Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state

We study the Hong–Mandel higher-order squeezing of both quadrature components for an arbitrary 2n^th-order (n ≠1) considering the most general Hermitian operator, X_θ = X₁ cos θ + iX₂ sin θ, in the superposed state, |Ψ〉 = K [|Ψ₀) + re^iϕ |0〉] of the orthogonal even coherent state and vacuum state. Here | Ψ₀〉 = K[|α, +〉 + |iα, +〉] is the orthogonal coherent state, |α, +〉 = K′[|α) + | – α〉] and |iα, +〉 = K″ [|iα, +〉 + | – iα, +〉] are even coherent states, operators X_1,2 are defined by X₁ + iX₂ = a, a is the annihilation operator, α, θ, r and ϕ are arbitrary parameters and the only restriction on these is the normalization condition of the superposed state |Ψ〉. We find that maximum simultaneous 2n^th-order Hong–Mandel squeezing of both quadrature components X_θ and X_θ+π/2 exhibited by the orthogonal even coherent state enhances in its superposition with vacuum state. We conclude that the values of higher-order momenta in the superposed state become much closer to the best minimum values of the corresponding values of higher-order momenta explored numerically so far than that obtained in orthogonal even coherent state. Variations of 2n^th-order squeezing for n = 2,3 and 4, i.e. fourth, sixth and eighth-order squeezing with different parameters have also been discussed.