Bose-Einstein condensation of 7Li has been studied in a magnetically trapped gas. Because of the effectively attractive interactions between 7Li atoms, many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms. We observe the condensate number to be limited to a maximum value between 650 and 1300 atoms. The measurements were made using a versatile phase-contrast imaging technique. We discuss our measurements, the current theoretical understanding of BEC in a gas with attractive interactions, and future experiments we hope to perform.
Bose-Einstein condensation (BEC) in ultra-cold magnetically-trapped
sp7Li vapor was experimentally observed and quantitative measurements of condensate number were made. Compared to other BEC experiments, lithium is unique due to its negative s-wave scattering length, corresponding to effectively attractive interactions. Due to this attraction, condensates are expected to undergo mechanical collapse if the condensate number exceeds a critical value. In this experiment, an upper limit of about 1000 condensate atoms is found, in agreement with theoretical predictions.\nIn the experiment, the atoms are confined by a set of six permanent magnets in the Ioffe configuration. Optical forces are used to slow and guide atoms from a thermal atomic beam into the magnetic trap. With about
10sp8 atoms loaded into the trap, the vapor is laser-cooled to near 200
muK and then evaporatively cooled by application of a resonantly-tuned microwave field. Evaporative cooling produces a million-fold increase in phase-space density, reaching quantum-degenerate conditions with about 10
sp5 atoms at temperatures near 300
muK. After cooling, the trapped atom distribution is observed by in situ imaging via an optical probe. Calculated atom distributions are fit to the image data.\nIn initial data, the imaging resolution was insufficient to see the spatially-narrow condensate peak, but as phase-space densities approached the expected phase transition, the images suddenly became distorted. Initial fits to the data suggested as many as 10
sp5 condensate atoms, in strong disagreement with theoretical predictions. An imaging model, accounting for imperfections in the imaging optics, shows that the sudden appearance of the distortions is a consequence of BEC, and that these distortions led to the initial over-estimation of cloud phase-space density and condensate number.\nImproved imaging was obtained using large probe detunings, a Phase-Contrast Polarization Imaging (PCPI) technique, and near-diffraction-limited imaging optics. The PCPI method exploits the birefringence of the trapped atoms. From the resulting images, quantitative estimates of condensate number are obtained and compared with theory.
The occupation number of a magnetically trapped Bose-Einstein condensate is limited for atoms with attractive interactions. It has been predicted that, as this limit is approached, the condensate will collapse by a collective process. The measured spread in condensate number for samples of
7Li atoms undergoing thermal equilibration is consistent with the occurrence of such collapses.
Bose-Einstein condensation (BEC) of 7Li has been investigated. Because the effective interaction between 7Li atoms is attractive, the condensate occupation number N 0 is limited to ∼ 1250 atoms, and when this limit is exceeded, the condensate becomes unstable with respect to mechanical collapse. The interplay of this limit and the natural growth of the condensate during BEC leads to complicated dynamical behavior, which has been studied both theoretically and experimentally. It has been modeled by solving the quantum Boltzmann equation, in conjunction with results from the nonlinear Schrodinger equation. It is found that N0 oscillates rapidly as the condensate alternately fills and collapses, and that the oscillations can persist for many cycles before the gas comes to equilibrium. Experimental evidence for these oscillations was obtained by repeatedly producing a condensate and measuring N 0. The results were seen to vary randomly from one measurement to the next, which is to be expected as the timing of the oscillations is intrinsically stochastic. The distribution of N0 values occurring was measured, and provides quantitative information on the condensate growth and collapse. The equilibration process itself was also observed, by quenching the gas into degeneracy and observing its relaxation.\nIn order to carry out these experiments, sensitive measurement and analysis techniques were developed which enabled N0 to be determined in situ with an accuracy of +/-20% and a precision of +/-60 atoms. The theoretical tools used to study quantum degenerate gases were also applied to the important experimental technique of evaporative cooling, which led to substantial optimization and improvements. As part of this study, the rate constant for dipolar relaxation was measured to be 1.05 +/- 0.1 x 10-14 cm3/s, in agreement with theoretical predictions.
Evidence for Bose-Einstein condensation of a gas of spin-polarized
7Li atoms is reported. Atoms confined to a permanent-magnet trap are laser cooled to 200 \ensuremath{\mu}K and are then evaporatively cooled to lower temperatures. Phase-space densities consistent with quantum degeneracy are measured for temperatures in the range of 100 to 400 nK. At these high phase-space densities, diffraction of a probe laser beam is observed. Modeling shows that this diffraction is a sensitive indicator of the presence of a spatially localized condensate. Although measurements of the number of condensate atoms have not been performed, the measured phase-space densities are consistent with a majority of the atoms being in the condensate, for total trap numbers as high as $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms. For
7Li, the spin-triplet
s-wave scattering length is known to be negative, corresponding to an attractive interatomic interaction. Previously, Bose-Einstein condensation was predicted not to occur in such a system.
The nature of Bose-Einstein condensation (BEC) in atomic vapours depends critically on the mean-field interaction of the atoms. When this interaction is attractive, the number of atoms in the condensate is limited. The interplay of this limit and the natural growth of the condensate during BEC leads to complicated dynamical behaviour. We develop a model for this behaviour based on the nonlinear Schrödinger equation and the quantum Boltzmann equation. The condensate occupation number is predicted to oscillate rapidly as the condensate alternately fills and collapses, and the oscillations are seen to persist for many cycles before the gas comes to equilibrium. Experimental evidence for these oscillations in the case of 7 Li is presented, along with details of the experimental apparatus and methods.