Multicomponent Bose-Einstein Condensates in Optical Lattices
The recent strong interest in photonic crystals is due to their remarkable ability to guide and control light. This ability combined with the effects of nonlinearity results in many new phenomena, such as the so-called 'gap solitons'. If in addition the effects of energy flow are considered in the material then stationary states of light such as discrete vortices may also exist. These are general phenomena, occuring not just in nonlinear light propagation in photonic crystals but in any nonlinear wave propagation in the presence of a periodic potential. As such, understanding the behaviour of the fundamental states in periodic systems, such as discrete vortices, has a broad application to many fields - from nonlinear optics to Bose-Einstein condensation.
|
Principal Investigator Tristram AlexanderOptical Sciences Centre, RSPhysSE Australian National University |
Project x67 |
RFCD Codes 240201
|
Significant Achievements, Anticipated Outcomes and Future Work
The results to date include the demonstration of strong stabilization of an optical vortex by a lattice in a two-dimensional self-focusing nonlinear medium. These results provided the theoretical analysis underpinning the first experimental observation of a discrete vortex. The numerical work performed on the APAC National Facility included a study of the generation of discrete vortices from a wide-class of singular beams and demonstrated the key importance of both the size and shape of the input vortex beam, and its position relative to the lattice, on the ensuing vortex dynamics. In particular two important classes of discrete vortices were identified, the "on-site" and "off-site" vortex solitons, centered on and off the lattice maxima respectively. The fundamental mechanism of vortex soliton existence was identified as a balance of energy flows around the vortex core. This energy balance condition led to the discovery of the first examples of "asymmetric" vortices which no longer possess the full symmetry of the underlying lattice. Examples of these vortices are rectangular, rhomboidal and even triangular in form. The nonlinearity was found to be a key mechanism preserving the rotational energy flow of these vortices. With a weak nonlinearity the locking of the vortex phase could be lost and the vortex would instead exhibit "charge-flipping" in which the energy flow would completely reverse its circulation direction.
Future work seeks to provide a theoretical basis for observing these asymmetric vortices and charge-flipping effects experimentally. This involves numerical studies of the vortex dynamics and generation in nonlinear media. Further work will examine the new effects associated with parametrically coupled vortices. Novel vortex phenomena such as non-integer topological charge and vortex algebra are expected to be found.
Computational Techniques Used
This project uses two sets of algorithms. A conjugate-gradient method is used to obtain two-dimensional asymmetric stationary solutions. The method involves minimizing an appropriate functional to find excited state solutions and requires predominantly the use of Fast Fourier Transforms (FFTs) to calculate gradients and derivatives. The particular package FFTW is used for this.
FFTs are also used in the second routine of this project, the time evolution of multidimensional initial input conditions. This beam propagation routine uses a split-step propagation algorithm involving the Fourth-Order Runge-Kutta method for advancing the nonlinear part of the equations and solving the linear part using FFTW.
Publications, Awards and External Funding
External Funding and Awards
None
Publications
D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk and Z. Chen, Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices, Physical Review Letters, 92, 2004