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Physical Review A

Interrupted evaporative cooling of 87Rb atoms trapped in a high magnetic field

Bruno Desruelle, Vincent Boyer, Stuart G. Murdoch, Guillaume Delannoy, Philippe Bouyer, Alain Aspect, Michel Lecrivain

Published Sep 1, 1999• 26 citations
Publisher

Abstract

Radio-frequency-induced evaporative cooling of ${}^{87}\mathrm{Rb}$ atoms in the $F=2,$ $m=2$ 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 $F=2,$ $m=2$ ground state; however, evaporation in the $F=1,$ $m=\ensuremath{-}1$ 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.

DOI
10.1103/physreva.60.r1759

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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−1m=\ensuremath{-}1m=\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 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.
We report the experimental achievement of 87Rb Bose-Einstein condensation in a magnetic trap with microwave and radio frequency (RF) induced evaporation. Evaporative cooling is realized by using 6.8 GHz microwave radiation driving the 87Rb atoms to transit from the ground-state hyperfine state |F = 2,mF =2> to |F = 1,mF = 1>. Compared with RF-induced evaporation, 87Rb atoms are hardly to achieve pure condensate by microwave evaporation cooling due to the effect of atoms in the |F = 1,mF = 1> state being pumped back into the trapping |F = 2,mF = 1> state.
We investigate how the nonlinear Zeeman shift affects the dynamics of rf field-induced evaporative cooling in magnetic traps. We demonstrate for the 87Rb{}^{87}\mathrm{Rb}87Rb F=2F=2F=2 trapping state with wave-packet simulations how the cooling stops when the rf field frequency goes below a certain limit. We examine the applicability of semiclassical models for the strong-field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent 87Rb{}^{87}\mathrm{Rb}87Rb experiment [Phys. Rev. A 60, R1759 (1999)].
We report the experimental achievement of 87 Rb Bose-Einstein condensation in a magnetic trap with microwave and radio frequency (RF) induced evaporation.Evaporative cooling is realized by using 6.8 GHz microwave radiation driving the 87 Rb atoms to transit from the ground-state hyperfine state |F = 2, mF = 2 to |F = 1, mF = 1 .Compared with RF-induced evaporation, 87 Rb atoms are hardly to achieve pure condensate by microwave evaporation cooling due to the effect of atoms in the |F = 1, mF = 1 state being pumped back into the trapping |F = 2, mF = 1 state.
We create Bose-Einstein Condensates of52Cr atoms in an optical trap. Intense radio-frequency fields are used to induce degeneracy between the Zeeman sub-states of the ground state atoms in the BEC despite an ambient static field of 100 mG. We demonstrate this effect by analyzing atom trajectories under the influence of dressed magnetic potentials. We investigate the problem of adiabaticity in the dressing process. In a further set of experiments, we transfer the atoms from the absolute ground state into the excited Zeeman sub-state and study the dipolar relaxation in ultra-cold gases of chromium atoms above and below the condensation threshold. We observe a minimum in the dipolar relaxation rate for a finite magnetic field value which enables a new determination of the scattering length.
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.