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arXiv:cond-mat/0603699 · Physical Review A

Vortex creation during magnetic trap manipulations of spinor Bose-Einstein condensates

A. P. Itin, Tōru Morishita, M. Satoh, Oleg I. Tolstikhin, Shinichi Watanabe

Published Jun 13, 2006• 4 citations
arXivHTMLPDF

Abstract

We investigate several mechanisms of vortex creation during splitting of a spinor Bose-Einstein condensate (BEC) in a magnetic double-well trap controlled by a pair of current carrying wires and bias magnetic fields. Our study is motivated by a recent MIT experiment on splitting BECs with a similar trap [Y. Shin et al., Phys. Rev. A 72, 021604 (2005)], where an unexpected fork-like structure appeared in the interference fringes indicating the presence of a singly quantized vortex in one of the interfering condensates. It is well known that in a spin-1 BEC in a quadrupole trap, a doubly quantized vortex is topologically produced by a ``slow'' reversal of bias magnetic field ${B}_{z}$. Since in the experiment a doubly quantized vortex had never been seen, Shin et al. ruled out the topological mechanism and concentrated on the nonadiabatic mechanical mechanism for explanation of the vortex creation. We find, however, that in the magnetic trap considered both mechanisms are possible: singly quantized vortices can be formed in a spin-1 BEC topologically (for example, during the magnetic field switching-off process). We therefore provide a possible alternative explanation for the interference patterns observed in the experiment. We also present a numerical example of creation of singly quantized vortices due to ``fast'' splitting; i.e., by a dynamical (nonadiabatic) mechanism.

DOI
10.1103/physreva.73.063615

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We investigate several mechanisms of vortex creation during splitting of a spinor Bose-Einstein condensate (BEC) in a magnetic double-well trap controlled by a pair of current carrying wires and bias magnetic fields. Our study is motivated by a recent MIT experiment on splitting BECs with a similar trap [Y. Shin et al., Phys. Rev. A 72, 021604 (2005)], where an unexpected fork-like structure appeared in the interference fringes indicating the presence of a singly quantized vortex in one of the interfering condensates. It is well known that in a spin-1 BEC in a quadrupole trap, a doubly quantized vortex is topologically produced by a slow'' reversal of bias magnetic field ${B}_{z}$. Since in the experiment a doubly quantized vortex had never been seen, Shin et al. ruled out the topological mechanism and concentrated on the nonadiabatic mechanical mechanism for explanation of the vortex creation. We find, however, that in the magnetic trap considered both mechanisms are possible: singly quantized vortices can be formed in a spin-1 BEC topologically (for example, during the magnetic field switching-off process). We therefore provide a possible alternative explanation for the interference patterns observed in the experiment. We also present a numerical example of creation of singly quantized vortices due to fast'' splitting; i.e., by a dynamical (nonadiabatic) mechanism.
We are interested in interplay between nonlinearity and non-adiabaticity in many-body quantum systems: Bose-Einstein condensates (BEC). Adiabatic (geometric) phases and dynamics of adiabatic invariants are conceptual issues in classical mechanics and have been used recently in studying dynamics of BEC and ingenious manipulations with it. We present here two our recent results related to this theme. The first concerns a vortex creation during splitting of a spinor BEC in a magnetic chip-based trap. Our study is motivated by a recent MIT experiment 1 , where a fork-like structure appeared in the interference fringes indicating the presence of a singly quantized (SQ) vortex in one of the interfering condensates. It is well-known that in a spin-1 BEC in a quadrupole trap a doubly quantized (DQ) vortex is topologically produced by a “slow” reversal of bias magnetic field Bz. This fact can be explained using an adiabatic (Berry) phase argument. Since in the experiment a DQ vortex had never been seen, Y. Shin et. al ruled out the topological mechanism and concentrated on the mechanical mechanism for explanation of the vortex creation. We find however that both mechanisms are possible: SQ vortices can be formed in a spin-1 BEC topologically during the magnetic field switching-off process 2 . We therefore provide a possible alternative explanation for the interference patterns observed in the experiment. The second example concerns dynamics of atom-molecule BEC systems being considered recently, in particular in relation to Feschbach resonance passage. We use rigorous separatrix crossing theory 3 to study dynamics of adiabatic invariants in corresponding models. Our results 4 contradict those of 5
Recently, the splitting of a topologically created doubly quantized vortex into two singly quantized vortices was experimentally investigated in dilute atomic cigar-shaped Bose-Einstein condensates [Y. Shin, Phys. Rev. Lett. 93, 160406 (2004)10.1103/PhysRevLett.93.160406]. In particular, the dependency of the splitting time on the peak particle density was studied. We present results of theoretical simulations which closely mimic the experimental setup. We show that the combination of gravitational sag and time dependency of the trapping potential alone suffices to split the doubly quantized vortex in time scales which are in good agreement with the experiments.
Abstract Quantized vortices appear in physical systems from superfluids and superconductors to liquid crystals and high energy physics. Unlike their scalar cousins, superfluids with complex internal structure can exhibit rich dynamics of decay and even fractional vorticity. Here, we experimentally and theoretically explore the creation and time evolution of vortex lines in the polar magnetic phase of a trapped spin-1 87Rb Bose–Einstein condensate. A process of phase-imprinting a nonsingular vortex, its decay into a pair of singular spinor vortices, and a rapid exchange of magnetic phases creates a pair of three-dimensional, singular singly-quantized vortex lines with core regions that are filled with atoms in the ferromagnetic phase. Atomic interactions guide the subsequent vortex dynamics, leading to core structures that suggest the decay of the singly-quantized vortices into half-quantum vortices.
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.
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^{23}\mathrm{Na}23Na atoms. Recently similar experiments have been conducted by Hirotani et al. in which a BEC of 87Rb^{87}\mathrm{Rb}87Rb atoms was used. In the latter experiments the authors found that fine-tuning of the field reverse time Trev{T}_{\mathrm{rev}}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\mathrm{Rb}Rb atom. The confining potential, which depends on the eigenvalue mB{m}_{B}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{m}_{B}=1mB​=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{T}_{\mathrm{rev}}Trev​ is properly tuned.
Fast creation of a single vortex in BEC of alkali-metal atoms at a prescribed position and time is still challenging, even though various methods to create single and multiple vortices have been proposed and demonstrated. Topological vortex formation is advantageous in this respect over other methods in that the position and time of vortex formation is highly controllable. This method requires inversion of the bias magnetic field along the axis of the condensate, which leads to unwanted atom loss due to nonadiabatic transitions when the bias field crosses zero. It is the purpose of this paper to propose a scheme that enables a fast creation of a vortex in much shorter time than needed for adiabatic control time by introducing the counterdiabatic field to avert the atom loss. We further introduce a gauge transformation so that the required magnetic field is generated by manipulating the current of the Ioffe bars, which makes our proposal experimentally feasible.