No Arabic abstract
We calculate the hydrodynamic solutions for a dilute Bose-Einstein condensate with long-range dipolar interactions in a rotating, elliptical harmonic trap, and analyse their dynamical stability. The static solutions and their regimes of instability vary non-trivially on the strength of the dipolar interactions. We comprehensively map out this behaviour, and in particular examine the experimental routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex lattice formation. Furthermore, we analyse the centre of mass and breathing modes of a rotating dipolar condensate.
Doubly quantized vortices were topologically imprinted in $|F=1>$ $^{23}$Na condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.
Our recent measurements on the expansion of a chromium dipolar condensate after release from an optical trapping potential are in good agreement with an exact solution of the hydrodynamic equations for dipolar Bose gases. We report here the theoretical method used to interpret the measurement data as well as more details of the experiment and its analysis. The theory reported here is a tool for the investigation of different dynamical situations in time-dependent harmonic traps.
We have measured the relative strength $epsilon_dd$ of the magnetic dipole-dipole interaction compared to the contact interaction in a chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of a dipolar chromium BEC with different orientations of the atomic magnetic dipole moments. By comparing them with numerical solutions of the hydrodynamic equations for dipolar condensates, we are able to determine $epsilon_dd = 0.159pm0.034$ with high accuracy. Since the absolute strength of the dipole-dipole interaction is known exactly, the relative strength of the dipoledipole interaction can be used to determine the s-wave scattering length $a = 5.08pm1.06cdot10^-9 m = 96pm20 a0$ of 52Cr. This is fully consistent with our previous measurements on the basis of Feshbach resonances.
We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the non-adiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyse the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar condensates, which is followed by collapse in three-dimensional geometries. We show that the nature of this instability is fundamentally different in two-dimensional condensates, due to the dipole-induced stabilization of two-dimensional bright solitons. As a consequence, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic confinement, the instability leads to transient pattern formation followed by the creation of stable two-dimensional solitons. This dynamics should be observable in on-going experiments, allowing for the creation of stable two-dimensional solitons for the first time ever in quantum gases.