Fig. 1. (a) Experimental setup of atomic deep cooling, consisting of rubidium atom source, precooling chamber, science chamber, ion pump, and titanium sublimation pump. (b) Rubidium 87 D₂ transition hyperfine structure, with frequency of each functional light during the laser cooling of atoms.

Fig. 2. Schematic diagram of the optical path of the experimental system. Fiber lasers 1 to 5 are 1064 nm fiber lasers. The waist width of fiber laser beams 1 and 2 is 80 µm, and the cross optical trap formed is a tightly combined trap. The width of fiber laser beams 3 and 4 is 300 µm, and the cross optical trap formed is loosely confined trap. Fiber laser 5 forms a standing wave under the adjustment of the opposite mirror. The momentum filtering pulse (fiber laser 5) and imaging light (fiber laser 6) share the same light path through the dichroic mirror.

Fig. 3. Schematic diagram of the physical process of cooling atoms in the experiment with momentum filtering. (a) Standing-wave pulse sequence with momentum filtering cooling effect, pulse width τ_p = 1.65 µs, pulse time interval τ_interval = N · T_Talbot/2 (N = 1, 3, 5…). (b) After the first pulse, an atomic cloud around 0ℏk is scattered to the momentum state of ±2nℏk (n = 0, 1, 2…); after the second pulse, atoms are scattered back to the initial momentum state. Atoms with high temperatures are removed from the cloud, resulting in colder atoms. (c) Experimental images of atoms corresponding to the momentum filtering process.

Fig. 4. (a) Temperature of atomic clouds at different momentum filtering pulse intervals. (b) Number of atoms at different pulse intervals. For both (a) and (b), T on the horizontal axis represents T_Talbot, and initial denotes the BEC state before performing momentum filtering. Blue symbols are the experimental results of momentum filtering implemented after evaporative cooling of the first stage tightly confined optical dipole trap. Red symbols show the experimental results of momentum filtering implemented after two-stage cooling.

Fig. 5. Experimental results of the combination of two-stage cooling and momentum filtering with the pulse interval of 3T_Talbot/2 at different TOFs: (a) temperature of atomic cloud, (b) number of atoms, (c) size of atomic cloud, and (d) images of BEC.