Squeezing in superposed coherent states

We study squeezing in the most general case of superposition of two coherent states by considering 〈ψ|(ΔXθ)2|ψ〉 where Xθ=X1cosθ+X2sinθ,X1+iX2=a is annihilation operator, θ is real, |ψ〉=Z1|α〉+Z2|β〉, |α〉 and |β〉 are coherent states and Z1,Z2,α,β are complex numbers. We find the absolute minimum value 0.11077 for infinite combinations with α−β=1.59912exp[±i(π/2)+iθ], Z1/Z2=exp(α∗β−αβ∗) with arbitrary values of α+β and θ. For this minimum value of 〈ψ|(ΔX0)2|ψ〉, the expectation value of photon number can vary from the minimum value 0.36084 (for α+β=0) to infinity. We note that the variation of 〈ψ|(ΔXθ)2|ψ〉 near the absolute minimum is less flat when the expectation value of photon number is larger. Thus squeezing can be observed at large intensities also, but settings of the parameters become more demanding.