Instability in a cold atom interferometer

In this thesis we present a theoretical anaylsis of the instability in a cold atom in-terferometer. Interferometers are often used to split a signal (e.g. optical beam, matter wave), where each part of the signal evolves separately, then the interferom-eter recombines the signal. Interference eects from the recombination can be used to extract information about the dierent environments that the split signal tra-versed. The interferometer considered here splits a matter wave, the wave function of a Bose-Einstein Condensate, by using a guiding potential and then recombines the matter wave. The recombination process is shown to be unstable and the nature of the instability is characterized. Acknowledgements It’s been a pleasure working with my advisor Professor Zozulya. He has taught me, or more precisely, re-taught me quantum mechanics from scratch. Before meeting him, a "ket " or a "bra " seemed like an unholy and unnecessary abstraction. Now, I am loathe to write down an actual function, and am perfectly happy living in