are different. These results are directed to the investigation of nonclassical properties in the radiation field produced by a parametric amplifier operated in a two-mode regime.

DOI
10.1103/physreva.43.3954

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We derive a closed-form expression for the number probability distribution of a ``generic'' two-mode field in a two-mode squeezed state. We discuss its dependence on the average particle number in the two modes and on the amount of squeezing. We show that the distribution exhibits oscillations for particle numbers appropriately greater than the average, similar to the one-mode case, although the conditions under which such an oscillatory behavior occurs are different. These results are directed to the investigation of nonclassical properties in the radiation field produced by a parametric amplifier operated in a two-mode regime.
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We derive the joint photon-number distribution for two-mode squeezed states with coherent amplitudes. For certain ranges of the parameters, the joint distribution exhibits nonclassical oscillations, which are the two-mode analog of the oscillations found in the single-mode case. These nonclassical oscillations are absent from the marginal distributions for each mode. The nonclassical features of the joint distribution may be explained using the interference--in--phase-space concept in four-dimensional phase space.
Squeezed states of the Jaynes-Cummings (JC) model are constructed and the statistical properties of the field oscillator in these states are studied. The presence of interaction between the field oscillator and the atom results in the appearance of slow temporal variations in the average values of the dynamic quantities. Two cases essentially differ: When only one of two modes of the JC model is excited, the variations in time, in particular, of the average value of the coordinate are governed by the mode anharmonicity. In the case when both modes of the JC model with close frequencies are excited, the temporal variations represent collapse and revival of oscillations with the frequency 2kn+12k\sqrt {n + 1} 2kn+1​ , where k is the constant of the atom-field oscillator interaction and n is the number of photons. The constructed squeezed vacuum states are not two-photon states, because the probability of finding an odd number of photons is not equal to zero and varies with time.
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.