In recent years, with advancements in cold atom physics and relevant experimental techniques, cold atom interferometry has emerged as an important tool, finding widespread applications in precision measurements and fundamental physics research. Research on high-precision and portable atomic interferometers has become very popular. In precision measurement experiments, the system miniaturization requires the downsizing of the vacuum chamber. A vertical fluorescence scheme for different atomic ground states can cancel the additional detection zones in traditional parallel detection schemes and achieve miniaturization of the vacuum chamber for the interferometers. This detection scheme is based on the sequence detection of atoms in distinctive states, where the atoms absorb energy from the detection beams, resulting in atomic temperature increase and subsequently detection efficiency decrease. Otherwise, the detection noise and the signal-to-noise ratio (SNR) should be evaluated to improve measurement precision. We hope that our scheme can optimize SNR and reduce the main detection noise.

Our study is based on sequence fluorescence detection, and the noise sources include the shot noise, the circuit noise, the intensity, and the frequency noise of the detection beams. Compared to traditional parallel detection schemes, the vertical detection scheme is greatly affected by shot noise. In this scheme, the atoms in the F=2 state and the total atoms are detected sequentially. The proportion of F=2 atoms in the total number of atoms is employed to represent the signal. This method is called normalized detection, whose application can reduce the shot noise in the signal. Furthermore, based on theoretical analysis, adjusting various parameters of the detection beams can minimize the detection shot noise, thereby optimizing SNR. Specifically, the atoms absorb energy from the detection beams, causing atomic temperature increase and subsequently detection efficiency degradation. Additionally, due to the presence of detuning in the detection beams, the sequence detection may result in the occurrence of non-closed transitions, which enhances the shot noise during the detection process. Our study evaluates the influence of detection beam frequency and duration.

The scan of the detection frequency after the first detection pulse is applied is shown in Fig. 2. With the detection time extended to 0.5 ms, the resonance spectrum obtained from the scan splits from a Gaussian-type resonance peak into two distinct peaks. An additional sideband can be observed as the vertically polarized vertical detection beams interact with the atoms, forming 1D molasses. Additionally, the resonance frequency shifts approximately 2 MHz compared to the resonance frequency during 0.5 ms detection duration. This requires shortening the duration of the detection beams to optimize the signal. On the other side, for the detection process, the fluctuation in the number of atoms falling into the dark state is also a major shot noise source. The influence of such fluctuations on the SNR can be assessed by theoretical calculations. When the detection duration is longer than the minimum detection duration, an optimized SNR is achieved. In the experiment, the standard deviation of detection is measured, and an optimal range of detection duration exists. Additionally, conducting detection within this range can achieve optimized detection results.

Generally, we provide a basic framework for a vertical detection scheme, utilizing fluorescence detection with detection beams in the vertical direction. Traditional detection schemes require two horizontal probe beams, necessitating additional areas and windows within the vacuum chamber for state detection of atoms, which is not conducive to the miniaturization of the atomic interferometer system as a whole. By adopting this vertical scheme, we successfully reduce the volume of the vacuum chamber and eliminate the extra detection areas provided by traditional horizontal detection schemes. We optimize the detection sequence, shorten the detection time, and achieve a normalized standard deviation of 0.014. Furthermore, our study measures the ratio of atoms participating in the cyclic transition in the experiment, and the SNR calculation helps us estimate the noise caused by non-closed transitions during the detection. Under the application of sequential detection in the experiment, fluctuations in the SNR are observed when the laser intensity, frequency, and duration change due to the loss caused by atoms participating in non-closed transitions. In this case, the optimal combination of the atomic cycling rate and detection time obtained via analysis reduces shot noise and optimizes the measurement precision. Additionally, eliminating extra noise such as circuit noise and noise caused by changes in the intensity and frequency of the probe beams can enhance the SNR. In future work, we will focus on further improving this detection scheme and exploring its applications in advanced cold atom experiments.