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arXiv:1005.2493 · Physical Review Letters

Collective Excitations of a Dipolar Bose-Einstein Condensate

G. Bismut, Benjamin Pasquiou, É. Maréchal, P. Pedri, L. Vernac, O. Gorceix, B. Laburthe-Tolra

Published Jul 23, 2010• 75 citations
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Abstract

We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas-Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a Gaussian ansatz.

DOI
10.1103/physrevlett.105.040404

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We propose a scheme for the measurement of the sss-wave scattering length aaa of an atom or molecule with significant dipole-dipole interaction with an accuracy at the percent level. The frequencies of the collective oscillations of a Bose-Einstein condensate are shifted by the magnetic dipole interaction. The shift is polarization dependent and proportional to the ratio ${\ensuremath{\epsilon}}_{\mathrm{dd}}$ of dipolar and sss-wave coupling constants. Measuring the differences in the frequencies for different polarization we can extract the value of ${\ensuremath{\epsilon}}_{\mathrm{dd}}$ and thus measure aaa. We calculate the frequency shifts for a large variety of nonaxisymmetric harmonic traps in the Thomas-Fermi limit and find optimal trapping geometries to maximize the shifts.
The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.
We present a general method for obtaining the exact static solutions and collective excitation frequencies of a trapped Bose-Einstein condensate (BEC) with dipolar atomic interactions in the Thomas-Fermi regime. The method incorporates analytic expressions for the dipolar potential of an arbitrary polynomial density profile, thereby reducing the problem of handling nonlocal dipolar interactions to the solution of algebraic equations. We comprehensively map out the static solutions and excitation modes, including non-cylindrically-symmetric traps, and also the case of negative scattering length where dipolar interactions stabilize an otherwise unstable condensate. The dynamical stability of the excitation modes gives insight into the onset of collapse of a dipolar BEC. We find that global collapse is consistently mediated by an anisotropic quadrupolar collective mode, although there are two trapping regimes in which the BEC is stable against quadrupole fluctuations even as the ratio of the dipolar to sss-wave interactions becomes infinite. Motivated by the possibility of a fragmented condensate in a dipolar Bose gas due to the partially attractive interactions, we pay special attention to the scissors modes, which can provide a signature of superfluidity, and identify a long-range restoring force which is peculiar to dipolar systems. As part of the supporting material for this paper we provide the computer program used to make the calculations, including a graphical user interface.
We report measurements of the Bose-Einstein condensate critical temperature shift due to dipolar interactions, employing samples of ultracold erbium atoms which feature significant (magnetic) dipole-dipole interactions in addition to tunable contact interactions. Using a highly prolate harmonic trapping potential, we observe a clear dependence of the critical temperature on the orientation of the dipoles relative to the trap axis. Our results are in good agreement with mean-field theory for a range of contact interaction strengths. This work creates an opportunity for further investigations into beyond-mean-field effects and the finite-temperature phase diagram in the more strongly dipolar regime where supersolid and droplet states emerge.
We calculate perturbatively the effect of a dipolar interaction upon the Bose-Einstein condensation temperature. This dipolar shift depends on the angle between the symmetry axes of the trap and the aligned atomic dipole moments, and is extremal for parallel or orthogonal orientations, respectively. The difference of both critical temperatures exhibits most clearly the dipole-dipole interaction and can be enhanced by increasing both the number of atoms and the anisotropy of the trap. Applying our results to chromium atoms, which have a large magnetic dipole moment, shows that this dipolar shift of the critical temperature could be measured in the ongoing Stuttgart experiment.