Considered as a fundamental step for the development of the atomic laser and
quantum computing, as well as the theoretical explanation of super fluidity, the Bose-
Einstein condensate (BEC) has emerged as one of the most important topics in modern
physics.
This project is devoted to the analysis of a condensate based on exciton-polaritons.
This BEC is characterized by a high critical temperature of condensation (about 20
K) and non-equilibrium dynamics. A mathematical model called complex Gross-
Pitaevskii equation (cGPE) is used to describe its behavior.
The steady state solutions of the cGPE are studied and a numerical method based
on a collocation method is proposed in order to find these solutions. Once the steady
state solutions are found, a linear stability analysis is performed, demonstrating that
the steady state solutions become unstable as the pumping spot radius increases.
Finally, the manifestations of these instabilities are analyzed by direct simulation of
the cGPE, using a second order time-splitting spectral method. As a result, it is
possible to see the formation of quantum vortices, which increase in number as the
pumping spot radius increases.
| Date of Award | Aug 2011 |
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| Original language | English (US) |
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| Awarding Institution | - Computer, Electrical and Mathematical Sciences and Engineering
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| Supervisor | Boon Ooi (Supervisor) |
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