Physics & Astronomy ETDs

Publication Date

8-28-2012

Abstract

This dissertation investigates the possibility of using a two-mode Bose-Einstein condensate (BEC) of N atoms to implement a nonlinear Ramsey interferometer whose detection uncertainty scales better than the optimal 1/N Heisenberg scaling of linear interferometry. Our theoretical analysis discusses several phenomena that get in the way of achieving the desired super-Heisenberg' scaling, such as the spatial degrees of freedom and the temporal evolution of the gas. Using heuristic estimates, we discuss the conditions for observing nonlinear- enhanced scalings in this system. The expansion of the condensate gets in the way of the scaling, and we deal with that by going to highly anisotropic traps. In view of realistic experimental parameters, we further investigate such issues by means of numerical simulations for a quasi-1D BEC. In this situation, there are still position-dependent phase shifts that need to be modeled precisely. This brings into question the accuracy of the quasi-1D approximation, both spatially and temporally. We study effects associated with the emergence of 3D behavior in highly anisotropic BECs. We study the ground-state properties of the gas analytically, by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined and the loosely confined directions. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the 3D Gross-Pitaevskii equation for experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. Lastly, we study the dynamics of two-mode BECs in highly anisotropic traps, also by means of perturbative techniques. We derive equations that effectively simulate the BEC interferometry protocol, which show how the corrections to the reduced- dimension approximation propagate in time and affect the dynamics of the condensate. We compare these theoretical results with the exact numerical results for the evolution of the two-mode BEC. This analysis leads to an improved model which provides a considerably refined account of the interference signal.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Advisor

Caves, Carlton

First Committee Member (Chair)

Deutsch, Ivan

Second Committee Member

Evans, Deborah

Third Committee Member

Boshier, Malcolm

Language

English

Keywords

Laser interferometry, Bose-Einstein gas, Anisotropy, Nonlinear optics.

Document Type

Dissertation

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