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arXiv:0901.1300 · New Journal of Physics

Coherent collapses of dipolar Bose–Einstein condensates for different trap geometries

Jonas Metz, Thierry Lahaye, B Fröhlich, Axel Griesmaier, Tilman Pfau, Hiroki Saito, Yuki Kawaguchi, Masahito Ueda

Published May 14, 2009• 68 citations
arXivHTMLPDF

Abstract

We experimentally investigate the collapse dynamics of dipolar Bose- Einstein condensates of chromium atoms in different harmonic trap geometries, from prolate to oblate. The evolutions of the condensates in the unstable regime are compared to three-dimensional simulations of the Gross-Pitaevskii equation including three-body losses. In order to probe the phase coherence of collapsed condensates, we induce the collapse in several condensates simultaneously and let them interfere.

DOI
10.1088/1367-2630/11/5/055032

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We experimentally investigate the collapse dynamics of dipolar Bose- Einstein condensates of chromium atoms in different harmonic trap geometries, from prolate to oblate. The evolutions of the condensates in the unstable regime are compared to three-dimensional simulations of the Gross-Pitaevskii equation including three-body losses. In order to probe the phase coherence of collapsed condensates, we induce the collapse in several condensates simultaneously and let them interfere.
We experimentally investigate how the collapse dynamics of a Cr-52 Bose-Einstein condensate depends on the external harmonic trap geometry. When the collapse is initiated by reducing the s-wave scattering length below its critical value, a complex dynamics is observed, involving a d-wave symmetric explosion. We find good agreement between our experiments and simulations of the Gross-Pitaevskii equation including 3-body losses. In order to probe the phase-coherence of collapsed condensates we induce the collapse in several condensates simultaneously and let them interfere.
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 nonadiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyze the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.
The purpose of this paper is to study the dynamics of solutions to an extended Gross–Pitaevskii equation that models the formation of droplets in a dipolar Bose–Einstein condensate (BEC). The formation of these droplets has been recently discovered by driving the BEC into the strongly dipolar regime. Surprisingly, instead of collapsing, the system formed stable droplets. So far, no rigorous mathematical explanation has been proved. To the best of our knowledge, only experimental results have been obtained. The goal of this paper is to validate this breakthrough discovery. Many predictions/ conjectures properties of these droplets have been stated by some research groups in physics and engineering. In particular, it has been claimed that the stability of these droplets is a consequence of the presence of the damping term in the extended Gross–Pitaevskii equation under study. This term describes the three-body loss process. To accurately model the dynamics of formation of these droplets, it is necessary to consider a time-dependent harmonic trapping potential as well as other terms with different types of nonlinearity among them that describe the Lee–Huang–Yang (LHY). This presents some challenges that will be solved in this paper.
Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.
The subject of this thesis is the experimental investigation of a dipolar 52-Chromium Bose-Einstein condensate (BEC) in a one-dimensional optical lattice potential. At first, the influence of the periodic landscape on the stability of the quantum gas is investigated. Based on these measurements, the collapse dynamics of the system, i.e. its time evolution after passing the threshold to the unstable regime, is observed and analyzed. Both the investigations aim to contribute to the basic understanding of dipolar quantum gases. In addition, they may provide a basis for further experiments with dipolar BECs in optical lattices. Amongst others, the observation of self-organized density structures is one of the biggest goals in this field of research.
We use a gradient-decent method to compute 3D ground states of dipolar Bose-Einstein conden- sates. We discover that in highly-prolate traps, whose long axis is parallel to the dipoles, can give rise to candlestick ground states. Direct numerical simulations of the dipolar Gross-Pitaevskii equation reveal that the nucleus of the candlestick mode undergoes collapse, while obtaining a highly flat pancake shape. The rate of this anisotropic collapse scales differently from what occurs in isotropic collapse. Stability analysis reveals a surprising cusp point in the mass vs. chemical potential curve, which may serve as a signature for this dynamics.