Maximum simultaneous squeezing and antibunching in superposed coherent states

Maximum simultaneous squeezing and antibunching in the superposition states, ψ =Z1α +Z2β , of two coherent states α and β , where Z1,Z2,α,β are complex numbers, is studied for the case α+β α−β. We show that the maximum squeezing for the operator Xθ=X1 cos θ+X2 sin θ, where Hermitian operator X1,2 are defined by X1+iX2=a, the annihilation operator and θ is the argument of (α+β), with the minimum value 0.11077 of ψ(ΔXθ)2ψ and maximum antibunching with the minimum value −0.55692 of Mandelʹs Q parameter occur for an infinite combinations with α−β=1.59912 exp[±i(π/2)+iθ], θ=arg(α+β) and Z1/Z2=exp(α*β−αβ*) and with α+β α−β