Number-phase uncertainty product for generalized squeezed states arising from the Pegg-Barnett Hermitian phase operator formalism
Istok P. Mendaš, Duska B Popovic · Physical Review A · 1995
The number-phase uncertainty relation based on the Pegg-Barnett Hermitian phase operator formalism is discussed for generalized squeezed states of the harmonic oscillator. The corresponding number-phase uncertainty product is calculated for the magnitudes of the squeeze and displacement 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 squeezed states (m=0, 1, and 2) and for different values of their combined phases. It is found that for a given magnitude of the squeeze parameter, 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 displacement parameter, the uncertainty product grows indefinitely as the magnitude of the squeeze parameter increases. It is also observed that the number-phase uncertainty product tends to zero for few-photon generalized squeezed states (when the magnitudes of both squeeze and displacement parameters tend to zero) so that, according to the Pegg-Barnett Hermitian phase formalism, it is possible to have generalized squeezed states with a number-phase uncertainty product smaller than 1/2.