Maximum simultaneous squeezing and antibunching in superposed coherent states

Maximum simultaneous squeezing and antibunching in the superposition states, |ψ〉=Z1|α〉+Z2|β〉, 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=X1cosθ+X2sinθ, 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)2|ψ〉 and maximum antibunching with the minimum value −0.55692 of Mandel's Q parameter occur for an infinite combinations with α−β=1.59912exp[±i(π/2)+iθ], θ=arg(α+β) and Z1/Z2=exp(α∗β−αβ∗) and with |α+β|⪢|α−β|.