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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Non-classical properties of states generated by the excitations of even/odd coherent states of light

V. V. Dodonov, Ya. A. Korennoy, Vladimir I. Man’ko, Y A Moukhin

Published Jun 1, 1996• 91 citations
Publisher

Abstract

Photon-added even and odd coherent states of light are introduced. The mathematical and physical properties of such states are studied. The behaviour of the squeezing coefficient and the Mandel parameter is investigated. The quasiprobability distributions and the distribution of the field quadrature are studied in detail. The cumulants and factorial moments of the photon distribution are calculated. Strong oscillations of the ratio of the cumulant to factorial moment are demonstrated.

DOI
10.1088/1355-5111/8/3/006

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Photon-added even and odd coherent states of light are introduced. The mathematical and physical properties of such states are studied. The behaviour of the squeezing coefficient and the Mandel parameter is investigated. The quasiprobability distributions and the distribution of the field quadrature are studied in detail. The cumulants and factorial moments of the photon distribution are calculated. Strong oscillations of the ratio of the cumulant to factorial moment are demonstrated.
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.
Photon distribution function, means and dispersions are found explicitly for the nonclassical state of light which is created from the photon--added coherent state ∣α,m⟩\vert α,m \rangle∣α,m⟩ due to a time--dependence of the frequency of the electromagnetic field oscillator. Generating function for factorial momenta is obtained. The Wigner function and Q--function are constructed explicitly for the excited photon--added coherent state of light. Influence of added photons on known oscillations of photon distribution function for squeezed light is demonstrated. oscillator are considered.
We introduce states defined by \ensuremath{\Vert}\ensuremath{\alpha},m〉=${\mathit{a}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathit{m}}$\ensuremath{\Vert}\ensuremath{\alpha}〉 up to a normalization constant, where \ensuremath{\Vert}\ensuremath{\alpha}〉 is a coherent state and m an integer. We study the mathematical and physical properties of such states. We demonstrate phase squeezing and the sub-Poissonian character of the fields in such states. We study in detail the quasiprobability distributions and the distribution of the field quadrature. We also show how such states can be produced in nonlinear processes in cavities.
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.
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.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.