A quantitative study of the micromotion of a P-band superfluid in a shaking lattice

The time-of-flight (TOF) momentum distribution of the micromotion of a P-band superfluid is investigated in a frequency-modulated optical lattice. Besides the P-band atoms converted from the S-band atoms, we find a small fraction of atoms are transferred to the D-band which can be revealed by the band mapping images. A p /2 phase lag can also be observed between the two satellite peaks of the D-band atoms and the two main peaks of the P-band superfluid in the oscillating TOF momentum distribution. Meanwhile, by deriving a fitting function for the TOF momentum distribution of the P-band superfluid, we find a large portion of atoms are actually thermalized due to lattice shaking. Based on this result, we introduced a generalized fitting function for the TOF momentum distribution at different time in a shaking cycle. Such a fitting function can roughly fit the experimentally observed oscillating momentum distribution and explain the micromotion of such a P-band superfluid. Thus, our results may deepen the understanding of the micromotion of the P-band superfluid in a frequency-modulated optical lattice.