## 2 Single-Atom Magnetic Optical Trap
When there is only one atom in the MOT, the output voltage of the pulse counter keeps at 3.8 V, the quadrupole magnetic field gradient stays at 232 Gauss/cm. When there is no atom in the MOT, the output voltage of the pulse counter varies between 1.50 V 1.79 V and let the loading rate of the MOT goes up. Under this circumstance, the output current of the power supply goes down automatically and the quadrupole magnetic field gradient change between 103 Gauss/cm and 116 Gauss/cm. For multi-atom condition, the output voltage of the pulse counter rises, and the loading rate of the MOT descends. On this occasion, the output current of the power supply rises and the quadrupole magnetic field gradient changes between 273 Gauss/cm and 316 Gauss/cm, and the atom number in the MOT cuts down. Figure 3 shows the probability of the single-atom in the MOT in the cases of trigger loop off or on respectively. The power of the 852-nm MOT cooling laser is 150 \(\upmu\)W, and the power of the 894-nm repumping laser is 50 \(\upmu\)W. When the trigger loop is off, the loading rate of the single-atom is merely 28.4%, and the 2 atoms loading rate reaches up to 56.8%. The loading rate of single-atom rises to 80.2% when the trigger loop is on, and the multi-atom rate declines sharply. Figure 1: Loading curve of the magneto-optical trap (MOT). The MOT is empty when the quadrupole magnetic field is turned off. After the quadrupole magnetic field is turned on, atoms are gradually loaded into the MOT. The typical time constant of the MOT is 5.81 \(\pm\) 0.14 s, and the corresponding pressure in the Cs vapor cell is approximately \(6\times 10^{-7}\) Pa.  
Figure 3: The loading probability of single-atom in the MOT. The trigger loop can suppress the probability of multi-atom in the MOT and improve the probability of single-atom. (**a,b**) When the trigger loop turned off, the loading probability of single-atom in the MOT within 300 s is only 28.4%, and the probability of multiple-atom and zero-atom is as high as 71.6%, which is obviously not conducive to the measurement in subsequent experiments. (**c,d**) For the trigger loop on, the probability of single-atom in the MOT increases to 80.2%, while the probability of multi-atom loading is significantly suppressed. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Atom** & **Photon Counts** & **Pulse Counter Analog Output** & **Power Supply** & **Quadrupole Magnetic Field** \\
**Numbers** & **(Count/50 ms)** & **Voltage (V)** & **Output Current (A)** & **Gradient Gauss/cm** \\ \hline - & **Lower** & **Upper** & **Lower** & **Upper** & **Lower** & **Upper** & **Lower** & **Upper** \\ - & **Bound** & **Bound** & **Bound** & **Bound** & **Bound** & **Bound** & **Bound** & **Bound** \\ \hline
0 & 0 & 499 & 1.50 & 1.79 & 7.0 & 7.9 & 103 & 116 \\ \hline
1 & 500 & 600 & 3.80 & 3.80 & 17.3 & 17.3 & 232 & 232 \\ \hline
2 & 601 & 1500 & 4.00 & 4.50 & 18.6 & 20.7 & 273 & 304 \\ \hline
3 & 1501 & 2500 & 4.51 & 4.70 & 20.8 & 21.5 & 306 & 316 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pulse counter and power supply parameter setting. Figure 2: Single-atom loading trigger loop. (**a**) Pulse counter adjusts the output voltage according to different photon counts. We use the output analog voltage to control the output current of power supply and the quadrupole magnetic field gradient. Keys to (a) single-photon counting module (SPCM); insulated gate bipolar transistor (IGBT); (**b**) The trigger loop dynamically changes the loading rate of atoms in the MOT by adjusting the quadrupole magnetic field gradient. We can see in Figure 3 that there is still certain photon-counting while there is no atom in the MOT. This is partly because the cooling and repumping laser hits the glass cell wall with scattering and reflecting, the scattered photons at certain specific angles will enter the fluorescence collection system.