Self-interfering matter-wave patterns generated by a moving laser obstacle in a two-dimensional Bose-Einstein condensate inside a power trap cut off by box potential boundaries

Abstract

We report the observation of highly energetic self-interfering matter-wave (SIMW) patterns generated by a moving obstacle in a two-dimensional Bose-Einstein condensate (BEC) inside a power trap cut off by hard-wall box potential boundaries. The obstacle initially excites circular dispersive waves radiating away from the center of the trap which are reflected from hard-wall box boundaries at the edges of the trap. The resulting interference between outgoing waves from the center of the trap and reflected waves from the box boundaries institutes, to the best of our knowledge, unprecedented standing wave patterns. For this purpose we simulated the time dependent GrossPitaevskii equation using the split-step Crank-Nicolson method. The obstacle is modelled by a moving impenetrable Gaussian potential barrier. Various trapping geometries are considered.

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

“…This constancy indicates order in ϕ(x, y; t). The largest occupancy is, as expected, for the (0, 0) state and some excitations to higher states with even (n x , n y ) are due to the initialization of the system in CN simulations [74,75]. |C nx,ny (t)| in frame (b) with either n x or n y odd are negligible of order ∼ 10 −9 and are rather noisy.…”

“…The system is a trapped two-dimensional (2D) BEC cut off by a hard-wall box potential (BP) boundary [74,75] and excited by a stirring laser. The external trap varies from harmonic to extremely anharmonic.…”

“…The units and numerics are the same as in our previous work [74,75]; they are reviewed here briefly for reference purposes. G, A, v, β, and t, all have the same units as before [74,75] …”

“…The role played by the hard-wall boundaries is noteworthy as they generate complicated structures in the density patterns of a trapped BEC, including those from the nonlinear Talbot effect [74,78]. These patterns arise from the self-interference of an expanding BEC with reflections coming in from the hard walls.…”

“…In addition, a detailed examination of the effects of different phasespace densities (different laser amplitudes) is still lacking. We therefore revisit our previous systems [74,75] with the same excitation methods and analyze their dynamics from a different perspective.…”