Finite one-dimensional impenetrable Bose systems: Occupation numbers

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 {lambda}{sub i} of effective single-particle states {phi}{sub i}, in the theoretical 1D impenetrable Bose gas. Bo...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2003-04, Vol.67 (4), Article 043607
Main Authors: Forrester, P. J., Frankel, N. E., Garoni, T. M., Witte, N. S.
Format: Article
Language:English
Subjects:
ALGEBRA
ALKALI METALS
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSE-EINSTEIN CONDENSATION
BOSE-EINSTEIN GAS
BOSONS
DENSITY MATRIX
EIGENFUNCTIONS
EIGENVALUES
GROUND STATES
OCCUPATION NUMBER
ONE-DIMENSIONAL CALCULATIONS
TRAPPING
TRAPS
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Summary: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 {lambda}{sub i} of effective single-particle states {phi}{sub i}, in the theoretical 1D impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The {lambda}{sub i} and {phi}{sub i} 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 {lambda}{sub i} are asymptotically proportional to {radical}(N) in both the circular and harmonically trapped cases.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.67.043607