Dynamic equation for evaporative cooling of trapped atoms in microgravity

In this paper, to investigate how atoms evaporate and cool in microgravity environments of the space station, we have developed the dynamic equation for evaporative cooling of trapped atoms and obtained the analytical expression of atomic temperature with respect to trapping laser parameters and gravitational acceleration. In our model, the evaporation of atoms is equivalent to applying a damping force to the trapped atoms, and the evaporative cooling process of trapped atoms is comprehended as the damped oscillation of trapped atoms in the optical dipole traps. By introducing the gravity in our model, we obtained the analytical model of temperature variation with gravity after cooling, and the theoretical results agree well with the evaporation experiment of rubidium-87 atoms on the ground. Our theoretical results show that, compared with the atomic evaporative cooling experiment on the ground, the microgravity environment of the space station can achieve cooler atomic gases when the losses of atoms, such as the one-body loss caused by background-gas collisions and the three-body recombination loss caused by interatomic inelastic collisions, can be ignored.

Figure 1

A schematic illustration of the experimental setup for the rubidium-87 atom Bose-Einstein condensate (BEC) experiment. The optical dipole traps consist of two crossed laser beams with an angle of ${60}^{\circ }$. The left and right ion pumps prepare the vacuum pressure of the science chamber and two-dimensional magneto-optical trap (2D-MOT) chamber at $3\times {10}^{-9}$ and $1\times {10}^{-7}\mathrm{Pa}$, respectively.

Figure 2

Here, ${\mathrm{U}}_0$ is the trap depth without gravity, ${\mathrm{w}}_0$ is the beam waist of the trapping laser. The trap potential $\mathrm{U}$ without gravity (red, dashed), including gravity (green solid), and the pure gravitational potential (blue, dash-dotted line) at $x=y=0$.

Figure 3

(a) Temperature vs evaporation time $t$ and (b) trap frequency during the evaporation process. Here, blue circles represent the experimental results on the ground ($\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$), the black dashed line and red solid line represent the theoretical result of $\mathrm{g}=0$ and $9.8\mathrm{m}/{\mathrm{s}}^2$, respectively.

Figure 4

The temperature $T$ as a function of (a) evaporation time $t$ and (b) trap frequency during the evaporative cooling process with different gravitational acceleration conditions.