Coupling collective modes in a trapped superfluid

Abstract

We consider a superfluid cloud composed of a Bose-Einstein condensate oscillating within a magnetic trap (dipole mode) where, due to the existence of a Feshbach resonance, an effective periodic time-dependent modulation in the scattering length is introduced. Under this condition, collective excitations such as the quadrupole mode can take place. We approach this problem by employing both the Gaussian and the Thomas-Fermi variational Ansätze. The resulting dynamic equations are analyzed by considering both linear approximations and numerical solutions, where we observe coupling between dipole and quadrupole modes. Aspects of this coupling related to the variation of the dipole oscillation amplitude are analyzed. This may be a relevant effect in situations where oscillation in a magnetic field in the presence of a bias field B takes place, and should be considered in the interpretation of experimental results.

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

“…V compares our results with the corresponding findings of Ref. [38]. In addition we discuss two special cases, when the bias magnetic field field approaches the Feshbach resonance and when it is far away from the Feshbach resonance.…”

“…In this paper, we consider a Bose-Einstein condensate confined in a magneto-optical Ioffe-Pritchard trap composed of a cylindrically symmetric harmonic potential with trap anisotropy λ plus a bias [38,39]:…”

“…[38,44,45]. For an axially symmetric trap, this time-dependent ansatz reads (11) where N = (π 3/2 u 2 ρ u z ) −1/2 is a normalization factor, while u ρ,z , z 0 , α ρ,z , and β ρ,z denote time-dependent variational parameters, which represent radial and axial condensate widths, the center-of-mass position, and the corresponding phases.…”

“…It turns out that the heuristic approximation in Ref. [38] is not valid neither on top of the Feshbach resonance, nor far away from it. Finally, in Sec.…”

“…There are also several nonlinear effects including second-and third-harmonic generation of the center-of-mass motion, and a nonlinear mode mixing has been identified. In the more recent work [38], the authors explored a different physical idea by investigating the coupling between dipole and quadrupole modes in the immediate vicinity of a Feshbach resonance. They started by considering a Bose-Einstein condensate in a magneto-optical Ioffe-Pritchard trap [39] with a controlled bias field, where the dipole mode is excited.…”