Dynamics of Quadruply Quantized Vortices in 87 Rb Bose–Einstein Condensates Confined in Magnetic and Optical Traps Takeshi KUWAMOTO  , Hayato USUDA, Satoshi TOJO, and Takuya HIRANO Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima, Tokyo 171-8588, Japan (Received September 11, 2009; accepted January 20, 2010; published March 10, 2010) 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 ¼ 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. KEYWORDS: quantized vortex, Bose–Einstein condensate, topological phase, optical dipole force trap, instability DOI: 10.1143/JPSJ.79.034004 1. Introduction Quantized vortices are characteristic phenomena of quantum fluids such as superfluid helium, 1) superconduc- tors, 2) and gaseous Bose–Einstein condensates 3) and play an important role in the dynamics of such quantum fluids. Vortices in gaseous condensates have been experimentally created by employing various methods such as dynamical phase imprinting, 4) rotation of an anisotropic potential, 5–8) slicing of an atomic cloud with a laser, 9) use of a soliton decay, 10,11) topological phase imprinting, 12,13) and trans- formation of an orbital angular momentum of a photon to an atom. 14) Especially, the last two methods are very distinct since they yield a multiply charged vortex. 15,16) To date, doubly and quadruply quantized vortex states have been created, 12–14) and their decay dynamics and time evolution have been studied. 17,18) The topological phase imprinting method has been applied to condensates confined in an Ioffe–Pritchard magnetic trap. 12,13) In order to create a vortex, atomic spins, which are initially almost parallel to the axial direction of the trap, are adiabatically rotated to the opposite direction by applying an additional bias magnetic field. During this process, each spin located at a different position in the trap follows the local magnetic field direction, and the phase winding with a magnitude of spin times 4 is imprinted onto the condensate wave function. 15,16) If the parameters of the Ioffe–Pritchard magnetic trap are maintained constant during applying the additional bias field, the final magnetic potential for weak-field-seeking atoms changes to a de- formed shape with a saddle point. As a result, the condensate is no longer trapped in the axial direction and continues to deform, thereby considerably affecting the generated vortex. The observation time of vortices is limited to less than few tens of milliseconds when the direction of axial magnetic field is reversed by the additional bias field alone. 12,13) In order to remove this limitation, a research group from MIT changed the direction of the currents that generate axial confinement of the magnetic trap in addition to the ramping of the bias field strength. They observed the dynamical instability of doubly quantized vortices in condensates for a trapping time of 80 ms. 17) On another front, a research group from Kyoto applied an optical dipole force in addition to employing the magnetic trap to suppress the deformation of condensates in the trap, and they measured the splitting of quadruply quantized vortices for approximately 10 ms. 18) Another promising method to control the deformation of condensates and perform long-term measurements of vortex dynamics involves transferring the condensates to an optical dipole force trap from the magnetic trap. In an optical trap, in contrast to the case of the magnetic trap, a magnetic field can be used as an experimentally controllable parameter, since the optical dipole force on atoms is insensitive to an external magnetic field. In addition, the optical trap liberates the inter- nal spin degrees of freedom of atoms, 19) thereby enabling the study of spinor condensates. 20,21) The spinor condensates in vortex states play important role for studying theoretically pre- dicted various topological structures such as skyrmions, 22,23) knot structures, 24) and half-quantum vortex. 25) In this study, we successfully transferred the vortex- imprinted condensates to a crossed-type optical trap from the magnetic trap. Quadruply quantized vortices were created in the magnetically trapped condensates by topological phase imprinting. The lifetime of the vortices in the magnetic trap was up to 10 ms which was approximately two times longer than that in previous study. 13) For the vortex-imprinted condensates transferred into the optical trap, the expansion of atomic cloud was considerably suppressed and vortices were observed even after 22-ms confinement. Additionally, we observed the plural vortices that were expected to be generated from the splitting of a quadruply quantized vortex. 2. Experimental The experimental setup and technique used for preparing 87 Rb Bose–Einstein condensates and a crossed-type far-off- resonant optical dipole force trap are described in detail in  Present address: Institute of Quantum Science, Nihon University, 7-24-1 Narashinodai, Funabashi, Chiba 274-8501, Japan. E-mail: kuwamoto@ phys.cst.nihon-u.ac.jp Journal of the Physical Society of Japan Vol. 79, No. 3, March, 2010, 034004 #2010 The Physical Society of Japan 034004-1