Atom Laser Modelling Controlling Bose-Einstein Condensates

Significant Achievements, Anticipated Outcomes and Future Work

This work has examined the stability of semiclassical models of atom lasers. A previous project showed that atom lasers were unstable unless the interactions between the atoms were sufficiently strong. We extended this work to include spatially selective pumping as well as non-zero interactions in a pumped and damped atom laser. The spatially dependent pumping allowed the system to be stable for a wider range of interactions. After that, it becomes unstable and evolves into an excited state. This work was published in Physical Review A. As spatially selective pumping schemes are difficult to produce and atomic interactions will increase the quantum noise of the system, we developed a model for using feedback to stabilise the state of a BEC. This model was implemented numerically, showing that our scheme allowed the system to always evolve towards the ground state. We characterised the efficiency of the system, and also published this work in Physical Review A. The future of this work will be to combine the two models and examine how the feedback scheme can stabilise the system in the presence of pumping and damping. This should dramatically improve the parameter regime in which stability can be achieved.

This project also provided support for other research programs in our group, including stochastic field simulations of atomic fields and the analysis of experimental atom laser results.

Computational Techniques Used

This project used the computational package XMDS (www.xmds.org) to integrate (possibly stochastic) partial differential equations in various numbers of dimensions. XMDS is a code generator that allows a high level description of a field problem to be automatically written in C++ code and then compiled using specialist compilers on a range of platforms. It contains several algorithms, the most commonly used being a fourth order Runge-Kutta integration where derivatives are calculated spectrally using a Fast Fourier Transform. This algorithm is memory efficient and fast. It is described fully in the documentation on the website. One of the supplementary results of this project has been development of this open source package.

The package uses the MPI version of FFTW to perform the calculations across multiple processors. When stochastic partial differential equations are used, the parallelisation is between different realisations of the integration. On the SC, the first type of integration is close to 100% efficient within a node. The second, more "embarrassingly parallel" method is essentially 100% efficient on the LC cluster.

Publications, Awards and External Funding

External Funding and Awards

This work was part of a project within the ARC Centre of Excellence for Quantum-Atom Optics. This Centre, formed in 2003, provided the salary for the Project PI and local computing facilities.

Publications

S.A.Haine and J.J.Hope, "Mode Selectivity and Stability of Continuously Pumped Atom Lasers", Phys. Rev. A, 68, 2003, 023607.
S.A.Haine, A.J.Ferris, J.D.Close and J.J.Hope, "Control of an atom laser using feedback", Phys. Rev. A, 69, 2004, 013605.
N.P. Robins, J.E. Lye, C.S. Fletcher, S.A. Haine, J. Dugue, C. Breme, J.J. Hope and J.D. Close, "Dynamical Effects of Backcoupling on an Atom Laser", Proceedings of the International Conference on Laser Spectroscopy, Palm Cove, Queensland (2003).