Dynamical Response of a Bose-Einstein Condensate to a Discontinuous Change in Internal State

Abstract

A two-photon transition is used to convert an arbitrary fraction of the ${}^{87}\mathrm{Rb}$ atoms in a $|{F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1〉$ condensate to the $|{F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1〉$ state. Transferring the entire population imposes a discontinuous change on the condensate's mean-field repulsion, which leaves a residual ringing in the condensate width. A calculation based on Gross-Pitaevskii theory agrees well with the observed behavior, and from the comparison we obtain the ratio of the intraspecies scattering lengths for the two states, ${a}_{|1,\ensuremath{-}1〉}{/a}_{|2,1〉}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.062(12)$.