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arXiv:cond-mat/0405041 · Physical Review Letters

Calibrating Dipolar Interaction in an Atomic Condensate

S. Yi, Li You

Published May 14, 2004• 41 citations
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Abstract

We reexamine the topic of a dipolar condensate with the recently derived more rigorous pseudopotential for dipole-dipole interaction [Phys. Rev. A 67, 033607 (2003)]]. Based on the highly successful variational technique, we find that all dipolar effects estimated before (using the bare dipole-dipole interaction) become significantly larger, i.e., are amplified by the new velocity-dependent pseudopotential, especially in the limit of large or small trap aspect ratios. This result points to a promising prospect for detecting dipolar effects inside an atomic condensate.

DOI
10.1103/physrevlett.92.193201

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•Feb 16, 2012•0 citations
We reexamine the topic of a dipolar condensate with the recently derived more rigorous pseudopotential for dipole-dipole interaction [Phys. Rev. A 67, 033607 (2003)]]. Based on the highly successful variational technique, we find that all dipolar effects estimated before (using the bare dipole-dipole interaction) become significantly larger, i.e., are amplified by the new velocity-dependent pseudopotential, especially in the limit of large or small trap aspect ratios. This result points to a promising prospect for detecting dipolar effects inside an atomic condensate.
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.
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.
We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low-energy pseudopotentials is proposed and justified by the agreement with results of numerical multichannel calculations. The time dependent variational method is adapted to reveal several interesting features observed in numerical solutions of condensate wave function. Collective low-energy shape oscillations and their stability inside electric fields are investigated. Our results shed new light into macroscopic coherence properties of interacting quantum degenerate atomic gases.
We discuss the low-energy shape oscillations of a magnetically trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g., as for 85Rb{}^{85}\mathrm{Rb}85Rb atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley et al., Nature (London) 412, 295 (2001)].
Quantized vortices are the hallmark of superfluidity, and are often sought out as the first observable feature in new superfluid systems. Following the recent experimental observation of vortices in Bose–Einstein condensates comprised of atoms with inherent long-range dipole-dipole interactions [ Nat. Phys. 18 , 1453-1458 (2022)], we thoroughly investigate vortex properties in the three-dimensional dominantly dipolar regime, where beyond-mean-field effects are crucial for stability, and investigate the interplay between trap geometry and magnetic field tilt angle.
In this thesis we study the effects of the dipole-dipole interaction on the physics of ultracold quantum gases, both bosonic and fermionic, within the theoretical framework provided by the mean-field regime. This kind of interaction takes place in ultracold atomic gases (for instance 52Cr or 164Dy) due to their atomic magnetic dipole moment, and in ultracold molecular gases due to the magnetic or electric dipole moment. \n \nIn the case of quantum gases of bosonic atoms, or Bose-Einstein condensates, the dipole-dipole interaction can be studied within mean-field approximation using the Gross-Pitaevskii equation, which now contains a new non-linear term due to the dipole-dipole interaction. We investigate, on the one hand dipolar condensates confined in harmonic traps, and on the other dipolar condensates confined in toroidal traps. In the harmonic geometry, our focus is on the study of the ground state and the quantized vortex state, where the density profile is characterized as well as some properties leading to the process of vortex formation, such as the critical frequency and the energy barrier that has to be overcome to bring the vortex from the surface to the centre of the gas. We finish the study of dipolar condensates in harmonic traps by dynamically simulating the precession frequency of an off-center vortex in a non-rotating condensate. \n \nIn the toroidal geometry the dipolar effects are strongly magnified when the polarization axis of the dipoles is perpendicular to the trap symmetry axis. In this case, the anisotropic structure of the density can be understood as the response of the system to the double-well effective potential along the ring. We have studied the dynamics of this system when the initial number of atoms in the left and right wells is imbalanced, predicting Josephson and self-trapping oscillations depending on the initial condition. This has led us to name this new system as Self-induced Josephson Junction. We have studied in detail the self-trapping regime and we have seen that the particle flux inversion is closely related to the crossing of vortices across the Josephson junctions. This result opens the door to establishing a more direct connection between the phase-slip regime, widely addressed in superfluid helium, and the self-trapping regime of condensates. \n \nIn the case of quantum gases of fermionic dipolar particles, we have studied how the radial quadrupole mode allows one to distinguish between hydrodynamic and collisionless regimes. We have analytically calculated the frequency of this mode in the mean-field approximation, generalizing the results from the Thomas-Fermi approximation for trapped ideal Fermi gases. On the one hand, we observe that the frequency in the hydrodynamic regime is smaller than in non-dipolar Fermi gases, while in the collisionless regime the frequency is larger or smaller than that corresponding to the non-interacting system depending on the geometry of the harmonic trap. On the other hand, we predict that reducing the trap deformation (aspect ratio) an observable jump in the frequency of the radial quadrupole mode would take place, which would correspond to the transition between the collisionless and hydrodynamic regimes, for instance when the gas undergoes the transition to the superfluid state.