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Scientific Reports

Vortex clustering in trapped Bose-Einstein condensates

Thomas A. Easton, Marios Kokmotos, Giovanni Barontini

Published Nov 8, 2023• 4 citations
Publisher

Abstract

We numerically study the formation of vortex clusters in trapped Bose-Einstein condensates where vortices are initially imprinted in a line. We show that such a system exhibits a rich phenomenology depending on the distance at which the vortices are imprinted and their number. In particular we observe that it is possible to obtain systems of twin vortex clusters, twin vortex clusters with orbiting satellite vortices, and triplets of clusters. By using a clustering algorithm we are able to quantitatively describe the formation and dynamics of the clusters. We finally utilise an analytical model to determine the range of parameters for which the clustering occurs. Our work sets the stage for possible experimental implementations where the formation of vortex clusters and more exotic bound states of vortices could be observed.

DOI
10.1038/s41598-023-46549-3

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We numerically study the formation of vortex clusters in trapped Bose-Einstein condensates where vortices are initially imprinted in a line. We show that such a system exhibits a rich phenomenology depending on the distance at which the vortices are imprinted and their number. In particular we observe that it is possible to obtain systems of twin vortex clusters, twin vortex clusters with orbiting satellite vortices, and triplets of clusters. By using a clustering algorithm we are able to quantitatively describe the formation and dynamics of the clusters. We finally utilise an analytical model to determine the range of parameters for which the clustering occurs. Our work sets the stage for possible experimental implementations where the formation of vortex clusters and more exotic bound states of vortices could be observed.
We study the formation of vortices in a Bose-Einstein condensate (BEC) that has been prepared by allowing isolated and independent condensed fragments to merge together. We focus on the experimental setup of Scherer et al. [Phys. Rev. Lett. 98, 110402 (2007)], where three BECs are created in a magnetic trap that is segmented into three regions by a repulsive optical potential; the BECs merge together as the optical potential is removed. First, we study the two-dimensional case; in particular, we examine the effects of the relative phases of the different fragments and the removal rate of the optical potential on the vortex formation. We find that many vortices are created by instant removal of the optical potential regardless of relative phases, and that fewer vortices are created if the intensity of the optical potential is gradually ramped down and the condensed fragments gradually merge. In all cases, self-annihilation of vortices of opposite charge is observed. We also find that for sufficiently long barrier ramp times, the initial relative phases between the fragments leave a clear imprint on the resulting topological configuration. Finally, we study the three-dimensional system and the formation of vortex lines and vortex rings due to the merger of the BEC fragments; our results illustrate how the relevant vorticity is manifested for appropriate phase differences, as well as how it may be masked by the planar projections observed experimentally.
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.
We report on the observation of vortex formation in a Bose-Einstein condensate of 87Rb^{87}\text{R}\text{b}87Rb atoms. Vortices are generated by superimposing an oscillating excitation to the trapping potential introduced by an external magnetic field. For small amplitudes of the external excitation field we observe a bending of the cloud axis. Increasing the amplitude we observe formation of a growing number of vortices in the sample. Shot-to-shot variations in both vortex number and position within the condensed cloud are observed, probably due to the intrinsic vortex nucleation dynamics. We discuss the possible formation of vortices and antivortices in the sample as well as possible mechanisms for vortex nucleation.
In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.
Motivated by recent experimental and theoretical studies of few-particle vortex clusters in Bose–Einstein condensates, we consider the ordinary differential equations of motion and systematically examine settings for up to N = 6 vortices. We analyze the existence of corresponding stationary state configurations and also consider their spectral stability properties. We compare our particle model results with the predictions of the full partial differential equation system. Whenever possible, we propose generalizations of these results in the context of clusters of N vortices. Some of these we can theoretically establish, especially for the N -vortex polygons, while others we state as conjectures, e.g. for the N -vortex line equilibrium.
In this brief review we summarize a number of recent developments in the study of vortices in Bose–Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.