Coherent phase states in the coordinate and Wigner representations

We study numerically the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying the main attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is, roughly, twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of (non)Gaussianity of CPS are considered.