Demonstrating Superpositions in Double-Well Bose-Einstein Condensates

Tania Haigh (2010). Demonstrating Superpositions in Double-Well Bose-Einstein Condensates MPhil Thesis, School of Mathematics & Physics, The University of Queensland.

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Author Tania Haigh
Thesis Title Demonstrating Superpositions in Double-Well Bose-Einstein Condensates
School, Centre or Institute School of Mathematics & Physics
Institution The University of Queensland
Publication date 2010-05
Thesis type MPhil Thesis
Supervisor Dr. Murray Olsen
Assoc. Prof. Matt Davis
Total pages 56
Total colour pages 5
Total black and white pages 51
Subjects 01 Mathematical Sciences
Abstract/Summary This thesis considers measurements that could be used to verify the existence of a coherent superposition, using the specific example of a superposition of a Bose-Einstein condensate in a double-well. There is significant interest in superposition states in atomic condensates, due to the possibility of large numbers of atoms being involved in the superposition, and while various experimental proposals exist for generating such states none have yet been successfully verified in this system. We use a number-state description of the condensate in a double well, which is a number-conserving approach with basis states specifying the number of atoms in each well. This allows us to consider 'NOON`-type states, i.e. a superposition of the 'N,0' state of all atoms localized in the left well and the '0,N' state where all N atoms are localized in the right hand well. MATLAB is used to solve for the ground state, dynamics, and measurement expectation values for the double-well condensate in this basis. We consider measurements that would distinguish this coherent superposition from a statistical mixture of the same states. Such a suitable measurement is the parity of the atoms in one well, after a Ramsey-type interference experiment has been performed. We have found that unambiguously distinguishing even a perfect 'NOON' state from a statistical mixture using standard detection methods will present experimental difficulties. We find that interactions between condensate atoms degrade the visibility of the parity oscillations, and we also consider the effects of detector inefficiency on these parity measurements. We suggest that a 'NOON'-type superposition state in the double-well system could be generated in a reasonable time frame by making use of a Feshbach resonance to tune the inter-atomic interactions from repulsive to negative. We find that even with imperfect superpositions, parity measurements retain their frequency dependence, which is the signature of NOON-type coherence.
Keyword Bose-einstein Condensate
superposition state
Additional Notes Colour pages: 26, 35, 36, 37, 43

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Created: Tue, 16 Nov 2010, 14:36:13 EST by Miss Tania Haigh on behalf of Library - Information Access Service