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Conference on Lasers and Electro-Optics

Vortex-antivortex labyrinth wavefunction

A. Yu. Okulov

Published Jan 1, 2008• 0 citations
Publisher

Abstract

We discuss a possibility of a pinning of quantized matter wave vortices by optical vortices in specially arranged optical dipole traps. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum to support ldquoantiferromagnet-likerdquo matter waves. The separable Hamiltonian for matter waves is proposed which allows to factorize of the 3D -wavefunction exactly in a product of 1D - harmonic oscillatorpsilas ground state and 2D - vortex-antivortex wavefunction. The wavefunctionpsilas phase gradient field associated with the field of classical velocities via Madelung transformation forms labyrinth-like structure. The macroscopic wavefunction of periodically spaced BEC superfluid vortices appears to be less influenced by decoherence.

DOI
10.1109/qels.2008.4553111

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Roeland Geurts, M. V. Miloševıć, François Maria Peeters

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arXiv:0810.4403•Physical Review A•Nov 5, 2008•12 citations
We discuss a possibility of a pinning of quantized matter wave vortices by optical vortices in specially arranged optical dipole traps. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum to support ldquoantiferromagnet-likerdquo matter waves. The separable Hamiltonian for matter waves is proposed which allows to factorize of the 3D -wavefunction exactly in a product of 1D - harmonic oscillatorpsilas ground state and 2D - vortex-antivortex wavefunction. The wavefunctionpsilas phase gradient field associated with the field of classical velocities via Madelung transformation forms labyrinth-like structure. The macroscopic wavefunction of periodically spaced BEC superfluid vortices appears to be less influenced by decoherence.
We discuss a possibility of a pinning of quantized matter wave vortices by optical vortices in specially arranged optical dipole traps. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum to support "antiferromagnet-like" matter waves. The separable Hamiltonian for matter waves is proposed which allows to factorize of the 3D - wavefunction exactly in a product of 1D - harmonic oscillator's ground state and 2D - vortex-antivortex wavefunction. The wavefunction's phase gradient field associated with the field of classical velocities via Madelung transformation forms labyrinth-like structure. The macroscopic wavefunction of periodically spaced BEC superfluid vortices appears to be less influenced by decoherence.
A mechanism of a pinning of the quantized matter wave vortices by optical vortices in a specially arranged optical dipole traps is discussed. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum and form the “antiferromagnet”-like matter waves. The separable Hamiltonian for matter waves in pancake trapping geometry is proposed and 3D-wavefunction is factorized in a product of wavefunctions of the 1D harmonic oscillator and 2D vortex-antivortex quantum state. The 2D wavefunction’s phase gradient field associated via Madelung transform with the field of classical velocities forms labyrinth-like structure. The macroscopic quantum state composed of periodically spaced counter-rotating BEC superfluid vortices has zero angular momentum and nonzero rotational energy.
Singular optical beams have been studied for many years after the pioneering work where the wave function of the laser radiation is presented as a steady-state solution of the wave equation for a harmonic oscillator. A major step in understanding the nature of singular beams has been made by introducing the concept of the angular momentum of light and analyzing local energy transfer in a vortex beam. It is now well accepted that the orbital angular momentum of light is an intrinsic feature of the optical vortex. However, the orbital angular momentum was always analyzed for travelling modes and the important issue of the orbital angular momentum associated with standing waves still remains open. The main motivation of our work is to reveal the structure of the orbital angular momentum in a standing wave formed by the counter-propagating optical vortices and study its suitability for an optical trapping and guiding. In this work we show that a superposition of two (or more) vortex beams generates a field structure which has a form of a standing wave in both the radial and longitudinal directions, but it is rotating simultaneously along the tangential direction. We demonstrate that then field of this optical vortex structure could be used as an optical trap and simultaneously transfer the angular momentum of the electromagnetic wave to an object inside the area of vortex localisation. We believe this study provides a basis for developing a novel concept of three-dimensional optical traps where vortices could be created in a local volume by a direct transfer of the angular orbital momentum of the electromagnetic wave to trapped objects.
Superfluids with strong spatial modulation can be experimentally produced in the area of cold atoms under the influence of optical lattices. Here we address 87Rb^{87}\mathrm{Rb}87Rb bosons at T=0T=0T=0 K in a flat geometry under the influence of a periodic potential with the Gross-Pitaevskii theory. The statics and dynamics of vortex excitations are studied in the case of one-dimensional (1D) and of two-dimensional (2D) optical lattices, as function of the intensity of the optical lattice. We compute how the vortex energy depends on the position of its core and the energy barrier that a vortex has to surmount in order to move in the superfluid. The dynamics of a vortex dipole, a pair of vortices of opposite chirality, differ profoundly from the case of a uniform superfluid. In the 1D case, when parallel ridges of density are present, the dynamics depends on the positions of the two vortices. If they are in the same channel between two ridges, then the two vortices approach each other until they annihilate each other in a short time. If the two vortices are in distinct channels, the dipole undergoes a rigid translation but with a velocity depending on the intensity of the optical lattice and this translation velocity can even change sign with respect to the case of the uniform superfluid. Superimposed on this translation an oscillatory motion is also present. A superposition of translation along a channel and an oscillation is also found with a single vortex when the system is bounded inside a circular trap. These oscillatory motions can be both longitudinal, i.e., along the channel, as well as transverse. In all cases the transverse motions are one sided, in the sense that the vortex core never crosses the equilibrium position nearest the starting position. In the case of the 2D lattices we study (square, triangular, and honeycomb), the two vortices of a dipole move mainly by jumps between equilibrium positions and approach each other until annihilation. This behavior has some similarity with what has been found for a vortex dipole in the supersolid state of dipolar bosons. We show that a rapid ramp down of the optical potential improves the visibility of the density holes at the vortex core.
In a numerical experiment based on Gross-Pitaevskii formalism, we demonstrate unique topological quantum coherence in optically trapped Bose-Einstein condensates (BECs). Exploring the fact that vortices in a rotating BEC can be pinned by a geometric arrangement of laser beams, we show the parameter range in which vortex-antivortex molecules or multiquantum vortices are formed as a consequence of the optically imposed symmetry. Being low-energy states, we discuss the conditions for spontaneous nucleation of these unique molecules and their direct experimental observation, and provoke the potential use of the phase print of an antivortex or a multiquantum vortex when realized in unconventional circumstances.