Exploring fractional revivals and sub-Planck structures: a walk in phase space with Wigner and Kirkwood

Abstract

The nonlinear evolution of certain quantum systems such as a Gaussian wave packet in an infinite potential well, can lead to fractional revivals of the initial wave packet. Analogously, a coherent state propagating through a Kerr medium can form the so-called Schrödinger cats and cat-like states. Recently, it was shown that a superposition of Schrödinger cats can give rise to sub-Planck structures in the Wigner distribution. The purpose of this review is to introduce and apply, in the above context, a phase space distribution ‘which differs but little from Wigner's and yet, had remained obscure for decades. This is the Kirkwood – Rihaczek (KR) distribution, which has aroused considerable interest in recent years. It is thus appropriate and timely to see how it compares with the Wigner distribution in analysing the above phenomena. Our detailed analysis shows that the KR distribution is just as adequate in explaining these phenomena as the Wigner distribution. Sub-Planck structures are obtained in the KR distribution as well, and despite important differences, the two phase space pictures are comparable.