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Journal of Modern Optics

Non-classical Properties of Even and Odd Coherent States

Christopher C. Gerry

Published Jun 1, 1993• 130 citations
Publisher

Abstract

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.

DOI
10.1080/09500349314551131

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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.
We present a detailed discussion of a type of four-photon coherent state defined as right eigenstates of the operator â 4 where â is the usual annihilation operator. There are actually four sets of states that need to be considered, namely those containing as the lowest number states ¦0>, ¦1>, ¦2>, or ¦3>. These correspond to the possible unique superpositions of the ordinary coherent states ¦±α> and ¦±iα>. We discuss the nonclassical properties of these states such as photon antibunching and squeezing. The usual second order squeezing does not exist for these states but higher order squeezing and square field amplitude squeezing do exist. Also discussed are the quasiprobability distributions, namely the P-function, the Q-function and the Wigner function. Finally, a method of generating these states based on the competition between a four-photon parametric process and incoherent losses from four-photon absorption is presented.
The higher-order squeezing and quasiprobability distribution function of even and odd coherent states are studied in this paper. The results show that the properties of higher-order squeezing of the two states exclude each other, and characteristic functions and Wigner functions are all not gaussian. Particularly, Wigner functions can not be perseved positive define. Quasiprobability density (QPD) of the two states are neither "elliptic" nor "crescent", but are two-petal-like shape, which shows that squeezing type can not be represented by the QPD figure of a state.
Abstract Two-mode nonlinear semi-coherent states and their even and odd superpositions are defined. Their non-classical properties, including photon statistics and squeezing, are then evaluated. We use the Mandel parameter and the second-order coherence function to study sub-Poissonian photon statistics and the photon antibunching effect. By calculating the variance of two-mode quadrature operators, we evaluate the squeezing effect for the introduced states. Next, we examine entanglement using concurrence. We have found that all states display non-classical properties within certain ranges of the parameters involved. The calculation of concurrence demonstrates that all states are entangled within specific ranges of parameters.
Two new classes of nonclassical states are defined by exciting Hillery's even and odd coherent states. Their physical properties are investigated numerically. It is found that they do not exhibit the squeezing effect but exhibit remarkable characteristics of sub-Poissonian distribution and antibunching. In sharp contrast to the case of excited Glauber coherent states, it is observed that the uncertainty of the field quadrature in excited even and odd coherent states increases with the degree of excitation. It is also seen that the Wigner functions associated with them take negative values for wider regions of parameters compared to those of Hillery's even and odd coherent states.