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arXiv:1404.4237 · Physical Review Letters

Observation of Solitonic Vortices in Bose-Einstein Condensates

Simone Donadello, Simone Serafini, Marek Tylutki, Лев П. Питаевский, F. Dalfovo, Giacomo Lamporesi, Gabriele Ferrari

Published Aug 4, 2014• 164 citations
arXivHTMLPDF

Abstract

We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.

DOI
10.1103/physrevlett.113.065302

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We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.
We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.
Symmetry breaking during phase transitions can lead to the formation of topological defects (such as vortex lines in superfluids). However, the usually studied Bose-Einstein condensates (BECs) have the shape of a cigar, a geometry that impedes vortex formation, survival, and detection. I show that, in elongated traps, one can expect the formation of gray solitons (long-lived, nontopological "phase defects") as a result of the same mechanism. Their number will rise approximately in proportion to the transition rate. This steep rise is due to the increasing size of the region of the BEC cigar where the phase of the condensate wave function is chosen locally (rather than passed on from the already formed BEC).
The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.
Quantum vortices in superfluid Bose Einstein condensates (BECs) are excellent candidates\nfor studying hydrodynamic phenomena, such as turbulence and chaos, due to the\nquantization of vortex circulation and the absence of dissipation in BECs. Since the early\n2000s, many experimental groups have successfully observed vortices in dilute atomic\nBECs.\n\nThis work mainly focuses on creating quantum chaos with a few vortices in a twodimensional\nBEC of Rubidium􀀀87. We use graphics processing unit (GPU) computing methods to simulate our BEC trapped inside a harmonic potential with tight trapping in one direction. The quantum vortices are created by rotating the condensate. After generating the ground state of the BEC with a small number of singly charged vortices with positive phase winding, we imprint a 4\\pi phase winding on top of one vortex in the opposite orientation to that of the original vortex. This phase imprinting annihilates the preexisting vortex and creates a new singly-charged vortex with negative phase winding. Due to the high resolution of our system and an excellent vortex tracking algorithm, the location of phase imprinting can be delicately controlled.\n\nBoth the individual vortex dynamics and the dynamics of the entire system of vortices\nafter flipping a vortex have shown strong signs of chaos. This chaotic nature is\nfurther confirmed both qualitatively and quantitatively by employing two chaos indicators\non our numerical results. These chaos indicators are the Lyapunov exponent spectrum\nand the Smaller ALignment Index (SALI). The Lyapunov exponent remains positive and\nconverges to a positive value during an experimentally realistic time period, which is the\nsmoking gun for chaotic behaviour.
The connection between quantized vortices and dark solitons in a waveguidelike trap geometry is explored in the framework of the nonlinear Schr\"odinger equation. Variation of the transverse confinement leads from the quasi-one-dimensional (1D) regime, where solitons are stable, to 2D (or 3D) confinement, where soliton stripes are subject to a transverse modulational instability known as the ``snake instability.'' We present numerical evidence of a regime of intermediate confinement where solitons decay into single, deformed vortices with solitonic properties rather than vortex pairs as associated with the ``snake'' metaphor. Further relaxing the transverse confinement leads to the production of two and then three vortices, which correlates perfectly with a Bogoliubov stability analysis. The decay of a stationary dark soliton (or, planar node) into a single solitonic vortex is predicted to be experimentally observable in a 3D harmonically confined dilute-gas Bose-Einstein condensate.