A long-standing unsolved problem in condensed-matter physics is the behavior of itinerant fermions near a quantum critical phase transition. It is believed that several important physical systems, such as the cuprate- and iron-based superconductors, display such behavior. Near a QCP, low-energy excitations couple strongly to the fermions, leading to a breakdown of the quasiparticle Fermi liquid picture. In recent years I have focused on such systems near long-wavelength transitions, especially nematic transitions – where the fermions spontaneously develop a quadrupole moment over large distances. In nematic systems, the quantum dynamics of the non-Fermi liquid fermions is strongly affected by classical constraints like charge conservation, leading to unique behavior and experimental signatures.

In recent years, there has been an explosion of activity regarding the response of quantum materials (i.e. physical systems dominated by quantum effects that can't be easily described by classical analogs) to ultrafast laser excitations. Such "pump-probe" experiments can excite a quantum system non-linearly, creating a very rich dynamics. Pump-probe techniques allow us to study materials on the timescales where quantum effects dominate, and to do so in real time. Even more excitingly, these platforms also may allow us to manipulate and control quantum materials, creating ultrafast switches and quantum devices. I am interested both in the fundamental real-time properties of quantum systems excited by ultrafast techniques, and in applying these techniques to quantum control of these materials.

Superfluids are an example of a strongly-correlated bosonic system. Superfluids exhibit beautiful excitations of angular momentum – vortices in the fluid with quantized fluid velocity. These objects are very strange – they are neither very localized nor very extended, and as a result, vortices interact strongly with one another, creating a strongly-correlated system within another one! At the same time, their structure is protected by the quantization – they are topological defects. One aspect I have studied is how the nonlinear behavior of the ‘classical’ fluid affects the quantum vortex excitations. For example, the vortex core structure can deform as a result of current flow. These deformations are themselves elementary excitations of the core itself, and are similar to the quantized cyclotron orbits of in the quantum Hall effect.