This thesis describes how to create and probe novel phases of matter and exotic (non-quasiparticle) behavior in cold atomic gases. It focuses on situations whose physics is relevant to condensed matter systems, and where open questions about these latter systems can be addressed. It also attempts to better understand several experimental anomalies in condensed matter systems.

The thesis is divided into five parts. The first section or chapter of each part gives an introduction to the motivation and background for the physics of that part; the last section or chapter gives an outlook for future studies. Parts 1-4 introduce and show different facets of how to learn about novel physics relevant to condensed matter using cold atomic systems. Part 5 constrains explanations of several ill-understood phenomena occurring in low-temperature quantum solids and condensed matter systems and attempts to construct mechanisms for their behavior.

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.