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arXiv:physics/0005014 · Physical Review A

Multifrequency evaporative cooling to Bose-Einstein condensation in a high magnetic field

Vincent Boyer, S. Murdoch, Yann Le Coq, Guillaume Delannoy, Philippe Bouyer, Alain Aspect

Published Jul 5, 2000• 5 citations
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Abstract

We demonstrate a way to circumvent the interruption of evaporative cooling observed at high bias field for ${}^{87}\mathrm{Rb}$ atoms trapped in the $(F=2,m=+2)$ ground state. Our scheme uses a three-frequency rf knife achieved by mixing two rf frequencies. This compensates part of the nonlinearity of the Zeeman effect, allowing us to achieve Bose-Einstein condensation where the standard one-frequency rf knife evaporation method did not work. We are able to get efficient evaporative cooling, provided that the residual detuning between the transition and the rf frequencies is smaller than the power broadening of the rf transitions at the end of the evaporation ramp.

DOI
10.1103/physreva.62.021601

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Laser Physics•Jan 1, 2004•0 citations
We demonstrate a way to circumvent the interruption of evaporative cooling observed at high bias field for 87Rb{}^{87}\mathrm{Rb}87Rb atoms trapped in the (F=2,m=+2)(F=2,m=+2)(F=2,m=+2) ground state. Our scheme uses a three-frequency rf knife achieved by mixing two rf frequencies. This compensates part of the nonlinearity of the Zeeman effect, allowing us to achieve Bose-Einstein condensation where the standard one-frequency rf knife evaporation method did not work. We are able to get efficient evaporative cooling, provided that the residual detuning between the transition and the rf frequencies is smaller than the power broadening of the rf transitions at the end of the evaporation ramp.
Radio-frequency-induced evaporative cooling of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in the F=2,F=2,F=2, m=2m=2m=2 ground state in a magnetic trap with a high bias field is found to be hampered, and eventually interrupted, by the presence of nonlinear Zeeman shifts. An experiment studying evaporation at a fixed adjustable rf frequency was used to illustrate this effect. These nonlinear shifts prevent us from reaching quantum degeneracy in the F=2,F=2,F=2, m=2m=2m=2 ground state; however, evaporation in the F=1,F=1,F=1, $m=\ensuremath{-}1$ ground state is not adversely affected, and we can produce a Bose-Einstein condensate (BEC). Our analysis shows that this effect can play a role in many BEC experiments.
We demonstrate direct evaporative cooling of 87{}^{87}87Rb atoms confined in a dimple trap produced by an atom chip. By changing the two chip currents and two external bias fields, we show theoretically that the trap depth can be lowered in a controlled way with no change in the trap frequencies or the value of the field at the trap center. Experimentally, we maximized the decrease in trap depth by allowing some loosening of the trap. In total, we reduced the trap depth by a factor of 20. The geometric mean of the trap frequencies was reduced by less than a factor of 6. The measured phase-space density in the final two stages increased by more than two orders of magnitude, and we estimate an increase of four orders of magnitude over the entire sequence. A subsequent rf evaporative sweep of only a few megahertz produced Bose-Einstein condensates. We also produce condensates in which raising the trap bottom pushes hotter atoms into an rf ``knife'' operating at a fixed frequency of 5 MHz.
We study the optimization of evaporative cooling in trapped bosonic atoms on the basis of quantum kinetic theory of a Bose gas. The optimized cooling trajectory for 87Rb{}^{87}\mathrm{Rb}87Rb atoms indicates that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against loss of trapped atoms caused by three-body recombination. The number of condensed atoms is largely enhanced by the optimization, more than two orders of magnitude in our present calculation using relevant experimental parameters, as compared with the typical value given by the conventional evaporative cooling where the frequency of radio-frequency magnetic field is swept exponentially. In addition to this optimized cooling, it is also shown that highly efficient evaporative cooling can be achieved by an initial exponential and then a rapid linear sweep of frequency.
We demonstrate novel methods for exciting the collective oscillations of Bose–Einstein condensates without directly deforming the confinement potential. The collective excitations were induced through the radio-frequency (rf) forced evaporative cooling of 87 Rb atoms confined in a magnetic trap. We studied two methods, the first involving a sinusoidal amplitude modulation of the rf field, and the other a fast sweep of the rf frequency, both performed during evaporation. An almost-pure low-energy quadrupole oscillation mode was observed with both methods. In the case of the rf-amplitude modulation (fast rf-frequency sweep), the collective excitations are likely to be induced by the periodic (bulk) emission of atoms from the trap. We also observed substantial loss of atoms from the trap when the rf amplitude was modulated with a frequency near the axial-trap frequency. This allows a precise determination of the magnetic-trap frequency.
We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.
The dynamics of evaporative cooling of magnetically trapped 87 Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. The theoretical optimization of the cooling trajectory clarifies that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against serious three-body recombination loss. The number of condensed atoms is expected to be largely enhanced by the optimization as compared with the typical value produced by the conventional evaporative cooling, where the frequency of the radio-frequency magnetic field is swept exponentially. Next, we precisely examine how the growth of a condensate depends on the experimental parameters of evaporative cooling in this inefficient exponential-sweep cooling. We find that, due to large nonlinear three-body loss, the number of condensed atoms finally becomes insensitive to the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. This result opens up the experimental possibility that the final number of condensed atoms can be well stabilized against the shot-to-shot fluctuations of experimental conditions in evaporative cooling.