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arXiv:cond-mat/9911017 · Physical Review A

Evaporative cooling of a two-component degenerate Fermi gas

Murray Holland, Brian DeMarco, D. S. Jin

Published Apr 18, 2000• 113 citations
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Abstract

We derive a quantum theory of evaporative cooling for a degenerate Fermi gas with two constituents and show that the optimum cooling trajectory is influenced significantly by the quantum statistics of the particles. The cooling efficiency is reduced at low temperatures due to Pauli blocking of available final states in each binary collision event. We compare the theoretical optimum trajectory with experimental data on cooling a quantum degenerate cloud of potassium-40, and show that temperatures as low as 0.3 times the Fermi temperature can now be achieved.

DOI
10.1103/physreva.61.053610

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We derive a quantum theory of evaporative cooling for a degenerate Fermi gas with two constituents and show that the optimum cooling trajectory is influenced significantly by the quantum statistics of the particles. The cooling efficiency is reduced at low temperatures due to Pauli blocking of available final states in each binary collision event. We compare the theoretical optimum trajectory with experimental data on cooling a quantum degenerate cloud of potassium-40, and show that temperatures as low as 0.3 times the Fermi temperature can now be achieved.
The evaporative cooling of a two-component mixture of trapped atomic fermions into quantum degeneracy is investigated using the semiclassical Boltzmann equation for fermions. The influence of Fermi blocking for temperatures well below the Fermi temperature is discussed. Comparison between collisional and relaxation rates for a Fermi degenerate gas are made, and the similarities and differences between the cooling kinetics of the Fermi gas mixture and a mixture of classical gases is investigated, and discussed using a simple model. The latter also serves to clarify the processes which terminate the cooling in the quantum degenerate regime. Finally, a brief discussion of mean-field effects is given.
In the quest toward realizing novel quantum matter in ultracold molecular gases, we perform a numerical study of evaporative cooling in ultracold gases of microwave-shielded polar fermionic molecules. Our Monte Carlo simulations incorporate accurate two-body elastic and inelastic scattering cross sections, realistic modeling of the optical dipole trap, and the influence of Pauli blocking at low temperatures. The simulations are benchmarked against data from evaporation studies performed with ultracold NaK molecules, showing excellent agreement. We further explore the prospects for optimizing the evaporation efficiency by varying the ramp rate and duration of the evaporation trajectory. Our simulation shows that it is possible to reach <10<10%<10 of the Fermi temperature under optimal conditions even in the presence of two-body molecular losses.
Fermi statistics suppress the elastic collisions that rethermalize a Fermi gas during evaporative cooling, creating a fundamental low-temperature bottleneck for producing quantum degenerate gases. We show that, for shielded single-component ultracold dipolar molecular Fermi gases in the Wigner threshold regime, this bottleneck is governed by universal threshold laws fixed by the effective dimensionality of the gas. In this regime, Fermi suppression of rethermalization scales quadratically with temperature in 3D but only linearly in 2D. Consequently, the thermalization-to-loss ratio is more favorable in 2D than in 3D, and these results suggest that 2D geometries are better suited for reaching deep degeneracy. We also present ab initio close-coupling calculations that agree well with experimental measurements on Fermi degenerate gases of KRb molecules, supporting our conclusions.
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. Magnetic trapping and evaporative cooling have been employed to cool a million /sup 40/K atoms to below the Fermi temperature, T/sub P/. Simultaneous evaporation of spin-mixed samples is used to overcome the lack of s-wave collisions between spin-polarized fermionic atoms at these ultralow temperatures. By releasing the gas from the magnetic trap and allowing it to expand, the energy and momentum distributions of this quantum degenerate gas were measured. Consistent with Fermi-Dirac (FD) quantum statistics, the total energy in the gas is higher than the classical expectation at the same temperature. Further, the momentum distribution was shown to be non-Gaussian (non-classical) and also congruent with FD statistics.
We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin states of magnetically trapped 40K. The relative Fermi energies are adjusted by controlling the population in each spin state. Thermodynamic measurements reveal a resulting imbalance in the mean energy per particle between the two species, which is a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of 2 reduction in the effective collision cross section in the quantum degenerate regime.