Coherent phase states in the coordinate and Wigner representations

TL;DR

This paper numerically analyzes coherent phase states (CPS), highlighting their differences from standard coherent states, especially in high-energy regimes, focusing on squeezing properties and uncertainty relations.

Contribution

It introduces a detailed numerical study of CPS, revealing their squeezing behavior and uncertainty properties, which differ from standard coherent states.

Findings

CPS can exhibit strong coordinate or momentum squeezing.

The uncertainty product in CPS increases logarithmically with mean photon number.

CPS show distinct non-Gaussian features compared to standard coherent states.

Abstract

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--Schr\"odinger 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.