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Journal of Physics B Atomic Molecular and Optical Physics

Coherence length for a trapped Bose gas

Stephen Mark Barnett, Sonja Franke‐Arnold, Aidan S. Arnold, C. Baxter

Published Sep 15, 2000• 18 citations
Publisher

Abstract

Abstract. Matter waves can be assigned a coherence length analogous to the corresponding quantity in optics. We show that there is a dramatic increase in coherence length associated with the appearance of Bose–Einstein condensation in a trapped ideal Bose gas. The large increase in coherence length occurs even for temperatures just below the critical temperature at which only a small proportion of the trapped atoms is to be found in the ground state. 1.

DOI
10.1088/0953-4075/33/19/325

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Abstract. Matter waves can be assigned a coherence length analogous to the corresponding quantity in optics. We show that there is a dramatic increase in coherence length associated with the appearance of Bose–Einstein condensation in a trapped ideal Bose gas. The large increase in coherence length occurs even for temperatures just below the critical temperature at which only a small proportion of the trapped atoms is to be found in the ground state. 1.
We study quantum coherence properties of a dilute gas at temperatures above, but not much above, the transition temperature of Bose-Einstein condensation. In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence greater than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a coherently condensed state, some unexplained experimental results [D. E. Miller et al., Phys. Rev. A 71, 043615 (2005)] can be explained.
We present an overview of our recent work describing the treatment of ultracold atomic Bose gases confined to two dimensions in a harmonic trap. We show how the gas goes through a number of regimes as the axially confining potential is increased and discuss the scattering properties of the gas in each of these regimes. We then use the formalism developed to investigate the phase-coherent Bose-Einstein condensate that is present in the trapped two-dimensional gas at temperatures that are low compared to the ideal gas critical temperature and to analyze the first-order coherence as a function of temperature. We identify the regime in which the gas loses its global phase coherence, although a macroscopic occupation of the ground state persists at a temperature well below the ideal gas critical temperature. We comment on the possible connection between this fluctuating regime and the Berezinskii-Kosterlitz-Thouless phase.
We study quantum coherence properties of a dilute gas at temperatures above, but not much above the transition temperature of Bose-Einstein condensation (BEC). In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence more than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a BEC-type state, some unexplained experimental results [Phys. Rev. A, 71, 043615 (2005)] can be explained.
The properties of a trapped ideal Bose gas in n -dimensional space are studied. General analytic expressions of the critical temperature of Bose-Einstein condensation, the jump of heat capacity at and the fraction of condensation at temperatures below have been derived. How these physical quantities depend on the external potential, particle characteristics and space dimensionality are discussed. We find that when a proper external potential is taken, Bose-Einstein condensation may occur in any dimensional space.
The phase transition of Bose-Einstein condensation was studied in the critical regime, where fluctuations extend far beyond the length scale of thermal de Broglie waves. We used matter-wave interference to measure the correlation length of these critical fluctuations as a function of temperature. Observations of the diverging behavior of the correlation length above the critical temperature enabled us to determine the critical exponent of the correlation length for a trapped, weakly interacting Bose gas to be nu = 0.67 +/- 0.13. This measurement has direct implications for the understanding of second-order phase transitions.