Efficient rapid production of a Bose-Einstein condensate by overcoming serious three-body loss

We report the efficient production of a large Bose-Einstein condensate in ${}^{87}\mathrm{Rb}$ atoms. This is achieved by quickly reducing the radio frequency of the magnetic field at a rate of $-96.8\mathrm{kHz}∕\mathrm{s}$ during the final stage of evaporative cooling, and we have produced a condensate with $(2.2\pm 0.1)\times {10}^6$ 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.

Figure 1

Time dependence of radio frequency during the final stage of evaporative cooling used in this experiment. The origin of the time scale represents the starting point of the evaporative cooling. The frequency changing rate for each rf sweep is $-96.8\mathrm{kHz}∕\mathrm{s}$ [(A) fast], $-32.3\mathrm{kHz}$ [(B) medium], and $-8.7\mathrm{kHz}∕\mathrm{s}$ [(C) slow], respectively. The drift of the trap minimum is $4.6\mathrm{kHz}∕\mathrm{s}$.

Figure 2

The increase in the number of condensed atoms $N_0$ for the three kinds of rf sweep: (a) experiment and (b) calculation. The experimental (calculated) data of the fast, medium, and slow rf sweeps are represented by the filled circles (solid line), open circles (dotted line), and filled diamonds (dashed line), respectively. The decay rate constants due to the background gas collisions, dipolar relaxation, and three-body recombination adopted in this calculation are $G_1=1∕70{\mathrm{s}}^{-1}$, $G_2=1.0\times {10}^{-15}{\mathrm{cm}}^3∕\mathrm{s}$ (Ref. 26), and $G_3=9.0\times {10}^{-29}{\mathrm{cm}}^6∕\mathrm{s}$ (Ref. [9]), respectively.

Figure 3

Loss rates for the three kinds of rf sweep normalized by the total number of trapped atoms at each time. (A), (B), and (C) represent the fast, medium, and slow rf sweeps, respectively. The solid curves [(A1), (B1), and (C1)] represent the loss rates caused by evaporation and the dashed ones [(A2), (B2), and (C2)] represent those caused by three-body recombination, respectively. $A–T_c$, $B–T_c$, and $C–T_c$ represent the BEC transition point for each rf sweep.