Dynamics of quantum droplets in Bose–Einstein condensates with three-body loss and external feeding

Abstract We consider quantum droplets in Bose–Einstein condensates with three-body recombination and external feeding in a spherically symmetric harmonic trap. A quantum droplet is a self-bound state which arises due to the delicate balance between the mean-field effect and quantum fluctuation. We find effective potentials for flat- and sharp-top droplets and show that the potentials in both cases are minimized for certain values of the width. The width of a droplet oscillates periodically with time and the oscillation amplitude depends sensitively on the initial width of a droplet around the minimum of the effective potential. The maximum width of a droplet decreases gradually with time due to the loss of atoms arising from the three-body recombination. It shows that this loss of atoms can be managed by appropriately feeding the condensate from an external source to generate stable droplets. We examine the stability of a droplet by fixed point analysis and find that the region of stability is affected with the change of external feeding and three-body loss.