Dynamics of quantum droplets in a one-dimensional optical lattice

We numerically investigate the dynamics of quantum droplets (QDs) forming in one-dimensional (1D) binary Bose gases held in optical lattice (OL). It is found that the OL potential strongly influence the stability of QDs. We demonstrate that both off-site QDs of ground states for the condensate norm N exceeding a critical value and on-site QDs of ground states regardless of the value of N are completely stable. The unstable off-site QDs of ground states in Guassian-shaped QDs may become stable by increasing the value of the self-interaction strength g. We further study the stability of dipole-model QDs. In contrast to the usual case of propagation in free space, where dipole-model QDs do not exist, we show that Guassian-shaped QDs can support stable dipole-model QDs in the presence of OL. The off-site dipole-model QDs in the large QDs are able to eliminate the decay and become stable by decreasing g to a suitable parametric region. Finally, we deal with the mobility and collision of QDs in OL. It is revealed that OL potential can destroy the slow-moving QDs radiating many linear modes, while the fast-moving QDs may be robust across the OL. Compared with the quasi-elastic collision of Gaussian-shaped QDs in free space, the slowly moving Gaussian-shaped QDs in shallow OL tend to merge after the collision.