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Journal of the Optical Society of America B

Sub-Poissonian photon statistics and higher-order squeezing behavior of Bernouilli states in the linear amplifier

P. García-Fernández, Francisco Javier Bermejo

Published Oct 1, 1987• 5 citations
Publisher

Abstract

A parameteric study was performed of the sub-Poissonian photon statistics and higher-order squeezing characteristics of Bernouilli states undergoing a linear amplification process. The necessary and sufficient conditions on the amplifier gain under which the output light exhibits sub-Poissonian photon statistics or squeezing were compared with exact numerical results, and good agreement was obtained. On the other hand, it was shown that Bernouilli states exhibit higher-order squeezing for some parameter ranges. The degree of higher-order squeezing decreases, and its duration becomes shorter, as the phase of the Bernouilli state increases.

DOI
10.1364/josab.4.001737

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A parameteric study was performed of the sub-Poissonian photon statistics and higher-order squeezing characteristics of Bernouilli states undergoing a linear amplification process. The necessary and sufficient conditions on the amplifier gain under which the output light exhibits sub-Poissonian photon statistics or squeezing were compared with exact numerical results, and good agreement was obtained. On the other hand, it was shown that Bernouilli states exhibit higher-order squeezing for some parameter ranges. The degree of higher-order squeezing decreases, and its duration becomes shorter, as the phase of the Bernouilli state increases.
We make a comparison between the necessary and sufficient conditions on the gain of the linear amplifier under which the light output exhibits sub-Poissonian photon statistics or squeezing and exact numerical results, obtained by solving the master equation by means of matrix procedures, and find good agreement. We find numerically that higher-order squeezing persists in a region in which sub-Poissonian statistics and second-order squeezing have already disappeared, for certain parameter ranges of input binomial states.
The necessary and sufficient conditions on the gain of the linear amplifier are determined under which the light output exhibits sub-Poissonian photon statistics or squeezing. It is found that for these effects the intensity gain must not exceed 2 under any circumstances. It is also shown that there exists a weaker sufficiency condition on the gain above which all nonclassical features of the field disappear. This suggests the possibility that other quantum effects may persist in the intermediate, still unexplored, domain of operation of the amplifier.
We study the photon statistics at the output of phase-sensitive amplifiers and absorbers. It is argued that the photon statistics is independent of a detailed description of the rigged energy reservoir; therefore, we use a simple phenomenological model including only three parameters. The mean number of photons and the Mandel parameter Q at the output are studied as a function of the reservoir state and the input state. General conditions for sub-Poissonian output light are stated with use of three characteristic moments of the input state. We find an interesting intermediate regime where the device can have a sub-Poissonian output for a certain class of super-Poissonian input states.
The squeezing and sub-Poissonian eects of light in third harmonic generation are investigated based on the fully quantum mechanical approach up to the rst order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium.The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established.The occurrence of amplitude squeezing eects in both the quadratures of the radiation eld in the fundamental mode is investigated and found to be dependent on the selective phase values of the eld amplitude.The photon statistics of the pump mode in this process have also been investigated and found to be sub-Poissonian in nature.It is shown that for particular phase values the amplitude squeezing and sub-Poissonian photon statistics of light occur simultaneously.It is observed that there is no possibility to produce squeezed light in the harmonic mode up to rst-order interaction in gt.Further, it is found that the normal squeezing in the harmonic mode directly depends upon the amplitude-cubed squeezing of the initial pump eld to the case of second-order interaction in gt.This gives a method of converting higher-order (amplitude-cubed) squeezing of the fundamental mode into normal squeezing of the harmonic mode and vice versa.