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/k2, 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.
Highlights
Efficient evaporation is obtained when the ratio η of the trap depth U to the thermal energy kBT is large
When inelastic processes are not important, the large value of η assures that evaporating atoms carry away a large amount of energy compared to the average thermal energy, assuring high efficiency, i.e., a large fraction of the initial atom number remains when degeneracy is achieved
⌽ Institute of Physics fixed large ratio η of the trap depth to the average thermal energy, we find that atom loss is reduced and high efficiency is achieved in Fermi gases which have small inelastic losses
Summary
We begin by reviewing the scaling laws. The optical trapping potential can be written generally as. For evaporative cooling from the classical regime to degeneracy, we can take the total energy to be that of a classical gas in a harmonic potential, E = 3NkBT For a fixed value of η, the mean square cloud size in the trap does not change This follows from the scaling of the total energy, which is six times the potential energy for one direction, x, i.e., E = 3NMωx x2 trap. We assume a harmonic approximation to a gaussian trap, where the trapping potential takes the form U(t)(1 − exp(−2x2/ax2)) Mωx2(t) x2/2, and for the y-direction, with ax the trap field 1/e radius in the x-direction, i.e., the intensity 1/e2 radius Both the energy E = 3NkBT = 3NU/η and the spring constant Mωx2 = 4U/ax are proportional to U.
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