Analysis of the Complex Gross-Pitaevskii Equation for the Bose-Einstein Condensation of Exciton-Polaritons

Handle URI:
http://hdl.handle.net/10754/209400
Title:
Analysis of the Complex Gross-Pitaevskii Equation for the Bose-Einstein Condensation of Exciton-Polaritons
Authors:
Núñez, Jesus
Abstract:
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.
Advisors:
Ooi, Boon S. ( 0000-0001-9606-5578 )
Committee Member:
Kasimov, Aslan; Ketcheson, David I. ( 0000-0002-1212-126X )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
Aug-2011
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorOoi, Boon S.en
dc.contributor.authorNúñez, Jesusen
dc.date.accessioned2012-02-04T08:35:14Z-
dc.date.available2012-02-04T08:35:14Z-
dc.date.issued2011-08en
dc.identifier.urihttp://hdl.handle.net/10754/209400en
dc.description.abstractConsidered 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.en
dc.language.isoenen
dc.titleAnalysis of the Complex Gross-Pitaevskii Equation for the Bose-Einstein Condensation of Exciton-Polaritonsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKasimov, Aslanen
dc.contributor.committeememberKetcheson, David I.en
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
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