Dimensional Reduction in Bose-Condensed Alkali-Metal Vapors

TL;DR

This paper explores how strong harmonic confinement causes dimensional reduction in Bose-Einstein condensates, affecting sound velocity and collective oscillations, with implications for understanding quantum gases in lower dimensions.

Contribution

It provides a detailed analysis of dimensional transitions in BECs and links collective oscillation frequencies to dimensionality and interaction types using a variational approach.

Findings

Sound velocity varies with dimensionality transition.

Collective oscillation frequencies depend on interactions and confinement.

Dimensional reduction influences BEC collective dynamics.

Abstract

We investigate the effects of dimensional reduction in atomic Bose-Einstein condensates (BECs) induced by a strong harmonic confinement in the cylindric radial direction or in the cylindric axial direction. The former case corresponds to a transition from 3D to 1D in cigar-shaped BECs, while the latter case corresponds to a transition from 3D to 2D in disc-shaped BECs. We analyze the first sound velocity in axially-homogeneous cigar-shaped BECs and in radially-homogeneous disc-shaped BECs. We consider also the dimensional reduction in a BEC confined by a harmonic potential both in the radial direction and in the axial direction. By using a variational approach, we calculate monopole and quadrupole collective oscillations of the BEC. We find that the frequencies of these collective oscillations are related to the dimensionality and to the repulsive or attractive inter-atomic interaction.