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Register a new userExact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit
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Added by
Andrew McCallum Martin
Publication date
2009
fields
Physics
and research's language is
English
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We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several novel routes to induce vortex lattice formation in a dipolar condensate.
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We have computed phase diagrams for rotating spin-1 Bose-Einstein condensates with long-range magnetic dipole-dipole interactions. Spin textures including vortex sheets, staggered half-quantum- and skyrmion vortex lattices and higher order topological defects have been found. These systems exhibit both superfluidity and magnetic crystalline ordering and they could be realized experimentally by imparting angular momentum in the condensate.
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 non-local 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 s-wave interactions becomes infinite. Motivated by the possibility of fragmented BEC 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 explore spatial symmetry breaking of a dipolar Bose Einstein condensate in the thermodynamic limit and reveal a critical point in the phase diagram at which crystallization occurs via a second order phase transition. This behavior is traced back to the significant effects of quantum fluctuations in dipolar condensates, which moreover stabilize a new supersolid phase, namely a regular honeycomb pattern with maximal modulational contrast and near-perfect superfluidity.
Based on the two-dimensional mean-field equations for pancake-shaped dipolar Bose-Einstein condensates in a rotating frame with both attractive and repulsive dipole-dipole interaction (DDI) as well as arbitrary polarization angle, we study the profiles of the single vortex state and show how the critical rotational frequency change with the s-wave contact interaction strengths, DDI strengths and the polarization angles. In addition, we find numerically that at the `magic angle $vartheta=arccos(sqrt{3}/3)$, the critical rotational frequency is almost independent of the DDI strength. By numerically solving the dipolar GPE at high rotational speed, we identify different patterns of vortex lattices which strongly depend on the polarization direction. As a result, we undergo a study of vortex lattice structures for the whole regime of polarization direction and find evidence that the vortex lattice orientation tends to be aligned with the direction of the dipoles.
The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilise linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
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