Abstract
We study coherent dynamics of two interacting Bose-Bose droplets by means of the extended Gross-Pitaevskii equation. The relative motion of the droplets couples to the phases of their components. The dynamics can be understood in terms of the evolution of zero-energy modes recovering symmetries spontaneously broken by the mean-field solution. These are translational symmetry and two U(1) symmetries, associated with the phases of the droplets' two components. A phase-dependent interaction potential and double Josephson-junction equations are introduced to explain the observed variety of different scenarios of collision. We show that the evolution of the droplets is a macroscopic manifestation of the hidden dynamics of their phases. The occurrence of nondissipative drag between the two supercurrents (Andreev-Bashkin effect) is mentioned.
Highlights
Quantum droplets are self-bound objects formed by ultracold atoms
The dynamics can be understood in terms of the evolution of zero-energy modes recovering symmetries spontaneously broken by the mean-field solution
IV we find an expression for the interaction potential between two separate quantum droplets overlapping with their tails
Summary
Quantum droplets are self-bound objects formed by ultracold atoms. Despite having densities about eight orders of magnitude smaller than air they behave like liquids. Our approach is based on numerical integration of the extended Gross-Pitaevskii (eGP) equations supported by analysis of equations of motion for zero-energy (Goldstone) modes of the system These twocomponent Josephson-junction equations allow for deeper understanding of the observed dynamics. We predict a host of different possible scenarios during the droplets’ approach This includes in particular a coherent transfer of atoms in the form of direct or alternating Josephson currents, which. The equations allow us to find effective simplified dynamics of a collision of interacting droplets in terms of their relative positions and velocities, coupled to their relative phases and Josephson currents. VI we present results of time-dependent numerical simulations of collisions for small and large droplets assuming different initial phases of the droplets These simulations are compared to predictions of the Josephson-junction model which allows for a clear physical picture of the observed dynamics.
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