A time frequency analysis of wave packet fractional revivals

TL;DR

This paper demonstrates that time-frequency analysis of the autocorrelation function is more effective than traditional methods for resolving fractional revivals of wave packets, especially when their coherence is short-lived, using Rydberg wave packets as a model.

Contribution

It introduces the use of time-frequency analysis for studying wave packet fractional revivals, showing its advantages over conventional time domain analysis.

Findings

Time-frequency analysis better resolves fractional revivals.

It accurately reconstructs initial wave packet states.

Analytical results agree with numerical simulations.

Abstract

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.