# Magneto-Optical Traps for Cold Atomic Gravimetry: Research Status and Development Trends
## 1 Introduction  
Gravity sensors can be used to detect any underground object that creates a difference in mass. This can help analyze geological formations and locate buried infrastructure. While technologies such as ground-penetrating radar can do this, they must send a signal underground and they are active technologies, which limits their measurement depth. The advantage of gravity measurement is that it is passive and does not require a signal to be sent underground, so the ground does not attenuate the signal. As long as the signal generated by the object at the surface is strong enough, it can be detected. In theory, there is no limit to the measurement depth. Laser interferometric gravimeters measure gravity using the free fall of an angular cone; their measurement accuracy is restricted by the optical diffraction limit. Cold atomic gravimeters (CAGs) using the interference of cold atoms, without mechanical wear and tear, do not require periodic calibration. The measurement speed is faster, and long-term continuous measurements can be achieved. The long-term precision of the atom gravimeters in a seismic station is better than 2 \(\mu\)Gal (1 \(\mu\)Gal = \(10^{-8}\)m/s\({}^{2}\)), which is comparable to the best classical gravimeter FG-5(X). The measurement sensitivity has already reached 38 \(\mu\)Gal/\(\sqrt{\rm Hz}\) with the potential for improvement [1]. CAGs are widely used for precise measurement due to their high sensitivity and accuracy. They have made outstanding contributions to geological monitoring [2; 3], metrological studies [4; 5], and fundamental physics research [6; 7] in recent years. They have also improved the accuracy of inertial navigation [8; 9]. High-precision gravity measurements are required for underwater gravity navigation. In the underwater navigation of submarines, conventional sonar technology cannot receive a signal in deep water. High-precision gravity maps of the seafloor can be used to help the submarine quickly locate and avoid obstacles on the seafloor. CAG uses cold atoms as measuring media. During the operation of a CAG, atoms are first cooled and trapped under the control of a magnetic and optical field. Then, the magnetic field is turned off and the trapped cold atomic cluster is allowed to fall freely or thrown vertically. The atoms are prepared to the magnetic field's insensitive state \(m_{F}=0\)At the first moment, t = 0, a \(\pi\)/2 pulse is applied to the atomic cluster, which is distributed from the ground state \(|a,\textbf{P}\rangle\) to the excited states of \(|a,\textbf{P}\rangle\) and \(|b,\textbf{P}+\mathrm{h}\mathbf{k_{eff}}\rangle\). The two clusters of split atoms have different momentums and evolve freely along different paths. The phase of the laser is transferred to the atoms. At time t = T, a \(\pi\) pulse is applied to the atomic cluster, and the atomic cluster on the two states reverses, as shown in Figure 1. At time t = 2T, another \(\pi\)/2 pulse is applied to the atomic cluster. A beam combination occurs to the atomic wave packet; interference happens due to the presence of phase difference. The fluorescence signal of atoms is probed to calculate the probability of distribution of the atom at different energy levels. The probability that atoms in the ground state energy level is \(P=(1-\cos\Delta\phi)/2\). The phase difference \(\Delta\Phi\) arises from the phase transfer of photons and atoms \(\Delta\Phi_{\mathrm{laser}}\) and the difference in the path of the free evolution of the atoms \(\Delta\Phi_{\mathrm{evolution}}\) under the effect of gravity. The phase difference satisfies the equation \(\Delta\Phi=(k_{\mathrm{eff}}\,g-2\pi\alpha)T^{2}\). \(K_{eff}\) is the effective laser wave vector. T is the time interval between two adjacent Raman laser pulse beams. \(\alpha\) is the scanning chirp rate. The frequency of Raman leap is chirped and scanned to compensate for the Doppler shift. When the Doppler shift is compensated, the cold atoms resonate with the Raman laser.