From single-particle excitations to sound waves in a box-trapped atomic Bose-Einstein condensate

We experimentally and theoretically investigate the lowest-lying axial excitation of an atomic Bose-Einstein condensate in a cylindrical box trap. By tuning the atomic density, we observe how the nature of the mode changes from a single-particle excitation (in the low-density limit) to a sound wave (in the high-density limit). Throughout this crossover the measured mode frequency agrees with Bogoliubov theory. Using approximate low-energy models we show that the evolution of the mode frequency is directly related to the interaction-induced shape changes of the condensate and the excitation. Finally, if we create a large-amplitude excitation, and then let the system evolve freely, we observe that the mode amplitude decays nonexponentially in time; this nonlinear behavior is indicative of interactions between the elementary excitations, but remains to be quantitatively understood.This work was supported by EPSRC (Grants No. EP/N011759/1 and No. EP/P009565/1), ERC (QBox), AFOSR, and ARO. N.N. acknowledges support from Trinity College (Cambridge) and the David and Lucile Packard Foundation. R.L. acknowledges support from the E.U. Marie-Curie program (Grant No. MSCA-IF-2015 704832) and Churchill College, Cambridge. R.P.S. acknowledges support from the Royal Societ