Longitudinal Atom Optics : Measuring the Density Matrix of a Matter Wave Beam by Richard Alan Rubenstein

This thesis describes recent developments of theoretical and experimental techniques for longitudinal atom optics and interferometry, in which time-dependent interactions are used to create coherences in the longitudinal momentum of a matter wave. We present a fully quantum mechanical treatment of the classic molecular beams resonance experiment, a beam of two state particles interacting with temporally oscillating potentials, showing that such oscillatory potentials shift not only the internal state, but also the momentum of an incident matter wave. Amplitude modulation of a matter wave adds coherent momentum sidebands within a single internal state. Two successive differentially detuned separated oscillatory fields (DSOF) can be used to detect a pre-existing momentum superposition or create one that rephases downstream. Phase modulation also generates coherent momentum sidebands which can rephase into amplitude modulation at a sufficient distance downstream. We employed a DSOF longitudinal atom interferometer to search for off-diagonal density matrix elements produced by a supersonic atom source. This search placed a stringent upper bound on the size of the off-diagonal matrix elements which could have been present within the limits of our search, effectively ruling out the existence of coherent wavepackets in the beam in this range. The DSOF interferometer, along with a novel deconvolution method, was used to measure the density matrix of a longitudinally modulated atomic beam which possessed complicated structure both along and off the diagonal. The results of this experiment, the first to determine the longitudinal quantum state of a matter wave beam, are compared with theoretical predictions. Thesis Supervisor: David E. Pritchard Title: Professor of Physics