Phase properties of displaced number states

Phase properties of the displaced number states are studied. Exact analytical formulae describing phase distributions based on different phase approaches are obtained and illustrated graphically. It is shown that the Pegg-Barnett phase distribution P( theta ) and the phase distribution Pw( theta ) associated with the Wigner function are very close to each other, while the phase distribution PQ( theta ) associated with the Q function carries less phase information. The results have clear interpretation in terms of the area of overlap in phase space.