We studied the nucleation of quadruple-quantized vortices in Bose–Einstein condensates confined in a quadrupole-Ioffe-configuration (QUIC) magnetic trap by means of the topological phase imprinting method, wherein the initially aligned atomic spins were adiabatically reversed by applying an external bias magnetic field. We calculated the change in the magnetic field distributions of the trap when a homogeneous or a gradient bias field was applied for reversing the spins, and almost the same results were obtained for both cases. We applied the gradient bias field using a single coil because of its simplicity and stability. Vortices were successfully created at the reversal time of atomic spins between 2 and 16 ms. Moreover, the vortices were observed at a holding time of up to 9 ms in the magnetic trap after a constant reversal time of 5 ms.
Topological phase imprinting is a unique technique for vortex formation in a Bose-Einstein condensate (BEC) of an alkali-metal gas, in that it does not involve rotation: the BEC is trapped in a quadrupole field with a uniform bias field which is reversed adiabatically leading to vortex formation at the center of the magnetic trap. The scenario has been experimentally verified by Leanhardt et al. employing
23Na atoms. Recently similar experiments have been conducted by Hirotani et al. in which a BEC of
87Rb atoms was used. In the latter experiments the authors found that fine-tuning of the field reverse time
Trev is required to achieve stable vortex formation. Otherwise, they often observed vortex fragmentation or a condensate without a vortex. It is shown in this paper that this behavior can be attributed to the heavy mass of the
Rb atom. The confining potential, which depends on the eigenvalue
mB of the hyperfine spin $\mathbit{F}$ along the magnetic field, is now shifted by the gravitational field perpendicular to the vortex line. Then the positions of two weak-field-seeking states with
mB=1 and 2 deviate from each other. This effect is more prominent for BECs with a heavy atomic mass, for which the deviation is greater and, moreover, the Thomas-Fermi radius is smaller. We found, by solving the Gross-Pitaevskii equation numerically, that two condensates interact in a very complicated way leading to fragmentation of vortices, unless
Trev is properly tuned.
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.
The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.
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.