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International Journal of Quantum Information

The generalized pair coherent states and the corresponding entangled coherent states

Won Sang Chung

Published Dec 1, 2015• 0 citations
Publisher

Abstract

In this paper, we consider the generalized Schrödinger cat states. Using these states, we obtain the corresponding quasi-Bell states and the reduced density operator. For these quasi-Bell states, we investigate the non-classical effects such as oscillatory photon statistics, sub-Poissonian property and violation of the Cauchy–Schwarz inequality.

DOI
10.1142/s0219749915500653

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In this paper, we consider the generalized Schrödinger cat states. Using these states, we obtain the corresponding quasi-Bell states and the reduced density operator. For these quasi-Bell states, we investigate the non-classical effects such as oscillatory photon statistics, sub-Poissonian property and violation of the Cauchy–Schwarz inequality.
Canonical coherent states of a quantum harmonic oscillator have been generalized by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight function. Superpositions of these states are considered in the present scenario as a generalization of the optical Schrödinger cat states. The Fock space is assumed to be canonical or finite-dimensional. The photon number distribution of these generalized Schrödinger cat states departs from the Poisson statistics in various ways for high photon numbers. For small nonvanishing values of the label, the photon number distribution is sub-Poissonian (nonclassical) or super-Poissonian, according to the interference properties. In fact, the sub- or super-Poissonian statistics is determined by the interplay between the relative phase and a critical value of the phase. The photon number distribution is uniquely sub-Poissonian for large values of the label.
Nonclassical features of entangled coherent states (two-mode superposition coherent states) based on two coherent states shifted in phase by π/2 are discussed. Analysis of Cauchy–Schwartz inequality, two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. Furthermore, it is also observed that special states have remarkably strong nonclassical properties than the entangled coherent states based on famous even–odd coherent states.
We examine the nonclassical properties of the pair coherent states defined as the simultaneous eigenstates of the operator that annihilates photons in pairs and of the operator that gives the relative occupation number in the two modes. We show that fields in such states have remarkable quantum features such as sub-Poissonian statistics correlations in the number fluctuations, squeezing, and violations of Cauchy–Schwarz inequalities. We show how such pair coherent states can be generated by the competition of different nonlinear processes in a two-photon medium. The quantam features occur not only in the transient domain but also survive in the steady state because of the balance between nonlinear processes.