Optically trapped ultracold atoms in optical lattices are important physical systems for conducting quantum computing, quantum simulation, and quantum precision measurement. The study of ultracold atoms in optical lattices serves as a bridge connecting the microscopic world and macroscopic condensed matter. It can be used to simulate strongly correlated quantum many-body systems, gauge fields, and novel topological quantum states. In these experiments, the depth of the optical lattice is a key parameter for regulating interaction strength and energy level structure. It directly affects the dynamical properties of atoms in the optical lattice, including Bloch oscillations, tunneling effects, and quantum phase transitions. Therefore, high-precision calibration of the optical lattice trap depth is crucial for achieving precise quantum control of ultracold atom systems.

We propose a high-precision methodology for calibrating the trap depth of optical lattices based on the principle of multiple-pulse Kapitza?Dirac (KD) diffraction. Accurate calibration of the optical lattice depth is achieved by measuring the high diffraction efficiency of the first-order momentum state of atoms within the optical lattice. To validate the effectiveness of this method, a comprehensive comparison is made with single-pulse KD diffraction, Raman?Nath (RN) diffraction, and parametric oscillation heating. In the experimental process, Bose?Einstein condensation (BEC) of ⁸⁷Rb atoms is initially realized using a crossed optical dipole trap. The atoms are then loaded into a one-dimensional optical lattice under various experimental conditions. Finally, the diffraction distribution of the atoms is observed in momentum space using time-of-flight expansion imaging. By carefully analyzing their dynamic behaviors, the depth of the optical lattice is precisely determined.

The multiple-pulse KD diffraction method proposed in this paper utilizes the interference effect produced by a multiple-pulse optical lattice sequence to enhance the diffraction resolution of atoms, thereby improving the accuracy of calibrating the depth of the optical lattice. A comprehensive and systematic measurement of the experimental process is performed for lattice depth calibration, and the practicality and limitations of the four methods—multiple-pulse KD diffraction, single-pulse KD diffraction, RN diffraction, and parametric oscillation heating—are analyzed. The optical lattice depths obtained using the single-pulse and multiple-pulse KD diffraction methods maintain a high degree of linearity with the detection voltage over the entire range, and these two methods are applicable to a wide range of depths and time intervals. However, the single-pulse KD diffraction method determines the depth of the optical lattice through the fitting of experimental data, which requires collecting a large amount of data. This fitting process introduces potential errors and increases the complexity of the measurement. In the multiple-pulse KD diffraction method, the transmission fidelity of diffraction orders is highly sensitive to the lattice depth, and no data fitting is required during the measurement process, which ensures highly accurate calibration of the optical lattice depth. When the laser interaction time is long, the optical lattice depth measured by the RN diffraction method is consistent with the first two methods. However, as the interaction time between the optical lattice and the atoms increases, the diffraction process must account for changes in atomic momentum, and thus the optical lattice depth obtained by this method may have deviations from the true value. The parametric oscillation heating method can be used for optical lattices of different depths and is effective within a wide parameter range. However, at low depths, the wide energy band of the optical lattice increases the frequency range of atomic loss due to resonant heating, which affects the determination of the resonant frequency and further increases measurement error.

Through the analysis of the experimental results, we assess the practicality and limitations of the four trap depth measurement methods. RN diffraction is suitable for cases with short interaction time between the optical lattice and the atoms, and its core mechanism is phase modulation based on the momentum state. When the optical lattice interaction time becomes longer, the momentum change becomes significant, which leads to the breakdown of the diffraction mode approximation. The KD diffraction method has the advantage of a broad range of applicability in both time and depth. It can accurately describe multi-stage diffraction phenomena and remains effective even at high depths. Compared to the single-pulse method, the multiple-pulse KD diffraction method is based on the interference effect. By applying a series of pre-set optical lattice pulses, all atoms are transferred to the first-order diffraction momentum state. Compared to RN diffraction and the single-pulse KD diffraction method, this approach improves the intensity and resolution of the diffraction signal, thereby enhancing the accuracy of depth measurements. Furthermore, it has a broad range of applicability in both time and depth. The advantage of the parametric oscillation heating method is its direct detection of the lattice band structure and calibration through the relationship between band transition frequency and depth. However, at low depths, the frequency range of atomic loss caused by resonance heating increases, which can affect the determination of the resonance frequency. The multiple-pulse KD diffraction method enhances lattice depth measurement accuracy. Therefore, this method is expected to provide a technical reference for optical lattice quantum precision measurements and quantum regulation.