Squeezing in superposed coherent states

Abstract

We study squeezing in the most general case of superposition of two coherent states by considering 〈 ψ|(Δ X θ ) 2| ψ〉 where X θ=X 1 cos θ+X 2 sin θ, X 1+ iX 2=a is annihilation operator, θ is real, | ψ〉= Z 1| α〉+ Z 2| β〉, | α〉 and | β〉 are coherent states and Z 1, Z 2, α, β are complex numbers. We find the absolute minimum value 0.11077 for infinite combinations with α−β=1.59912 exp[± i(π/2)+ iθ] , Z 1/Z 2= exp(α ∗β−αβ ∗) with arbitrary values of α+ β and θ. For this minimum value of 〈 ψ|(Δ X 0) 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|(Δ X θ ) 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.