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 not equal 1) considering the most general Hermitian operator, X-theta = X-1 cos theta + iX(2) sin theta, in the superposed state, |Psi > = K [|Psi(0)) + re(i phi) |0 >] of the orthogonal even coherent state and vacuum state. Here | Psi(0)> = K[|alpha, +> + |i alpha, +>] is the orthogonal coherent state, |alpha, +> = K '[|alpha) + | - alpha >] and |i alpha, +> = K '' [|i alpha, +> + | - i alpha, +>] are even coherent states, operators X-1,X-2 are defined by X-1 + iX(2) = a, a is the annihilation operator, alpha, theta, r and phi are arbitrary parameters and the only restriction on these is the normalization condition of the superposed state |Psi >. We find that maximum simultaneous 2n(th)-order Hong-Mandel squeezing of both quadrature components X-theta and X theta+pi/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.