Squeezed states, photon-number distributions, and U(1) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(1)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(1) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.