Higher-order Hong-Mandel's squeezing in superposed coherent states

We study 2nth order Hong and Mandel's squeezing of the Hermitian operator, X-0 X-1 cos theta+X(2)sin theta in the most general superposition state, vertical bar psi > = Z(1)vertical bar alpha > + Z(2)vertical bar beta > of two coherent states vertical bar alpha > and vertical bar beta >. Here operators X-1,X-2 are defined by X-1 + i X-2 = a, the annihilation operator, angle theta and complex numbers Z(1,2) alpha, beta are arbitrary and the only restriction on these is the normalization condition of vertical bar psi >. We find maximum 2nth-order Hong-Mandel squeezing of X-0 in the superposed coherent state vertical bar psi > for an infinite combinations with alpha-beta = A(2n)exp[+/- i1/2 pi + i theta], Z(2)/Z(1) = exp [1/2(beta alpha*-beta*alpha)] and with arbitrary values of (alpha+beta) and theta. Here A(2n) is a constant which depends on the order of squeezing. The maximum percentage of 2nth order Hong-Mandel squeezing and their respective constants A(2n) have been reported for some values of n. We conclude that any large percentage of squeezing can be obtained by suitably choosing of the order 2n. For the order greater than 128 we obtained more than 99% higher-order squeezing at very low intensity of the optical field. Variations of higher-order squeezing with different parameters near its maxima have also been discussed. (C) 2010 Elsevier B.V. All rights reserved.