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Journal of Modern Optics

The quantum statistical properties of superposition coherent states with thermal noise

Kaicheng Zhu, Huiqin Tang, Cuiliang Li, Duzhi Huang, Xinguang Li, Xiangru Li

Published Feb 1, 1996• 6 citations
Publisher

Abstract

We investigate a free monochromatic electromagnetic field which is in the even or odd coherent state with thermal noise. The main tool in our analysis is the characteristic function. We establish an alystic formula for an arbitrary correlation function. We point out the non-classical oscillations of the photon-number distribution and find its generating function as well as the degree of purity of the field. We also examine the squeezing properties and antibunching feature. Besides, the usual quasiprobability densities are derived.

DOI
10.1080/09500349608232745

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We investigate a free monochromatic electromagnetic field which is in the even or odd coherent state with thermal noise. The main tool in our analysis is the characteristic function. We establish an alystic formula for an arbitrary correlation function. We point out the non-classical oscillations of the photon-number distribution and find its generating function as well as the degree of purity of the field. We also examine the squeezing properties and antibunching feature. Besides, the usual quasiprobability densities are derived.
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Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components q1{q}_{1}q1​ and q2{q}_{2}q2​ is examined. The \ensuremath{\delta}- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.
New states of electromagnetic field, i.e. even and odd negative binomial states are introduced here. These states interpolate between the even (odd) coherent states and the even (odd) quasi-thermal states. Various statistical properties of these states such as the mean photon number, second-order coherence function, normal squeezing are calculated. The Wigner function for these states are also discussed. These results may be useful for carrying out systematic study of the non-classical properties of `Schrödinger cat states' as one moves from even (odd) coherent state to even (odd) quasi-thermal state.
We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a 2. We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.