Non-linear wave packet dynamics of coherent states of various symmetry groups

J Banerji,G S Agarwal

doi:10.1364/oe.5.000220

Abstract

We present a comparative study of the non-linear wave packet dynamics of two-mode coherent states of the Heisenberg-Weyl group, the SU(1,1) group and the SU(2) group under the action of a model anharmonic Hamiltonian. In each case, we find certain generic signatures of non-linear evolution such as quick onset of decoherence followed by Schrödinger cat formation and revival. We also report important differences in the evolution of coherent states belonging to different symmetry groups.

Highlights

The quantum phenomena of revival and fractional revival have been studied in many diverse systems and situations such as Rydberg atoms [1, 2, 3], the Jaynes-Cummings model [4], light propagation in Kerr media [5, 6] and even transient signals from multilevel quantum systems [7]
The literature deals mostly with systems whose energy spectrum depends on a single quantum number with an associated revival time scale
We focus on the non-linear wavepacket dynamics of coherent states under the action of a generic two-mode Hamiltonian

Summary

Introduction

The quantum phenomena of revival and fractional revival (or the formation of Schrodinger cat and cat-like states) have been studied in many diverse systems and situations such as Rydberg atoms [1, 2, 3], the Jaynes-Cummings model [4], light propagation in Kerr media [5, 6] and even transient signals from multilevel quantum systems [7]. The literature deals mostly with systems whose energy spectrum depends on a single quantum number with an associated revival time scale. There are many systems whose energy levels depend non-linearly on at least two quantum numbers [8, 9, 10]. We focus on the non-linear wavepacket dynamics of coherent states under the action of a generic two-mode Hamiltonian. For example, the much studied pair [11] and Perelomov [12, 13, 14] coherent states belong to the SU(1,1) group and are special cases of what may be called generalized SU(1,1) coherent states [10]. Our objective is to present a comparative study of how coherent states of various symmetry groups evolve under the action of the same two-mode generic Hamiltonian. Through a series of pictures and movies, we show how the initial coherent structure is lost due to quantum dephasing and regained later on to form spectacular and varied quasi-coherent structures leading up to the formation of Schrodinger cats in some cases and to full revival in all cases

Coherent states

Wave packet dynamics

Conclusion