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Physical Review A

Evaporative cooling at low trap depth

Robert deCarvalho, John M. Doyle

Published Nov 18, 2004• 17 citations
Publisher

Abstract

A quantitative, analytic model of evaporative cooling covering both the small- $(<4)$ and large- $(>4)$ $\ensuremath{\eta}$ regimes is presented. $\ensuremath{\eta}$ is the dimensionless parameter defined as the trap depth divided by the temperature of the trapped sample. Although some of the same general properties present at large $\ensuremath{\eta}$ are also present at small $\ensuremath{\eta}$, there are significant quantitative differences. These differences must be taken into account in order to accurately extract from the trapping data quantitative measurements of, for example, collisional atomic cross sections.

DOI
10.1103/physreva.70.053409

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A quantitative, analytic model of evaporative cooling covering both the small- (<4)(<4)(<4) and large- (>4)(>4)(>4) \ensuremathη\ensuremath{\eta}\ensuremathη regimes is presented. \ensuremathη\ensuremath{\eta}\ensuremathη is the dimensionless parameter defined as the trap depth divided by the temperature of the trapped sample. Although some of the same general properties present at large \ensuremathη\ensuremath{\eta}\ensuremathη are also present at small \ensuremathη\ensuremath{\eta}\ensuremathη, there are significant quantitative differences. These differences must be taken into account in order to accurately extract from the trapping data quantitative measurements of, for example, collisional atomic cross sections.
We apply kinetic theory to the problem of evaporative cooling of a dilute collisional gas in a trap. Assuming ``sufficient ergodicity'' (phase-space distribution only a function of energy) and s-wave collisions with an energy-independent cross section, an equation for the evolution of the energy distribution of trapped atoms is derived for arbitrary trap shapes. Numerical integration of this kinetic equation demonstrates that during evaporation the gas is accurately characterized by a Boltzmann distribution of atom energies, truncated at the trap depth. Adopting the assumption of a truncated Boltzmann distribution, closed expressions are obtained for the thermodynamic properties of the gas as well as for the particle and energy loss rates due to evaporation. We give analytical expressions both for power-law traps and for a realistic trapping potential (Ioffe quadrupole trap). As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas. \textcopyright{} 1996 The American Physical Society.
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.
Metastable helium is buffer gas cooled, magnetically trapped, and evaporatively cooled in large numbers. 1011{10}^{11}1011 4He∗^{4}\mathrm{He}^{*}4He∗ atoms are trapped at an initial temperature of 400mK400\phantom{\rule{0.3em}{0ex}}\mathrm{mK}400mK and evaporatively cooled into the ultracold regime, resulting in a cloud of $2\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{9}$ atoms at $1.4\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. Efficient evaporation indicates low collisional loss for 4He∗^{4}\mathrm{He}^{*}4He∗ in both the ultracold and multi-partial-wave regime, in agreement with theory.
We discuss the kinetic theory for evaporative cooling of a dilute collisional gas in a trap. The analysis in O. J. Luiten et al., Phys. Rev. A 53, 381 (1996) is extended to incorporate a time-dependent trap strength and truncation energy. We employ the equations obtained to predict the efficiency of evaporative cooling of sodium atoms in a Ioffe trap and realize that a time-dependent trap strength can be crucial for the cooling. The calculations are classical in the sense that no effects of quantum statistics are taken into account: nevertheless the results of the calculations are useful in order to reveal experimental routes towards a Bose-Einstein condensate of sodium atoms.
Laser cooled sodium atoms are trapped in an optical dipole force trap formed by the intersection of two 1.06 \ensuremath{\mu}m laser beams. Densities as high as $4\ifmmode\times\else\texttimes\fi{}{10}^{12}$ atoms/cm3{\mathrm{m}}^{3}m3 at a temperature of $\ensuremath{\sim}140$ \ensuremath{\mu}K have been obtained in a $\ensuremath{\sim}900$ \ensuremath{\mu}K deep trap. By reducing the trap depth over a 2 s interval, we have evaporatively cooled the atoms to a final temperature of $\ensuremath{\sim}4$ \ensuremath{\mu}K at a density of $6\ifmmode\times\else\texttimes\fi{}{10}^{11}$ atoms/cm3{\mathrm{m}}^{3}m3. This corresponds to a factor of 28 increase in atomic phase-space density.