Existence of Long-Range Order for Trapped Interacting Bosons

Abstract

We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.Comment: 4 pages, 1 figure, RevTex4. Title changed at the request of editors; to appear in Phys. Rev. Letter