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 2 n th-order squeezing of the Hermitian operator, X-theta equivalent to X-1 cos theta + X-2 sin theta and amplitude nth-power squeezing of the Hermitian operator, Y-theta((n)) = Y-1((n)) cos theta + Y-2((n)) sin theta in superposed state vertical bar psi > = K[vertical bar alpha, +> + rei phi vertical bar 0 >], of vacuum state and even coherent state defined by vertical bar alpha, +> = K+[vertical bar alpha > + vertical bar -alpha >]. Here operators X-1,X-2 are defined by X-1 + i X-2 = a, operators Y-1,2((n)) are defined by Y-1((n)) + i Y-2((n)) = a n, a is the annihilation operator, alpha, theta, r and phi are arbitrary and the only restriction on these is the normalization condition of the superposed state. We show that the Hong-Mandel 2 n 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.