Atomic wave packet dynamics in finite time-dependent optical lattices

TL;DR

This paper analyzes how atomic wave packets behave in finite, time-dependent optical lattices, revealing their potential to form matter wave cavities with long trapping times and complex collapse-revival dynamics.

Contribution

It provides an analytical framework for understanding transmission and trapping of atomic wave packets in finite, dynamic optical lattices, highlighting their analogy to photonic crystal behavior.

Findings

Wave packets can be trapped between band gaps acting as mirrors.

Long trapping times are achievable in such optical lattice resonators.

Collapse and revival dynamics are demonstrated through numerical simulations.

Abstract

Atomic wave packets in optical lattices which are both spatially finite and time-dependent exhibit many striking similarities with light pulses in photonic crystals. We analytically characterize the transmission properties of such a potential geometry for an ideal gas in terms of a position-dependent band structure. In particular, we find that at specific energies, wave packets at the center of the finite lattice may be enclosed by pairs of band gaps. These act as mirrors between which the atomic wave packet is reflected, thereby effectively yielding a matter wave cavity. We show that long trapping times may be obtained in such a resonator and investigate the collapse and revival dynamics of the atomic wave packet by numerical evaluation of the Schr\"odinger equation.