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arXiv:1102.0640 · Physical Review A

Rotational properties of dipolar Bose-Einstein condensates confined in anisotropic harmonic potentials

Francesc Malet, Tom Kristensen, S. M. Reimann, G. M. Kavoulakis

Published Mar 30, 2011• 31 citations
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Abstract

We study the rotational properties of a dipolar Bose-Einstein condensate confined in a quasi-two-dimensional anisotropic trap for an arbitrary orientation of the dipoles with respect to their plane of motion. Within the mean-field approximation, we find that the lowest-energy state of the system depends strongly on the relative strength between the dipolar and the contact interactions, as well as on the size and the orientation of the dipoles and the size and the orientation of the deformation of the trapping potential.

DOI
10.1103/physreva.83.033628

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We study the rotational properties of a dipolar Bose-Einstein condensate confined in a quasi-two-dimensional anisotropic trap for an arbitrary orientation of the dipoles with respect to their plane of motion. Within the mean-field approximation, we find that the lowest-energy state of the system depends strongly on the relative strength between the dipolar and the contact interactions, as well as on the size and the orientation of the dipoles and the size and the orientation of the deformation of the trapping potential.
We investigated the low-lying collective excitations of quasi-two-dimensional dipolar Bose-Einstein condensates confined in a rotating harmonic potential using the Bogoliubov--de Gennes equation. By varying the trap rotation frequency and dipolar interaction strength, we show how the anisotropic dipole-dipole interaction modifies the collective excitations of the condensates. In particular, under strong dipolar interaction, the vortex-displacement excitations differ significantly from the nondipolar case.
The effect of dipolar orientation with respect to the condensate plane on the mean-field dynamics of dipolar Bose-Einstein condensates in a pancake-shaped confinement is discussed. The stability of a quasi-two-dimensional condensate, with respect to the tilting angle, is found to be different from a two-dimensional layer of dipoles, indicating the relevance of the transverse extension while characterizing two-dimensional dipolar systems. An anisotropic excitation spectrum exhibiting a highly tunable, rotonlike minimum can arise entirely from the dipole-dipole interactions, by tilting the dipoles. At the magic angle and in the absence of contact interactions, the long-wavelength excitations are not phononlike and always unstable. The post-roton-instability dynamics, in contrast to phonon instability, in a uniform condensate, is featured by a transient, defect-free, stripe pattern, which eventually undergoes local collapses, and driving the condensate back into the stable regime can make them sustained for longer. Hopping between stripes has been observed before it melts into a uniform state in the presence of dissipation. Finally, we discuss a class of solutions, in which a quasi-two-dimensional condensate is self-trapped in one direction, as well as a regime of interaction parameters, including attractive short-range interactions, at which a two-dimensional anisotropic soliton can be stabilized, and we show that a chromium condensate with a relatively small number of atoms is well suited for this.
We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the ring with respect to the polarization direction of the dipoles. In the presence of long-range anisotropic dipolar and short-range contact interactions, the anisotropic density distribution of the dipolar BEC in both traps is discussed in detail. The stability condition of the dipolar BEC in both traps is illustrated in a phase plot of dipolar and contact interactions. We also study and discuss the properties of a vortex dipolar BEC in these traps.
We consider a dilute gas of dipole moments in an arbitrary harmonic trap and treat both the short-range, isotropic $\ensuremath{\delta}$ interaction and the long-range, anisotropic dipole-dipole interaction perturbatively. In this way, we calculate the leading shift of the critical temperature with respect to that of an ideal gas as a function of the relative orientation of the dipole moments with respect to the harmonic trap axes. In particular, we determine those magic angles, where the dipolar shift of the Bose-Einstein condensation temperature vanishes. Furthermore, we show for the parameters of the ongoing 52Cr^{52}\mathrm{Cr}52Cr BEC experiment of Pfau and co-workers that this dipolar shift can be enhanced by increasing the number of particles, the geometrical mean trap frequency, and the anisotropy of the trap.
We investigate the impact of interplay between the contact interaction and the dipole-dipole interaction on the rotational properties of dipolar Bose-Einstein condensate, rotating in an axially confined double-well potential. The dynamics is governed by a quasi-two-dimensional Gross-Pitaevskii equation with phenomenological dissipation and non-local dipole-dipole interaction integral. In the present study, we consider using three different dipolar atoms namely 52Cr, 168Er and 164Dy with increasing order of dipole-dipole interaction strength respectively. From our numerical simulation, we see, at the critical frequency, the vortex core starts to emerge from the peripheries of the BEC. Further, we observe that the critical frequency of vortex nucleation decreases with an increase of dipole-dipole interaction strength and contact interaction strength and these interactions also enhance the number of vortices. We also find that the increase in average angular momentum per atom with rotational frequency suddenly shifts from linear to non-linear progression after attaining the critical rotational frequency. From the results obtained in the present study, it is quite clear that dipole-dipole interaction and contact interaction compliments with each other, has a considerable influence on the rotational properties of dipolar BECs.
We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.