Quantum Vortex in a Vectorial Bose-Einstein Condensate

Quantum vortices in the multi-component Bose-Einstein condensation (BEC) are investigated theoretically. It is found that three kinds of the vortex configurations are possible and their physical properties are discussed in details, including the density distribution and the spin texture. By using the Bogoliubov theory extended to the three component BEC, the collective modes for these vortices are evaluated. The local vortex stability for these vortices are examined in light of the existence of the negative eigenvalue, yielding a narrow magnetization window for the local intrinsic stable region where the multi-components work together to stabilize a vortex in a self-organized way.Comment: 8 pages, 14 eps figure

Vortex phase diagram in trapped Bose-Einstein condensation

The vortex phase diagram in the external rotation frequency versus temperature is calculated for dilute Bose-Einstein condensed gases. It is determined within the Bogoliubov-Popov theory for a finite temperature where the condensate and non-condensate fractions are treated in an equal footing. The temperature dependences of various thermodynamic instability lines for the vortex nucleation are computed to construct the phase diagram. Experiments are proposed to resolve a recent controversy on the vortex creation problem associated with the quantized vortex observation in $^{87}$Rb atom gases.Comment: 11 pages, 8 figure

Axisymmetric versus Non-axisymmetric Vortices in Spinor Bose-Einstein Condensates

The structure and stability of various vortices in F=1 spinor Bose-Einstein condensates are investigated by solving the extended Gross-Pitaevskii equation under rotation. We perform an extensive search for stable vortices, considering both axisymmetric and non-axisymmetric vortices and covering a wide range of ferromagnetic and antiferromagnetic interactions. The topological defect called Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for ferromagnetic case. The phase diagram is established in a plane of external rotation Omega vs total magnetization M by comparing the free energies of possible vortices. It is shown that there are qualitative differences between axisymmetric and non-axisymmetric vortices which are manifested in the Omega- and M-dependences.Comment: 9 pages, 9 figure

Spin textures in slowly rotating Bose-Einstein Condensates

Slowly rotating spin-1 Bose-Einstein condensates are studied through a variational approach based upon lowest Landau level calculus. The author finds that in a gas with ferromagnetic interactions, such as $^{87}$Rb, angular momentum is predominantly carried by clusters of two different types of skyrmion textures in the spin-vector order parameter. Conversely, in a gas with antiferromagnetic interactions, such as $^{23}$Na, angular momentum is carried by $\pi$-disclinations in the nematic order parameter which arises from spin fluctuations. For experimentally relevant parameters, the cores of these $\pi$-disclinations are ferromagnetic, and can be imaged with polarized light.Comment: 14 pages, 12 low resolution bitmapped figures, RevTeX4. High resolution figures available from author. Suplementary movies available from autho

On the effect of the thermal gas component to the stability of vortices in trapped Bose-Einstein condensates

We study the stability of vortices in trapped single-component Bose-Einstein condensates within self-consistent mean-field theories--especially we consider the Hartree-Fock-Bogoliubov-Popov theory and its recently proposed gapless extensions. It is shown that for sufficiently repulsively interacting systems the anomalous negative-energy modes related to vortex instabilities are lifted to positive energies due to partial filling of the vortex core with noncondensed gas. Such a behavior implies that within these theories the vortex states are eventually stable against transfer of condensate matter to the anomalous core modes. This self-stabilization of vortices, shown to occur under very general circumstances, is contrasted to the predictions of the non-self-consistent Bogoliubov approximation, which is known to exhibit anomalous modes for all vortex configurations and thus implying instability of these states. In addition, the shortcomings of these approximations in describing the properties of vortices are analysed, and the need of a self-consistent theory taking properly into account the coupled dynamics of the condensate and the noncondensate atoms is emphasized.Comment: 8 page

Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates

The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards dissection into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al. Phys. Rev. Lett. 89, 190403 (2002)].Comment: 4 pages, 3 figures (to be published in PRA

Mermin-Ho vortex in ferromagnetic spinor Bose-Einstein condensates

The Mermin-Ho and Anderson-Toulouse coreless non-singular vortices are demonstrated to be thermodynamically stable in ferromagnetic spinor Bose-Einstein condensates with the hyperfine state F=1. The phase diagram is established in a plane of the rotation drive vs the total magnetization by comparing the energies for other competing non-axis-symmetric or singular vortices. Their stability is also checked by evaluating collective modes.Comment: 4 pages, 4 figure

Splitting times of doubly quantized vortices in dilute Bose-Einstein condensates

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 et al., Phys. Rev. Lett. 93, 160406 (2004)]. 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 set-up. Contrary to previous theoretical studies, claiming that thermal excitations are the essential mechanism in initiating the splitting, 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. We also study the dynamics of the resulting singly quantized vortices which typically intertwine--especially, a peculiar vortex chain structure appears for certain parameter values.Comment: 5 pages, 5 figure

Double Phase Transitions in Magnetized Spinor Bose-Einstein Condensation

It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always double BEC transitions from single component BEC to multiple component BEC. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase diagram for the temperature vs the polarization, the spatial spin structure, the distribution of non-condensates and the excitation spectrum are examined for the harmonically trapped systems.Comment: 6 pages, 7 figures. Submitted to J. Phys. Soc. Jp