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

A two-photon transition is used to convert an arbitrary fraction of the ${}^{87}\mathrm{Rb}$ atoms in a $|{F=1,m}_f=-1\mathrm{}〉$ condensate to the $|{F=2,m}_f=1\mathrm{}〉$ 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, $a_{|1,-1〉}{/a}_{|2,1〉}=1.062\mathrm{}\left(12\right)$.