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Quantum Electronics and Laser Science Conference

Modeling the evaporative cooling of fermionic atoms in an optical trap

Kenneth M. O’Hara, S. R. Granade, Michael E. Gehm, M.-S. Chang, John E. Thomas

Published Nov 13, 2002• 3 citations
Publisher

Abstract

Summary form only given. Evaporative cooling of atoms in an optical trap has recently received renewed attention as a means for obtaining degeneracy in an optically trapped bosonic Cs vapor as well as a fermionic Li gas. We have developed a new model describing the evaporative cooling process for atoms confined in a time-dependent optical potential formed by a single focused Gaussian laser beam. We find that a substantial increase in the phase-space density can be obtained by adiabatically reducing the trap laser power and thereby the trap well depth as a function of time. Since we are specifically interested in the evaporative cooling of fermionic /sup 6/Li atoms, we have included the effect of Fermi statistics in the model. Although the collision rate is suppressed as the temperature T is reduced below the Fermi temperature T/sub F/, we find that values of T/T/sub F//spl Lt/1 can be achieved for suitable initial conditions.

DOI
10.1109/qels.2001.962209

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Summary form only given. Evaporative cooling of atoms in an optical trap has recently received renewed attention as a means for obtaining degeneracy in an optically trapped bosonic Cs vapor as well as a fermionic Li gas. We have developed a new model describing the evaporative cooling process for atoms confined in a time-dependent optical potential formed by a single focused Gaussian laser beam. We find that a substantial increase in the phase-space density can be obtained by adiabatically reducing the trap laser power and thereby the trap well depth as a function of time. Since we are specifically interested in the evaporative cooling of fermionic /sup 6/Li atoms, we have included the effect of Fermi statistics in the model. Although the collision rate is suppressed as the temperature T is reduced below the Fermi temperature T/sub F/, we find that values of T/T/sub F//spl Lt/1 can be achieved for suitable initial conditions.
Summary form only given. Cold, dense gases of fermions offer exciting new opportunities for fundamental studies of quantum degeneracy, collective behavior, and superfluidity. Fermionic /sup 6/Li has been the subject of numerous theoretical treatments. This is due in part to its anomalously large and negative triplet scattering length, a/sub T/=-2160 a/sub O/, which arises from a near zero energy resonance. The large scattering length leads to two-state mixtures which are predicted to undergo a transition to a superfluid state at a relatively high temperature. To increase our well depth, we retroreflect the CO/sub 2/ beam which forms our optical trap, nearly doubling the intensity of the trapping field and thus the well depth. We will discuss this technique and its effect on evaporative cooling, and report our progress towards producing a degenerate gas of /sup 6/Li.
We derive scaling laws for the number of atoms, collision rate, and phase-space density as a function of trap depth for evaporative cooling in an adiabadically lowered optical trap. The results are in excellent agreement with a Boltzmann equation model and show that very large increases in phase-space density can be obtained without excessive slowing of the evaporation rate. Predictions are in reasonable agreement with a recent experiment that achieves Bose-Einstein condensation by evaporation in an optical trap. We also discuss evaporation of fermionic mixtures and explain why Pauli blocking does not strongly inhibit cooling.
Summary form only given. We have recently produced a degenerate mixture of the two lowest hyperfine states of fermionic /sup 6/Li in a stable, single-beam CO/sub 2/ laser trap. The trap is loaded from a magneto-optical trap (MOT) at an initial temperature of 150 /spl mu/K. Degeneracy is obtained by forced evaporation, accomplished by continuously lowering the trap depth; the trap is then adiabatically recompressed to full depth. After 60 seconds of forced evaporation, more than 10/sup 5/ atoms remain at temperatures below half of the Fermi temperature. These results are consistent with scaling laws we have derived for the phase-space density as a function of trap depth. This degenerate system is predicted to exhibit a Feshbach resonance at 850 G.
Summary form only given. The last five years has seen an explosive growth in activity in the field of quantum degenerate gases, and there are now many realizations of Bose-Einstein condensation (BEC) of trapped atomic gasses. However, only one experiment has produced a quantum degenerate Fermi gas. The ultimate goal of the experiment discussed here is to achieve a BCS phase transition in a trapped gas of fermionic /sup 6/Li atoms. This requires a phase-space density that is much higher than that needed for BEC, as the temperature must be made much less than the Fermi temperature.BEC in trapped gases has only been achieved using forced evaporative cooling. Since this method depends on elastic collisions, however, it fails for an ultracold Fermi gas, as the Pauli principle forbids s-wave collisions between identical fermions. To circumvent this obstacle, we simultaneously trap a /sup 7/Li-/sup 6/Li mixture, and use rf-induced evaporation to cool /sup 7/Li. /sup 6/Li is then cooled via thermalizing elastic collisions with the /sup 7/Li. The clover-leaf-type magnetic trap is loaded from a two-species magneto-optical trap (MOT).
Summary form only given. Optical dipole traps facilitate storage of atoms independent of their magnetic sub-state. Trapping at high densities is thus not limited by two-body collisions changing the spin state of the atom, which in the particular case of cesium have so far prevented the attainment of Bose-Einstein condensation in magnetic traps. For evaporative cooling of Cs we use the gravito-optical surface trap (GOST) which consists of a horizontal evanescent-wave (EW) atom mirror in combination with a blue-detuned hollow beam (HE) for transverse confinement. Starting conditions for evaporative cooling are prepared by optical cooling, based on inelastic reflections from the EW.
Summary form only given. Recently, we have created a Bose condensate of /sup 87/Rb atoms directly in an optical trap formed by tightly focused laser beams. Following initial loading from a laser cooled gas, evaporative cooling through the BEC transition is achieved by simply lowering the depth of the optical trap. Our success is due in part to a high initial phase space density realized in the loading of our optical dipole trap and in part to the tight confinement of the atoms that permits rapid evaporative cooling to the BEC transition in 2 s.