Determining the Momentum Width of a Trapped Bose-Einstein Condensate by One-Dimensional-Optical-Lattice Pulse Sequences

We experimentally measured the ultra-narrow momentum width of an optical trapped Bose-Einstein condensate (BEC) in situ based on matter-wave interference, which validates our previous theoretical work [arXiv: 2205.02416]. By sweeping the interval of double stand-wave pulses, the BEC wave packet was splitted into different diffraction orders and then we counted the oscillation curve of the population of zero-momentum state to calibrate the momentum width. Compared with our simplified theory, we observed an accelerated evolution of interference fringes in time-domain. We evaluated this interference process minutely by numerically calculating the Gross-Pitaevskii equation and using Wigner function to intuitively demonstrate the influence of the external potential and nonlinear term. We confirmed that the reduction of interference fringe evolution period actually originates from the synergistic cooperation of the mean-field interaction of the BEC and spatial density modulation caused by the interference between different momentum states. Our approach could be generalized to other ultra-cold atomic gases with different momentum distributions, and in principle a single shot can obtain the result. This quantum thermometry is particularly suitable for momentum width calibration in practical deep cooling experiments, while for atomic samples at pK level the mean-field interaction can be safely ignored.