# Magneto-Optical Traps for Cold Atomic Gravimetry: Research Status and Development Trends
## 2 Working Principle of the MOT  
### Cooling of the Atoms  
A moving atom is subject to the Doppler effect in laser beams. If the atom moves in an opposite direction to that of the beam propagation, the magnitude of this motion is \(kv\); \(v\) is the projection of the atomic velocity in the direction of beam propagation. \(\hbar k\) is the momentum of the photon. F\({}_{1}\) is the force on the atom against the direction of laser propagation; F\({}_{2}\) is the force on the atom with the same direction of laser propagation [22,23]:  
\[\begin{array}{l}F_{1}=-\hbar k\frac{\Gamma}{2}\frac{I/I_{\text{sat}}}{4(\delta +kv)^{2}/I^{2}+(1+2I/I_{\text{sat}})}\\ F_{2}=+\hbar k\frac{\Gamma}{2}\frac{I/I_{\text{sat}}}{4(\delta-kv)^{2}/I^{2}+(1 +2I/I_{\text{sat}})}\end{array} \tag{1}\]  
As can be seen in the above equation, the laser has a decelerating effect on moving atoms only when the direction of the atomic motion goes against the direction of the beam, and the laser frequency is tuned below the atomic resonance frequency. In one-dimensional Doppler cooling, the cooling force is generally achieved by using two separate laser beams. As shown in Figure 1, each beam of intensity \(I\) exerts a force on the atom, and the combined force on the atom is \(F\).  
\[F=F_{1}+F_{2} \tag{2}\]  
\(I\) is laser intensity; \(I_{sat}\) is saturation laser intensity; \(\Gamma\) is the natural line width, and \(\delta\) is the detuning. Figure 2 shows that near \(\
u=0\), the combined force on the atom varies linearly with velocity. When the direction of the incident laser is the same as the direction of the motion of the atom with velocity magnitude \(\
u\), the laser detuning felt by the atom is \(\delta+kv\), and when the direction of the incident laser beam goes against the direction of motion of the atom, the laser detuning felt by the atom is \(\delta-kv\). Therefore, if the atom propagates in the opposite direction to the laser beam, the atom can absorb photons into the excited state, but the direction of the radiation pressure of the laser received at this time is goes against the direction of the atom's motion, thus achieving the effect of decelerating the atom and realizing the Doppler cooling process. The best cooling effect can be obtained by choosing an appropriate amount of optical detuning (\(\pm\delta\)) so that the combined force of the radiation pressure on the atom is maximized.  
In 1987, [PERSON] and [PERSON] continued to apply cooling laser beam to keep the atoms in the optical molasses after turning off the gradient magnetic field, and found that the temperature of the atoms obtained from the final confinement was well below the Doppler cooling limit; the result suggested the existence of a polarization gradient cooling mechanism in MOT [24,25]. Considering the multi-energy level structure of the atoms, the final cooling temperature is proportional to the optical shift of the ground state energy level. Increasing laser detuning or decreasing laser power can reduce the optical shift to further decrease the cooling temperature, resulting in sub-Doppler cooling [26].  
Figure 2: The scattering force exerted on an atom by two laser beams with a detuning of \(\delta\).