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New Journal of Physics

Evaporative cooling of unitary Fermi gas mixtures in optical traps

Le Luo, Bason E. Clancy, J Joseph, Joseph M. Kinast, Andrei V. Turlapov, John E. Thomas

Published Sep 27, 2006• 49 citations
Publisher

Abstract

We measure the scaling laws for the number of atoms and the cloud size as a function of trap depth for evaporative cooling of a unitary Fermi gas in an optical trap. A unitary Fermi gas comprises a trapped mixture of atoms in two hyperfine states which is tuned to a collisional (Feshbach) resonance using a bias magnetic field. Near resonance, the zero energy s-wave scattering length diverges, and the s-wave scattering cross-section is limited by unitarity to be 4π/ k 2 , where k is the relative wavevector of the colliding particles. In this case, the collision cross-section for evaporation scales inversely with the trap depth, enabling runaway evaporation under certain conditions. We demonstrate high evaporation efficiency, which is achieved by maintaining a high ratio η of trap depth to thermal energy as the trap depth is lowered. We derive and demonstrate a trap lowering curve which maintains η constant for a unitary gas. This evaporation curve yields a quantum degenerate sample from a classical gas in a fraction of a second, with only a factor of three loss in atom number.

DOI
10.1088/1367-2630/8/9/213

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We measure the scaling laws for the number of atoms and the cloud size as a function of trap depth for evaporative cooling of a unitary Fermi gas in an optical trap. A unitary Fermi gas comprises a trapped mixture of atoms in two hyperfine states which is tuned to a collisional (Feshbach) resonance using a bias magnetic field. Near resonance, the zero energy s-wave scattering length diverges, and the s-wave scattering cross-section is limited by unitarity to be 4π/ k 2 , where k is the relative wavevector of the colliding particles. In this case, the collision cross-section for evaporation scales inversely with the trap depth, enabling runaway evaporation under certain conditions. We demonstrate high evaporation efficiency, which is achieved by maintaining a high ratio η of trap depth to thermal energy as the trap depth is lowered. We derive and demonstrate a trap lowering curve which maintains η constant for a unitary gas. This evaporation curve yields a quantum degenerate sample from a classical gas in a fraction of a second, with only a factor of three loss in atom number.
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. 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 present a rapid evaporative cooling scheme for a strongly interacting 6Li^{6}\mathrm{Li}6Li Fermi gas in an optical dipole trap. The method uses a magnetic-field-gradient--induced tilt of the trapping potential to accelerate cooling in the unitarity-limited regime. In evaporation based only on lowering the optical trap depth, the unitarity-limited scattering cross section can support runaway cooling; however, the cooling rate slows around T/TF≃0.5T/T_F \simeq 0.5T/TF​≃0.5, and the runaway behavior is no longer maintained. We improve on this approach by applying a magnetic-field gradient when the gas temperature reaches about half the Fermi temperature. The induced tilt opens an escape channel for energetic atoms while keeping the trap frequencies nearly unchanged. This modification increases the cooling speed and cools the gas below the superfluid transition temperature, reaching T/TF=0.16T/T_F = 0.16T/TF​=0.16 on a timescale of ∼25 ms\sim 25\,\mathrm{ms}∼25ms. Our results provide a simple and robust route for rapidly cooling a strongly interacting Fermi gas into the superfluid regime, facilitating studies of the physics of unitary Fermi superfluids.
The low-temperature unitary Bose gas is a fundamental paradigm in few-body and many-body physics, attracting wide theoretical and experimental interest. Here, we present experiments performed with unitary 133Cs and 7Li atoms in two different setups, which enable quantitative comparison of the three-body recombination rate in the low-temperature domain. We develop a theoretical model that describes the dynamic competition between two-body evaporation and three-body recombination in a harmonically trapped unitary atomic gas above the condensation temperature. We identify a universal "magic" trap depth where, within some parameter range, evaporative cooling is balanced by recombination heating and the gas temperature stays constant. Our model is developed for the usual three-dimensional evaporation regime as well as the two-dimensional evaporation case, and it fully supports our experimental findings. Combined 133Cs and 7Li experimental data allow investigations of loss dynamics over 2 orders of magnitude in temperature and 4 orders of magnitude in three-body loss rate. We confirm the 1/T2 temperature universality law. In particular, we measure, for the first time, the Efimov inelasticity parameter η*=0.098(7) for the 47.8-G d-wave Feshbach resonance in 133Cs. Our result supports the universal loss dynamics of trapped unitary Bose gases up to a single parameter η*.
Optical traps provide tight confinement and very long storage times for atomic gases. Using a single focused beam from a CO2 laser, we confine a mixture of spin-up and spin-down fermionic 6Li atoms, achieving storage times of ten minutes, and evaporative cooling to quantum degeneracy in seconds. A bias magnetic field tunes the gas to a collisional (Feshbach) resonance, producing extremely strong spin-pairing. This system now tests current many-body predictions for high-temperature superconductors, universal interactions in neutron stars, and hydrodynamic flow of quark-gluon plasmas, a state of matter that existed microseconds after the Big Bang.
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.