Simultaneous higher-order Hong–Mandel's squeezing and higher-order sub-Poissonian photon statistics in superposed coherent states

We study maximum simultaneous 2n  th-order Hong and Mandel's squeezing of the most general the Hermitian operator, Xθ≡X1cosθ+X2sinθXθ≡X1cosθ+X2sinθ, and nth-order sub-Poissonian photon statistics (connected with expectation value of 2n  th power of number fluctuation), in the most general superposition state, |ψ〉=Z1|α〉+Z2|β〉ψ=Z1α+Z2β of two coherent states |α〉α and |β〉β. Here Hermitian operators X1,2 are defined by X1 + iX2 = a, the annihilation operator, complex numbers Z1,2, α, β are all arbitrary and the only restriction on these is the normalization condition of the state. We find a linear relationship between these two non-classical effects when the angle θ = arg(α + β  ) and |α+β|≫|α−β|α+β≫α−β. We show that maximum simultaneous 2nth-order Hong and Mandel's squeezing for the operator Xθ and n  th-order sub-Poissonian photon statistics in the state occur for an infinite combinations with α−β=A2nexp[±i(1/2)π+iθ]α−β=A2nexp±i1/2π+iθ; A2nA2n is a constant which depends on the order of squeezing, Z2/Z1=exp[(1/2)(βα*−β*α)]Z2/Z1=exp1/2(βα*−β*α) and with θ = arg(α + β  ) and |α+β|≫|α−β|α+β≫α−β. We also illustrate analytically and numerically by an example that both effects occur simultaneously for high-intensity field but for observation of such effects, sensitive settings of the parameters are required.