Fourth-order squeezing in superposed coherent states

We study the fourth-order squeezing in the most general case of superposition of two coherent states by considering <psi(DeltaX(theta))(4)\psi> where X-theta = X-1 cos theta + X-2 sin theta, X-1 + iX(2) = a is annihilation operator, theta is real, \psi> Z(1) \alpha> + Z(2) \beta>, \alpha> and \beta> are coherent states and Z(1), Z(2), alpha, beta are complex numbers. We find the absolute minimum value 0.050693 for an infinite combinations with alpha - beta = 1.30848 exp[+/-i(pi/2) + itheta], Z(1)/Z(2) = exp(alpha*beta - alphabeta*) with arbitrary values of alpha + beta and theta. For this minimum value of <psi\(DeltaXtheta)(4)\psi>, the expectation value of photon number can vary from the minimum value 0.36084 (for alpha + beta = 0) to infinity. We note that the variation of <psi\(DeltaX(theta))(4)\psi> near the absolute minimum is less flat when the expectation value of photon number is larger. Thus the fourth-order squeezing can be observed at large intensities also, but settings of the parameters become more demanding.