Localised Matter-Wave States in Optical Superlattices
Optical periodic potentials (or optical lattices) are well-known for being defect-free and easy to manipulate. Recent experiments involve loading Bose-Einstein Condensates (BECs) into optical lattices. This results in a macroscopic quantum system of coherent matter waves in a periodic potential whose properties can be easily and precisely controlled. Optical superlattices (optical lattices with more than one order of periodicity) open up new gaps in the band-gap structure of the system. The properties of these new gaps can be even more easily fine-tuned. In this work we computationally model the transmission of a nonlinear localised matter wave through one-dimensional and two dimensional optical superlattices. By engineering the properties of the superlattice we hope to produce bright gap matter-wave solitons in a condensate with repulsive inter-atomic interactions. We also investigate the mobility and stability properties of dark solitons in optical superlattices and single-periodic lattices. A further field of study we will be looking at are the interactions of bright matter-wave solitons in a combined optical lattice and harmonic potential.
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Principal Investigator Elena OstrovskayaNonlinear Physics Group, RSPhysSE Australian National University |
Project x63 |
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Co-Investigators Beata DabrowskaPearl Louis Nonlinear Physics Group, RSPhysSE Australian National University |
RFCD Codes 240200 |
Significant Achievements, Anticipated Outcomes and Future Work
The APAC National Facility allowed us to look at the dynamical behaviour of localised solutions of BECs in single- and double-periodic optical lattices. Utilising a mean-field model, we demonstrated the effect of the Peierls-Nabarro potential, a "pinning" potential that arises in lattice potentials, on the mobility properties of dark solitons. We found that the properties of the Peierls-Nabarro potential can be manipulated by changing the shape of the superlattice without changing the lattice height or periodicity. This is demonstrated in examples where we control the strength of the repulsive interactions between pairs of matter-wave dark solitons in superlattices. The results from the dynamical system qualitatively match the predicted results from calculations of the Peierls-Nabarro potential using stationary solutions of the time-independent system.
We also found that bright solitons in the mini-gaps opened by the double-periodic superlattice can be created from the collision of two Gaussian wavepackets. Changing the shape of the superlattice whilst keeping the lattice height and periodicity constant allows us to control the magnitude of the effective dispersion at the edges of the mini-gaps opened by the superlattice. This in turn allows us to control the properties of the bright solitons formed by the colliding wavepackets as bright solitons are formed from the interaction of nonlinearity and dispersion. Thus we demonstrated that superlattices can be used for the dispersion management of bright matter-wave solitons.
Currently we are completing the work on the dispersion management of bright solitons in superlattices. We have also started work on the interactions of bright solitons in a combined optical lattice and harmonic potential, and on extension of the analysis of the nonlinear localisation to optical lattices in more than one spatial dimension.
Computational Techniques Used
Our dynamical simulations used a split-step method developed at the University of Otago which uses an interaction picture fourth order Runge-Kutta integration method that improves efficiency and reduces memory overhead. The code was implemented using the xmds code generator. The solution of stationary model equations in two and three spatial dimensions is performed by using Sobolev gradient descent method.
Publications, Awards and External Funding
External Funding and Awards
The project was supported by the ARC Discovery grant "Nonlinear atom optics of Bose-Einstein condensates in optical lattices" (2003-2005) and the ARC Centre of Excellence for Quantum-Atom Optics (2003-2007).
Publications
P.J.Y. Louis, E.A. Ostrovskaya and Yu S. Kivshar, Matter-Wave Dark Solitons in Optical Lattices, J. Opt. B, 2004, in press.
P.J.Y. Louis, E.A. Ostrovskaya, C.M. Savage and Yu S. Kivshar, Bose-Einstein Condensates in Optical Lattices: Band-gap structure and solitons, Phys.
Rev. A 67, 2003, 013602.
E.A. Ostrovskaya and Yu.S. Kivshar, Matter-wave gap solitons in atomic band-gap structures, Phys. Rev.
Lett. 90, 2003, 160407.