# Magneto-Optical Traps for Cold Atomic Gravimetry: Research Status and Development Trends
## 3 Classification and Application of MOTs
### Application of Conventional Six-Beam MOT  
The initial six-beam MOT is realized by six red-detuned polarized laser beams and a gradient magnetic field. A three-dimensional standing wave optical field was created by three pairs of orthogonal laser beams, which converted from a linearly polarized laser to a circularly polarized laser after passing through six quarter-wave plates. A pair of inverse Helmholtz coils, spaced at the coil radius, provided a linear gradient magnetic field to overcome the limitations of [PERSON]'s optical theorem. The center of the magnetic field coincides with the center of the optical field. The magnitude of the magnetic field is 0 at the center of the field and increases linearly in the x, y, and z directions. The first stable six-beam MOT was achieved in 1990 by [PERSON] et al. at the American Institute of Astrophysics [45], with a structure similar to that shown in Figure 3b. I is the current in the coil; the arrow direction indicates the current direction. The MOT trapped about \(1.8\times 10^{7}\) atoms with atomic temperatures down to \(1.1\pm 0.2\mu\)k, the lowest temperature achieved in atomic trap studies at that time. The advantage of the six-beam MOT is that the structure is simple and easy to implement, and the number of captured atoms is relatively stable despite changes in the shape of the atomic clusters. Six-beam MOTs are widely used in CAG because of the high number of cold atoms trapped and the ability to achieve extremely low cooling temperatures.  
In 2013, the dynamic measurement of gravity was achieved with the GAIN gravimeter developed by [PERSON] et al. at Humboldt University in Germany, which used a six-beam MOT.  
Figure 4: Schematic of the time-of-flight method for cold atom temperature measurement.  
The structure of GAIN is shown in Figure 5. K\({}_{1}\) and K\({}_{2}\) are the wave numbers of the Roman transitions. RF is a radio frequency signal. The temperature of the atomic clusters was 2 \(\upmu\)k, and the number of trapped \({}^{87}Rb\) atoms reached 10\({}^{9}\) in 0.6 s. They show the best reported performance of mobile CAG in data, with an accuracy of 3.9 \(\upmu\)Gal and a short-term noise of 9.6 \(\upmu\)Gal/\(\sqrt{\text{Hz}}\)[46; 47].  
The gravimeter designed by [PERSON] et al. at the French Aerospace Laboratory used a six-beam MOT to trap about 10\({}^{6}\) atoms in 20 ms; it obtained cold atomic with a temperature of 1.9 \(\upmu\)k. The group successfully completed gravity dynamics measurements at sea in 2018 under linear and circular navigation conditions. Despite rough sea conditions, they obtained precision below 1 mGal [48]. Airborne gravity dynamics measurements were completed in Iceland in 2020, with an estimated error between 1.7 and 3.9 mGal [49]. In 2021, a six-beam MOT was used in the rubidium atomic absolute gravimeter, which developed by [PERSON] et al. This MOT captured about 10\({}^{8}\) atoms with a cooling temperature of 5 \(\upmu\)k [50].  
Six-beam MOTs are widely used in cold atomic gravimetry; they are capable of trapping more than 10\({}^{7}\) atoms with cooling temperatures in the \(\upmu\)k range, fully meeting the measurement accuracy requirements of atomic gravimetry.