Condensates in annuli: dimensionality of the variance

Abstract

Static and dynamic properties of Bose-Einstein condensates in annular traps are investigated by solving the many-boson Schrödinger equation numerically accurately using the multiconfigurational time-dependent Hartree for bosons method. We concentrate on weakly-interacting bosons exhibiting low depletion. Analysis of the mean-field position variance, which accounts for the shape of the density only, and the many-body position variance, which incorporates a tiny amount of excitations through the reduced two-particle density matrix, shows that the former behaves essentially as a quasi-one-dimensional quantity whereas the latter as a two-dimensional quantity. This brings another dimension to the physics of bosons in ring-shaped traps.

GRAPHICAL ABSTRACT

Keywords:

• Bose-Einstein condensates
• density
• variance
• dimensionality
• MCTDHB

PACS numbers:

• 03.75.Kk
• 67.85.De
• 03.75.Hh
• 67.85.Bc
• 03.65.-w

Acknowledgments

This paper is dedicated to Professor Nimrod Moiseyev, $\stackrel{>}{\mathrm{N}}$imrod, a dear friend for long time and my advisor, on the occasion of his 70th birthday. We thank Raphael Beinke, Sudip Haldar, Lorenz Cederbaum, Kaspar Sakmann, Shachar Klaiman, and Alexej Streltsov for discussions. Computation time on the BwForCluster and the Cray XC40 system Hazelhen at the High Performance Computing Center Stuttgart (HLRS) is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the Israel Science Foundation (Grant No. 600/15).