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Physical Review A

Optimized evaporative cooling for sodium Bose-Einstein condensation against three-body loss

Takahiko Shobu, Hironobu Yamaoka, Hiromitsu Imai, Atsuo Morinaga, Makoto Yamashita

Published Sep 20, 2011• 8 citations
Publisher

Abstract

We report on a highly efficient evaporative cooling optimized experimentally. We successfully created sodium Bose-Einstein condensates with 6.4\ifmmode\times\else\texttimes\fi{}10${}^{7}$ atoms starting from 6.6\ifmmode\times\else\texttimes\fi{}10${}^{9}$ thermal atoms trapped in a magnetic trap by employing a fast linear sweep of radio frequency at the final stage of evaporative cooling so as to overcome the serious three-body losses. The experimental results such as the cooling trajectory and the condensate growth quantitatively agree with the numerical simulations of evaporative cooling on the basis of the kinetic theory of a Bose gas carefully taking into account our specific experimental conditions. We further discuss theoretically a possibility of producing large condensates, more than 10${}^{8}$ sodium atoms, by simply increasing the number of initial thermal trapped atoms and the corresponding optimization of evaporative cooling.

DOI
10.1103/physreva.84.033626

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We report on a highly efficient evaporative cooling optimized experimentally. We successfully created sodium Bose-Einstein condensates with 6.4\ifmmode\times\else\texttimes\fi{}107{}^{7}7 atoms starting from 6.6\ifmmode\times\else\texttimes\fi{}109{}^{9}9 thermal atoms trapped in a magnetic trap by employing a fast linear sweep of radio frequency at the final stage of evaporative cooling so as to overcome the serious three-body losses. The experimental results such as the cooling trajectory and the condensate growth quantitatively agree with the numerical simulations of evaporative cooling on the basis of the kinetic theory of a Bose gas carefully taking into account our specific experimental conditions. We further discuss theoretically a possibility of producing large condensates, more than 108{}^{8}8 sodium atoms, by simply increasing the number of initial thermal trapped atoms and the corresponding optimization of evaporative cooling.
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.
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 report the efficient production of a large Bose-Einstein condensate in 87Rb^{87}\mathrm{Rb}87Rb atoms. This is achieved by quickly reducing the radio frequency of the magnetic field at a rate of $\ensuremath{-}96.8\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}∕\mathrm{s}$ during the final stage of evaporative cooling, and we have produced a condensate with $(2.2\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms against a serious three-body recombination loss. We observed the dependence of the cooling efficiency on the rate at which the truncated energy changes by measuring the condensate growth for three kinds of radio-frequency sweep. The experimental results quantitatively agree with calculations based on the quantum kinetic theory of a Bose gas.
We have developed an apparatus for creating Bose–Einstein condensates of sodium atoms. Radio-frequency-induced forced evaporative cooling was studied experimentally and optimized to stably create sodium condensates containing a large number of atoms. The transition temperature, the spatial distribution of the condensate, and the aspect ratio of the Bose–Einstein condensate were analyzed quantitatively and compared with theoretical predictions. Several methods of ramping down the rf for evaporative cooling were tested.
The dynamics of evaporative cooling of magnetically trapped 87Rb{}^{87}\mathrm{Rb}87Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. We carried out the quantitative calculations of the time evolution of conventional evaporative cooling where the frequency of the radio-frequency magnetic field is swept exponentially. This ``exponential-sweep cooling'' is known to become inefficient at the final stage of the cooling process due to a serious three-body recombination loss. We precisely examine how the growth of a Bose-Einstein condensate depends on the experimental parameters of evaporative cooling, such as the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. It is shown that three-body recombination drastically depletes the trapped 87Rb{}^{87}\mathrm{Rb}87Rb atoms as the system approaches the quantum degenerate region and the number of condensed atoms finally becomes insensitive to these experimental parameters. This result indicates that the final number of condensed atoms is well stabilized by a large nonlinear three-body loss against the fluctuations of experimental conditions in evaporative cooling.
We present a combined computational and experimental study to optimize the efficiency of evaporative cooling for atoms in optical dipole traps. By employing a kinetic model of evaporation, we provide a strategy for determining the optimal relation between atom temperature, trap depth, and average trap frequency during evaporation given experimental initial conditions. We then experimentally implement a highly efficient evaporation process in an optical dipole trap, showing excellent agreement between the theory and experiment. This method has allowed the creation of pure Bose-Einstein condensates of 87{}^{87}87Rb with $2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ atoms starting from only $5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms initially loaded in the optical dipole trap, achieving an evaporation efficiency ${\ensuremath{\gamma}}_{\mathrm{eff}}$ of 4.0 during evaporation.