Merging and oscillations of dipolar Bose-Einstein condensate droplets

Abstract

We investigate the dynamics of Bose-Einstein condensate droplets composed of $^{164}$Dy atoms formed in a double-well potential following removal of the interwell barrier. By solving the dipolar Gross-Pitaevskii equation, we determine phase diagrams of ground-state configurations as functions of the atom number confined in the double-well potential. For an interwell separation $2d=3\,\mu\mathrm{m}$, we consider the relative dipolar-to-contact interaction strengths $\varepsilon_{dd}=1.4$, $1.45$, and $1.5$. Symmetry-broken lowest-energy configurations are found for $\varepsilon_{dd}=1.5$ and, over a reduced range of atom numbers, for $\varepsilon_{dd}=1.45$, whereas no symmetry-broken states are found for $\varepsilon_{dd}=1.4$ up to $N=5\times10^4$. We analyze the subsequent time evolution after removal of the central barrier, revealing both droplet oscillations and merger events leading to the formation of larger droplets. The oscillations are driven by the external potential and by the repulsive tails of the in-plane component of the dipolar interaction. For the two-droplet states at $\varepsilon_{dd}=1.5$ and $2d=3\,\mu\mathrm{m}$, merging is found for $N=8000$ and $8800$, whereas the droplets remain separated for the investigated cases with $N\geq9000$. Increasing the initial separation to $2d=5\,\mu\mathrm{m}$ shifts the approximate upper atom number for merging to $N\simeq1.65\times10^4$, demonstrating that the crossover is controlled by the competition between the post-quench excess energy and the repulsive inter-droplet barrier.