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Physical Review A

Transformations of the nonclassical states by an optical amplifier

G. S. Agarwal, Katsushi Tara

Published Apr 1, 1993• 29 citations
Publisher

Abstract

We consider nonclassical properties of the field at the output of an amplifier under the operational condition that the output exhibits neither squeezing nor sub-Poissonian statistics but has the nonclassical P function. We also present explicit results for the output P function when the input is strictly a quantum-mechanical state similar to a Fock state. The nonclassical properties of the marginal distribution associated with the output are derived. The domain where the marginal distribution remains nonclassical is different from the domain over which the output P function is nonclassical. The amplifier is shown to be a useful device for direct measurements of the quasiprobabilities.

DOI
10.1103/physreva.47.3160

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We consider nonclassical properties of the field at the output of an amplifier under the operational condition that the output exhibits neither squeezing nor sub-Poissonian statistics but has the nonclassical P function. We also present explicit results for the output P function when the input is strictly a quantum-mechanical state similar to a Fock state. The nonclassical properties of the marginal distribution associated with the output are derived. The domain where the marginal distribution remains nonclassical is different from the domain over which the output P function is nonclassical. The amplifier is shown to be a useful device for direct measurements of the quasiprobabilities.
The existence of positive well-defined quasiprobabilities is known to be related to the measure of nonclassicality for a given field state. We test the coincidence of the loss of well-known nonclassical properties with the appearance of the positive well-defined quasiprobabilities for various fields influenced by phase-insensitive reservoirs. For Gaussian fields the appearance of a positive Glauber-Sudarshan P function coincides with the loss of nonclassical properties in quadrature fluctuations and in photon statistics. We find that when an initial Fock state dissipates or is amplified the initial field loses its nonclassicality in photon statistics before the P function becomes positive, which is different from the Gaussian field. The Wigner function may be positive even when the decaying Fock state is sub-Poissonian. For the amplification of the Fock state, however, the Wigner function is positive only when the field is super-Poissonian. For the dissipation and amplification of the Fock state the point when a certain quasiprobability function becomes positive definite depends only on the average number of photons N of the heat bath. \textcopyright{} 1996 The American Physical Society.
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.
In the framework of Hamiltonian formalism nonclassical effects of an optical field propagating inside a directional coupler containing nondegenerate parametric amplification have been studied. We investigate the effect of switching between the input modes and the out going fields from the coupler. Particular attention has been paid to two mode squeezing, second-order correlation function, quasiprobability distribution functions, and photon-number distribution. Incident number and coherent states are considered. It has been shown that when one of the modes enters the coupler in the Fock state and the other modes are in vacuum states, the coupler can serve as a generator for coherent state. Furthermore, regimes for generation and transmission of squeezed and/or sub-Poissonian light are found.
We study the statistical properties of squeezed Kerr states generated by squeezing, with a two-photon parametric process, the output of a Kerr medium whose input is coherent light. The squeezing has the effect of allowing the photon statistics to depend on the Kerr nonlinearity. Without the squeezing the statistics are Poissonian, but after squeezing they may be either sub-Poissonian or super-Poissonian. We also study the Q-function quasiprobability distribution for these states and related distributions associated with the quantum-mechanical phase. Finally, we show that quadrature squeezing can be enhanced and that squeezing and sub-Poissonian statistics can coexist.
Truncated output states can be generated by the conditional measurement if the coherent state and arbitrary Fock state are regarded as the input states of beam splitters.The properties of this kind of truncated optical states are studied in this paper.The results have shown that the output states in one out port have stronger nonclassical properties of squeeze and sub-Poissonian distribution when zero photon is measured in the other out port,and the nonclassical properties can become stronger with the increase of input number state.When m(m＞0) photon is measured in one of the out ports,each output state after conditional measurement has the same property in optical field but also exhibits apparent nonclassical effects such as squeezing and sub-Poissonian distribution.It should be noted particularly that the number state corresponding to the measurement in output state after conditional measurement would be truncated if the single number state is input.
The s-parametrized characteristic function for the output light is given. The s-ordered distribution functions for the output of a linear amplifier are investigated. The input light field of the linear amplifier is assumed to be a squeezed displaced Fock state. Various moments are calculated by using the s-ordered characteristic function for the output linear amplifier. The various distribution functions of the output fields are plotted as functions of the interaction time. The phase distribution for the output light is discussed.