Far from equilibrium dynamics of a 2D ultracold Bose gas in an harmonic trap : dynamical symmetry and breathers

Jérôme Beugnon
Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL, Sorbonne Université

We study experimentally the dynamics of a cold gas of particles confined in a single plane. We prepare uniformly-filled clouds with different shapes (disk, squares, triangles) and monitor the time evolution of their density profile when applying an isotropic harmonic confinement. We operate in a regime where the gas is well described by a classical field whose evolution is given by the Gross-Pitaevskii (GP) equation. We show that the presence of a dynamical symmetry, described by the SO(2,1) group, leads to conserved quantities in the time evolution and allows us to relate different experimental situations by a scaling transform. Suprisingly, we also observe, for specific shapes, time periodic solutions of the GP equation, that we identify as breathers. Reference : arXiv:1903:04528