Abstract
Bosons in the form of ultracold alkali-metal atoms can be confined to a one-dimensional (1D) domain by the use of harmonic traps. This motivates the study of the ground-state occupations of effective single-particle states in the theoretical 1D impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The and are the eigenvalues and eigenfunctions, respectively, of the one-body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed i the occupations are asymptotically proportional to in both the circular and harmonically trapped cases.
- Received 5 November 2002
DOI:https://doi.org/10.1103/PhysRevA.67.043607
©2003 American Physical Society