Quantum Phase Transitions in Cold Atoms and Low Temperature Solids 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 cla