NUMBER-PHASE UNCERTAINTY PRODUCT FOR GENERALIZED SQUEEZED STATES ARISING FROM THE PEGG-BARNETT HERMITIAN PHASE OPERATOR-FORMALISM

The number-phase uncertainty relation based on the Pegg-Barnett Hermit ian phase operator formalism is discussed for generalized squeezed sta tes of the harmonic oscillator. The corresponding number-phase uncerta inty product is calculated for the magnitudes of the squeeze and displ acement parameters ranging from 0 to 3/2 in the former case and from 0 to 4 in the latter case for the first few classes of generalized sque ezed states (m = 0, 1, and 2) and for different values of their combin ed phases. It is found that for a given magnitude of the squeeze param eter, the number-phase uncertainty product tends to the fixed limiting value m + 1/2 when the magnitude of the displacement parameter tends to infinity. On the other hand, for a fixed magnitude of the displacem ent parameter, the uncertainty product grows indefinitely as the magni tude of the squeeze parameter increases. It is also observed that the number-phase uncertainty product tends to zero for few-photon generali zed squeezed states (when the magnitudes of both squeeze and displacem ent parameters tend to zero) so that, according to the Pegg-Barnett He rmitian phase formalism, it is possible to have generalized squeezed s tates with a number-phase uncertainty product smaller than 1/2.