Spatial and Temporal Periodic Density Patterns in Driven Bose-Einstein Condensates

TL;DR

This paper investigates how driven Bose-Einstein condensates form distinct density patterns depending on trap geometry and excitation method, revealing energy redistribution and stability differences between modulation types.

Contribution

It introduces a combined variational and numerical analysis of driven BECs, highlighting geometry-dependent pattern formation and contrasting effects of trap versus interaction modulation.

Findings

Density patterns depend on trap shape: fringes in prolate, rings in oblate.

Energy redistribution correlates with pattern onset.

Trap modulation destabilizes the system faster than interaction modulation.

Abstract

The study of collective excitations is a crucial tool for understanding many-body quantum systems. For instance, they play a central role in the exploration of superfluidity and other quantum macroscopic phenomena in Bose and Fermi systems. In this work we present a variational and a numerical study of a parametrically driven Bose-Einstein condensate confined in a cylindrical harmonic trap in which the aspect ratio can be varied from a prolate (cigar-shaped) to an oblate (pancake-shaped) system. The excitation can be applied by periodically modulating the harmonic frequencies of the trap or, alternatively, the interatomic interaction strength at a frequency that matches that of the system breathing mode. As a result, we observe the formation of dynamical density patterns that depend on the geometry of the trap: a fringe pattern in a prolate system and a ring pattern in an oblate one. By decomposing the total energy into its kinetic, potential, and interaction terms, we show that the onset of these patterns coincides with the redistribution of kinetic energy along the weakly trapped directions of the sample, indicating the three-dimensional nature of the studied phenomena. Finally, our analysis shows that the difference between the two excitation mechanisms lies on the system stability. Modulating the trap destabilizes the system quicker than modulating the interactions, leading to earlier formation of the patterns.