Accurate Calculation of the Height of Cold Atoms Throw-Up

After the laser trapping and cooling, the cold atoms in a cesium fountain clock undergo a short period of upward acceleration and uniform motion due to the frequency detuning of the upward and the downward lasers. Then, with the cooling laser shut down, the cold atoms keep going up to the apex under the gravity and then fall down to the detection area to be detected by the detection laser. The height of cold atoms throw-up is the distance from the MOT center to the apex. Previous calculations ignored the acceleration and uniform upward movement of the cold atoms, resulting in a systematic error. This paper corrects for the error by considering three different movement processes of the cold atoms and accurately calculates the height of the cold atoms throw-up from the experimental data of the time-of-flight signal.