相位作为光学晶格中玻色-爱因斯坦凝体的波函数中的重要参数, 在实验中无法通过吸收成像或者原位成像从动量空间原子分布中直接得到波函数的相位信息。为了研究一维光晶格中玻色-爱因斯坦凝体相位分布对动量空间原子分布的影响, 建立了深度学习网络模型。首先, 通过理论计算得到的32 000组数据作为训练集和验证集。然后, 在分析波函数的相位特征与动量空间的基础上, 提出卷积循环神经网络模型进行光晶格中超冷原子动量预测的方法。经验证, 模型训练得到的结果与理论求解薛定谔方程得到的结果相差1.76, 相较BP (Back Propagation)神经网络结果, 平均误差降低了83%, 所得结论为机器学习在物理学领域的应用提供了新的思路。

Phase information is an important parameter in the wave function of a Bose-Einstein condensate in an optical lattice. However, in experiments, the phase information of the wave function cannot be obtained directly from the atom distribution in momentum space by absorption imaging or in-situ imaging. Thus, a deep learning network model was developed to study the influence of the phase distribution of a Bose-Einstein condensate on the atom distribution in momentum space. Thirty-two thousand data sets obtained by theoretical calculations were used as training and verification sets. Based on the analysis of the phase characteristics and momentum space of the wave function, a method for predicting the momentum of supercooled atoms in an optical lattice was developed using a convolutional recurrent neural network model. After the model verification, a difference between the model training and Schrodinger equation results is 1.76, which is 83% less than the average error of a back propagation neural network. Our approach provides a new application of machine learning in the field of physics.