Enhancement of the Hong-Mandel higher-order squeezing and amplitude odd-power squeezing in even coherent state by its superposition with vacuum state

We study the Hong-Mandel 2n th-order squeezing of the Hermitian operator, X_θ ≡ X₁cosθ + X₂sinθ and amplitude n th-power squeezing of the Hermitian operator, Y_θ^{(n)} ≡ Y₁^{(n)}cosθ + Y₂^{(n)}sinθ in superposed state |ψ⟩ = K[|α,+⟩ + re^{iφ}|0⟩], of vacuum state and even coherent state defined by |α,+⟩ = K_+[|α⟩+|-α⟩]. Here operators X_{1,2} are defined by X₁ + iX₂ = a, operators Y_{1,2}^{(n)} are defined by Y₁^{(n)} + iY₂^{(n)} = aⁿ, a is the annihilation operator, α, θ, r and φ are arbitrary and the only restriction on these is the normalization condition of the superposed state. We show that the Hong-Mandel 2n th-order squeezing and amplitude odd-power squeezing exhibited by even coherent state enhance in its superposition with vacuum state. Variations of these higher-orders squeezing with different parameters near its maxima have also been discussed.