2ND-ORDER SQUEEZED STATES

We examine the generalized squeezed states defined as eigenstates of a linear combination of the lowering and raising operators a(2) and (a( dagger))(2), respectively. This approach is entirely equivalent to the minimum-uncertainty method applied to the amplitude-squared operators . We solve the eigenvalue equation in Glauber's coherent-state represe ntation and find two independent solutions. Their Fock-state expansion s, one containing only even and the other only odd number states, reve al a, strong nonclassical character. We show that the calculation of t he mean photon number is sufficient to obtain the expectation values o f interest. Consequently, photon statistics is investigated in both ca ses by using the generating function of the photon-number distribution . We find the conditions under which the second-order squeezed states display photon antibunching and quadrature squeezing. Also discussed i s the preservation of their amplitude-squared squeezing by linear ampl ification at gains exceeding 2. Analytically, our results are simple f ormulas in terms of Kummer and Gauss hypergeometric functions that all ow straightforward numerical calculations.