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

We study 2nth order Hong and Mandel's squeezing of the Hermitian operator, Xθ ≡ X1cosθ + X2sinθ in the most general superposition state, |ψ〉 = Z1|α〉 + Z2|β〉 of two coherent states |α〉 and |β〉. Here operators X1,2 are defined by X1 + i X2 = a, the annihilation operator, angle θ and complex numbers Z1,2 , α, β are arbitrary and the only restriction on these is the normalization condition of |ψ〉. We find maximum 2nth-order Hong–Mandel squeezing of Xθ in the superposed coherent state |ψ〉 for an infinite combinations with α−β=A2nexp±i12π+iθ, Z2/Z1=exp12βα*−β*α and with arbitrary values of (α + β) and θ. Here A2n is a constant which depends on the order of squeezing. The maximum percentage of 2nth order Hong–Mandel squeezing and their respective constants A2n 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.