Near-Resonant Spatial Images of Confined Bose-Einstein Condensates in a 4-Dee Magnetic Bottle

We present quantitative measurements of the spatial density profile of Bose-Einstein condensates of sodium atoms confined in a 4-Dee magnetic bottle. The condensates are imaged in transmission with near-resonant laser light. We demonstrate that the Thomas-Fermi surface of a condensate can be determined to better than 1%. More generally, we obtain excellent agreement with mean-field theory. We conclude that precision measurements of atomic scattering lengths and interactions between phase-separated cold atoms in a harmonic trap can be performed with high precision using this method. @S1050-2947~98!51707-6# PACS number~s!: 03.75.Fi Recently Bose-Einstein condensates ~BECs! have been created from dilute, ultracold atomic clouds of Rb, Li, and Na @1‐5# through a combination of laser @6# and evaporative cooling @7#. Evidence for condensation in Refs. @1# and @3‐5# rely on time-of-flight measurements on atomic clouds after release from the magnetic traps in which they are initially confined; valuable information on condensate dynamics has been obtained from studying such release data @8#. Alternatively, it is possible to probe confined condensates directly without the transformations associated with release processes. This has been done with dark-field and phase-contrast imaging @9‐11#. In this Rapid Communication, we describe such a capability obtained with near-resonant absorption imaging in a BEC setup based on a 4-Dee magnetic bottle in which we routinely create multimillion atom condensates of sodium atoms. The name ‘‘4-Dee’’ stems from the fact that the shape of each of the four coils needed to create the confining field for spin aligned atoms resembles the letter‘‘D.’’ Figure 1~b! shows the configuration of these coils. We present quantitative in situ spatial images of the condensate surface region and perform detailed comparisons of density profile measurements on pure condensates ~no visible noncondensate component! to ground-state mean-field calculations. These condensates, confined in a harmonic trap and with large numbers of atoms ~Thomas-Fermi limit @12#!, have sharply defined boundaries that can be determined with high precision with near-resonant imaging. Combined with an in