Oscillatory stability of quantum droplets in  -symmetric optical lattice

Abstract We study stability and collisions of quantum droplets (QDs) forming in a binary bosonic condensate trapped in parity-time (   )-symmetric optical lattices. It is found that the stability of QDs in the   -symmetric system depends strongly on the values of the imaginary part W 0 of the   -symmetric optical lattices, self-repulsion strength g , and the condensate norm N . As expected, the   -symmetric QDs are entirely unstable in the broken   -symmetric phase. However, the   -symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken   -symmetric phase. Finally, collisions between   -symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable   -symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.