Breakdown of the Kohn theorem near a Feshbach resonance in a magnetic trap

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We study the collective excitation frequencies of a harmonically trapped ${}^{85}$Rb Bose-Einstein condensate (BEC) in the vicinity of a Feshbach resonance. To this end, we solve the underlying Gross-Pitaevskii (GP) equation by using a Gaussian variational approach and obtain the coupled set of ordinary differential equations for the widths and the center of mass of the condensate. A linearization shows that the dipole-mode frequency decreases when the bias magnetic field approaches the Feshbach resonance, so the Kohn theorem is violated.