Simultaneous higher-order Hong and Mandel's squeezing of both quadrature components in orthogonal even coherent state

We study higher-order Hong and Mandel's squeezing of both quadrature components for an arbitrary 2nth order (n ≠ 1) considering the most general Hermitian quadrature operator, Xθ = X1 cos θ + X2 sin θ  , in the orthogonal even coherent state defined by |ψ〉=K[|α,+〉+|iα,+〉]ψ=K[α,++iα,+]. Here |α,+〉=K′[|α〉+|−α〉]α,+=K′[α+−α] and |iα,+〉=K″[|iα〉+|−iα〉]iα,+=K″[iα+−iα] are even coherent states, |α〉 is coherent state, α = Aeiθα, K=cosh|α|2/2[cosh|α|2+cos|α|2]K=coshα2/2[coshα2+cosα2], and K′=K″=[2(1+e−2|α|2)]−1/2K′=K″=[2(1+e−2α2)]−1/2. We find that maximum simultaneous 2nth-order Hong and Mandel's squeezing of both quadrature components Xθ and Xθ+π/2 in the state |ψ〉 occurs at θ = θα ± (π/4) for an arbitrary order 2n (n ≠ 1). We conclude that any large amount of higher-order squeezing in the state |ψ〉 can be obtained by choosing suitably a large 2n but in this case minimum values of the 2nth-order moments become less close to the corresponding best minimum values explored numerically so far. Variations of 2nth order squeezing for n = 2, 3 and 4, i.e., for fourth-order, sixth-order and eighth-order squeezing with different parameters have also been discussed.