The first part of this thesis describes the behavior of ultracold atoms confined in a rotating optical lattice. We consider gases of strongly-interacting bosons and non- interacting fermions in ring and square lattice geometries. We derive modified Hubbard models to describe the gas and use the quasi-angular momentum (QAM) representation to label the eigenstates. Exact level crossings between states of different QAM are predicted. We identify signatures of these transitions in the momentum distribution, indicating that these states should be distinguishable in time-of-flight experiments.
The second part of this thesis describes a scheme for nondestructively probing the dynamics of atoms in optical lattices by coupling to the modes of an optical resonator. The cavity fields set up both the optical lattice and the probe field so that no external interrogation fields are necessary. The probe is weak so that the atoms can be continuously monitored without affecting the atomic motion. This scheme is applied to a measurement of Bloch oscillations; SNR\textquoterights as high as 104 are predicted.
In the third part of this thesis, we study the dynamics of atoms in a tilted lattice near the Mott-insulator regime. The dynamics involve the creation and annihilation of dipoles, states generated from the unit-filled states by introducing defects where an atom has hopped exactly one site to the left. We describe how these states can be experimentally distinguished by coupling the atoms to the modes of an optical cavity.
Finally, we describe a quantum non-demolition measurement of the cavity photon number using Raman interferometry of atoms coupled to the cavity modes. Using Bayesian inference, we show that there is a measurement protocol for which the cavity photon number can be determined with just a few measurements.
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}, year = {2010}, publisher = {University of Colorado Boulder}, address = {Boulder}, }