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Dynamics of quantum droplets in a one-dimensional optical lattice. (English) Zbl 1450.81079

Summary: 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.

MSC:

81V80 Quantum optics
81V73 Bosonic systems in quantum theory
78A37 Ion traps
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
81U05 \(2\)-body potential quantum scattering theory
35Q40 PDEs in connection with quantum mechanics
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