The primary focus of this thesis is to theoretically describe
nanokelvin experiments in cold atomic gases, which offer the
potential to revolutionize our understanding of strongly correlated
many-body systems. The thesis attacks major challenges of the
field: it proposes and analyzes experimental protocols to create
new and interesting states of matter and introduces theoretical
techniques to describe probes of these states. The phenomena
considered include the fractional quantum Hall effect, spectroscopy
of strongly correlated states, and quantum criticality, among
others. The thesis also clarifies experiments on disordered quantum
solids, which display a variety of exotic phenomena and are
candidates to exhibit so-called "supersolidity." It collects
experimental results and constrains their interpretation through
theoretical considerations. This Doctoral Thesis has been accepted
by Cornell University, Ithaca, USA.
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