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Journal of the Physical Society of Japan

Density Dependence of Charge-4 Vortex Splitting in Bose–Einstein Condensates

Hitoshi Shibayama, Akinori Tsukada, Takahisa Yoshihara, T. Kuwamoto

Published Apr 14, 2016• 6 citations
Publisher

Abstract

We studied the axial-direction density dependence of the splitting of a charge-4 vortex created in 87Rb Bose–Einstein condensates. Vortices were generated by topological phase imprinting, and the axial density of the condensates was controlled by an optical potential. Linear and triangular arrangements of four single-charged vortices that emerged through the charge-4 vortex collapse were observed. The splitting of the charge-4 vortices was suppressed by maintaining the density outside the l = 2 unstable mode regions where linear arrangements were formed. In addition, we studied vortex dynamics in a high density region for which investigations have not been previously performed.

DOI
10.7566/jpsj.85.054401

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We studied the axial-direction density dependence of the splitting of a charge-4 vortex created in 87Rb Bose–Einstein condensates. Vortices were generated by topological phase imprinting, and the axial density of the condensates was controlled by an optical potential. Linear and triangular arrangements of four single-charged vortices that emerged through the charge-4 vortex collapse were observed. The splitting of the charge-4 vortices was suppressed by maintaining the density outside the l = 2 unstable mode regions where linear arrangements were formed. In addition, we studied vortex dynamics in a high density region for which investigations have not been previously performed.
We studied the dynamics of quadruply quantized vortices in 87 Rb Bose–Einstein condensates. Vortices were created in magnetically trapped condensates with hyperfine spin F = 2 by employing topological phase imprinting technique, wherein the direction of atomic spin is adiabatically reversed by applying a bias magnetic field. Vortices were observed for a holding time of up to 10 ms. Disappearance of the vortices was attributed to considerable expansion and excitation of the condensates, which were caused by the distortion of the magnetic potential. In order to observe the long-term behavior of the vortices, we transferred the condensates to a crossed-type optical dipole force trap after creating the vortices. In this case, the vortices were observed for a holding time of up to 22 ms. We also observed density profiles, which indicated the presence of split vortices.
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.
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We consider the splitting mechanism of a multiply charged vortex into singly charged vortices in a Bose-Einstein condensate confined in a harmonic potential at zero temperature. The Bogoliubov equations support unstable modes with complex eigenfrequencies (CE modes), which cause the splitting instability without the influence of thermal atoms. The investigation of the excitation spectra shows that the negative-energy (NE) mode plays an important role in the appearance of the CE modes. The configuration of vortices in splitting is determined by the angular momentum of the associated NE mode. This structure has also been confirmed by the numerical simulation of the time-dependent Gross-Pitaevskii equation.
The splitting process of quadruply charged vortices into less charged vortices is studied at zero temperature. We solve the Bogoliubov-de Gennes (BdG) equation numerically and classify the excitations by angular momentum l relative to the condensates. Unstable modes having complex eigenvalues appear when l = 2-6. It is found that two excitations are coupled with each other when their total energy and angular momentum are zero and yield a pair of complex eigenvalues. The decay process is also numerically simulated by solving the time-dependent Gross-Pitaevskii equation. The behavior of a condensate shows good agreement with the results of BdG. The quadruply charged vortex splits into four singly quantized vortices, which are arranged as a line, triangle, and square according to the angular momentum of the excited eigenmode. We also observe the effect of nonlinearity.