Coherent Phase States in the Coordinate and Wigner Representations

Abstract

In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the 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 the (non)Gaussianity of CPS are considered.

Keywords

• Robertson–Schrödinger uncertainty relations
• squeezing
• wave functions
• probability density
• Wigner function
• super-Gaussian and sub-Gaussian states