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arXiv:cond-mat/0112176 · Journal of Optics B Quantum and Semiclassical Optics

Vortices in atomic-molecular Bose-Einstein condensates

Tristram J. Alexander, Elena A. Ostrovskaya, Yuri S. Kivshar, Paul S. Julienne

Published Feb 1, 2002• 25 citations
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Abstract

The structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates is analysed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process. New types of topological vortex states are predicted to exist in the coherently coupled two-component condensates even without a trap, and their nontrivial dynamics in the presence of losses is demonstrated.

DOI
10.1088/1464-4266/4/2/365

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The structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates is analysed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process. New types of topological vortex states are predicted to exist in the coherently coupled two-component condensates even without a trap, and their nontrivial dynamics in the presence of losses is demonstrated.
Abstract We propose a theoretical framework, based on the two-component Gross–Pitaevskii equation (GPE), for the investigation of vortex solitons (VSs) in hybrid atomic–molecular Bose–Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential. Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration, while the temporal dynamics are simulated using the fourth-order Runge–Kutta algorithm. The analysis reveals stable rhombus-shaped VS shapes with topological charges m = 1 and 2 of the atomic component. The stability domains and spatial structure of these VSs are governed by three key parameters: the parametric-coupling strength ( χ ), atomic-molecular interaction strength ( g 12 ), and the optical-lattice potential depth ( V 0 ). By varying χ and g 12 , we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes, highlighting the nontrivial nonlinear dynamics of the system. This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.
We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
Abstract We study the coupled atomic–molecular quantized ring vortices of 87 Rb Bose–Einstein condensates trapped in a rotating 3D anisotropic cylindrical trap using both time-independent and time-dependent Gross–Pitaevskii approaches. For atomic to molecular conversion and vice versa, a two-photon Raman photoassociation scheme has been used. Atomic and molecular stationary state solutions show that the different number of nodes and crests formed in the density profile (as a function of r and z ) for different combinations of radial ( n ) and axial ( n z ) quantum numbers at a fixed azimuthal quantum number l = 2, give rise to different structures around the 3D ring vortex centered at r = 0. We have considered both spontaneous and induced decays and compared the results with those without considering the decays. The out-of-phase oscillation of atomic and molecular numbers in two vortex states, both in the presence and absence of external decays, is the signature of coherence due to the atomic–molecular coupling. This coherence is also implemented in the evolution of coupled atomic and molecular vortices. The intensity of molecular ring vortices grows with time at the expense of that of atomic ring vortices, and vice versa. It is found that the intensity of the coupled atomic and molecular ring vortices starts to oscillate out of phase during evolution. Dependence of the atomic–molecular conversion efficiency and the lifetime of the system on the laser intensity of photoassociation lasers and the total number of atoms in two different vortex states reveals that the formation of atomic–molecular coupled vortices and the efficiency of formation can be controlled by varying these parameters. Linear stability analysis of vortex states as a function of different system parameters shows that the atomic vortices are more stable than molecular vortices, and the stable atomic and molecular vortices can be achieved by controlling these parameters.
We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of 87Rb^{87}\text{R}\text{b}87Rb in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter ${x}_{pk}\ensuremath{\ge}{10}^{\ensuremath{-}3}$. We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of 85Rb^{85}\text{R}\text{b}85Rb. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.