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Register a new userOn an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions
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We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s-wave case, but with a different aspect ratio. Various properties such as electrostriction and stability are discussed.
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We study a gaseous Bose-Einstein condensate with laser-induced dipole-dipole interactions using the Hartree-Fock-Bogoliubov theory within the Popov approximation. The dipolar interactions introduce long-range atom-atom correlations, which manifest themselves as increased depletion at momenta similar to that of the laser wavelength, as well as a roton dip in the excitation spectrum. Surprisingly, the roton dip and the corresponding peak in the depletion are enhanced by raising the temperature above absolute zero.
We derive the exact density profile of a harmonically trapped Bose-Einstein condensate (BEC) which has dipole-dipole interactions as well as the usual s-wave contact interaction, in the Thomas-Fermi limit. Remarkably, despite the non-local anisotropic nature of the dipolar interaction, the density turns out to be an inverted parabola, just as in the pure s-wave case, but with a modified aspect ratio. The ``scaling solution approach of Kagan, Surkov, and Shlyapnikov [Phys. Rev. A 54, 1753 (1996)] and Castin and Dum [Phys. Rev. Lett. 77}, 5315 (1996)] for a BEC in a time-dependent trap can therefore be applied to a dipolar BEC, and we use it to obtain the exact monopole and quadrupole shape oscillation frequencies.
We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar, pancake and spherical geometries. This also naturally gives the criteria for the mean-field one- and two-dimensional regimes. Our predictions, including the Thomas-Fermi density profiles, are shown to be in excellent agreement with numerical solutions. Importantly, the anisotropy of the interactions has a profound effect on the Thomas-Fermi/low-dimensional criteria.
A quantum vortex dipole, comprised of a closely bound pair of vortices of equal strength with opposite circulation, is a spatially localized travelling excitation of a planar superfluid that carries linear momentum, suggesting a possible analogy with ray optics. We investigate numerically and analytically the motion of a quantum vortex dipole incident upon a step-change in the background superfluid density of an otherwise uniform two-dimensional Bose-Einstein condensate. Due to the conservation of fluid momentum and energy, the incident and refracted angles of the dipole satisfy a relation analogous to Snells law, when crossing the interface between regions of different density. The predictions of the analogue Snells law relation are confirmed for a wide range of incident angles by systematic numerical simulations of the Gross-Piteavskii equation. Near the critical angle for total internal reflection, we identify a regime of anomalous Snells law behaviour where the finite size of the dipole causes transient capture by the interface. Remarkably, despite the extra complexity of the surface interaction, the incoming and outgoing dipole paths obey Snells law.
We point out the possibility of having a roton-type excitation spectrum in a quasi-1D Bose-Einstein condensate with dipole-dipole interactions. Normally such a system is quite unstable due to the attractive portion of the dipolar interaction. However, by reversing the sign of the dipolar interaction using either a rotating magnetic field or a laser with circular polarization, a stable cigar-shaped configuration can be achieved whose spectrum contains a `roton minimum analogous to that found in helium II. Dipolar gases also offer the exciting prospect to tune the depth of this `roton minimum by directly controlling the interparticle interaction strength. When the minimum touches the zero-energy axis the system is once again unstable, possibly to the formation of a density wave.
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