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

We experimentally verified our prior theoretical work [J. Opt. Soc. Am. B 39, 3012 (2022)] by employing matter-wave interference to measure the ultranarrow momentum width of an optically trapped Bose-Einstein condensate (BEC) in situ. Splitting the BEC wave packet into various diffraction orders through double stand-wave pulses, we calibrated the momentum width by fitting the oscillation curve of the population of the zero-momentum state. The observed interference fringes exhibited slight deviations from our simplified theory. We numerically calculated the Gross-Pitaevskii equation and utilized Wigner function to gain insight into the impact of the external trap potential and nonlinear term of BEC. We found that the discrepancy was caused by the combined effects of the mean-field interaction and spatial density modulation of BEC. This quantum thermometry is straightforward to apply and is especially well suited for temperature calibration in deep cooling experiments. For atomic samples at the pK level after deep cooling, interatomic interactions can be safely disregarded, enabling momentum-width calibration in a single shot.