# Magneto-Optical Traps for Cold Atomic Gravimetry: Research Status and Development Trends
## 2 Working Principle of the MOT
### Trapping of the Atoms  
The trapping of atoms in MOTs is mainly based on the scattering force of the laser. The gradient magnetic field generated by a pair of inverse Helmholtz coils causes the magnitude and direction of the pressure of laser radiation on the atoms to vary with the spatial position, while providing atoms in the coil region with a scattering force directed toward the center of the magnetic field. As shown in Figure 3a, \(\delta\) is laser detuning, \(\delta_{+}\) is positive detuning, and \(\delta_{-}\) is negative detuning. Taking the one-dimensional case as an example, consider a two-energy atom with only one energy level in the ground state(g) and total angular momentum J = 0. There is no Zeeman shift or splitting in the magnetic field. The excited state(e) J = 1 splits into three magneton energy levels \(m_{J}=-1\),0,1 due to the Zeeman effect in a weak magnetic field generated by a pair of inverse Helmholtz coils. The leap of this atom is as follows: \(J=0\to J=1\). The magnetic field is zero at the origin of the coordinates and increases linearly along the axes. The energy level produces a Zeeman shift; the ground state remains unchanged. The excited \(m_{J}=1\) sublevel increases linearly along the coordinate axis and decreases linearly along the negative direction. The opposite is true for the \(m_{J}=-1\) sublevel. There is no change in the m = 0 sublevel. A pair of opposite laser beams of the same intensity, tuned to their frequencies, are negatively detuned for the atoms at z = 0, while the directions of polarization are \(\sigma+\) and \(\sigma-\). The laser frequency at Z > 0 is closer to the leap frequency of \(m_{J}=0\to m_{J}=-1\) due to the Doppler effect, and will absorb more \(\sigma-\) photons. The atom is subjected to a restoring force pointing to the origin of the coordinates. Similarly, the laser frequency at Z < 0 is closer to the leap frequency of \(m_{J}=0\to m_{J}=1\) due to the Doppler effect and will absorb more \(\sigma+\) photons. In summary, atoms that deviate from the center of the magnetic field are subjected to a scattering force directed toward the center, which traps the atoms in the center of the field. The actual alkali metal atoms also have a hyperfine energy level structure in the ground state, but the principle of cooling and trapping atoms is the same.  
To ensure effective interferometric processes in atomic gravimetry applications, the MOT usually needs to capture cold atoms of order \(10^{7}\), and the atomic temperature needs to be reduced to \(\upmu\)k level to achieve good measurement accuracy. The number of cold atoms trapped in MOTs is typically measured by various methods [27], such as fluorescence intensity calculation [28], resonance absorption detection, and fluorescence detection [29; 30]. The fluorescence emitted by the atoms is received by a photomultiplier (PMT). Photocurrent signals are converted into voltage signals by the current-voltage conversion circuit and are finally detected. The fluorescence intensity represents the number of atoms resonantly absorbed by the laser at that frequency. The time-of-flight method [31; 32] is commonly used to measure the temperature of cold atomic clusters. The principle of the time-of-flight  
Figure 3: Trapping of cold atoms: (**a**) is the atomic-level stuffing displacement diagram and (**b**) is the three-dimensional MOT schematic.  
method is to measure the thermal motion of the atoms. The motion of the atoms is closely related to their temperature. After the magnetic field is turned off, the atoms fall freely under the influence of gravity. The cooling temperature as well as the initial velocity distribution can be determined by recording the time they need to reach the detection area. The measurement principle is shown in Figure 4.