Research
As a theoretical physicist, I have conducted research broadly centered on quantum information science and condensed matter physics. My interests include problems of direct experimental relevance, such as how to realize components of a quantum computation architecture in particular physical systems, and how to control them efficiently. It also includes more formal, mathematical problems: the generation and structure of entanglement in quantum systems, phase transitions, topological insulators, disorder, and topological superconductors.
Such a wide variety of problems demands a wide variety of techniques. Formal, mathematical problems will often admit elegant analytical solutions or partial solutions. Other problems may not be as easily expressed formally, but are amenable to phenomenological approaches or numerical simulations. Even if only to validate analytical results, clarify the precise statement of the problem, or gain intuition from small example cases, numerics are indispensable. I have often found that an important step in research is recognizing the boundaries of the utility of each of these approaches within research, and I am comfortable with both.
During my postdoc at Virginia Tech, I have worked in the groups of Prof. Sophia Economou and Prof. Edwin Barnes. We have investigated candidate quantum systems to support the generation of highly entangled photonic states (known as cluster states) for use in quantum computing and quantum communications. We have designed approaches for generating such states from emitters such as trapped ions, self-assembled quantum dots, and defect color centers in, e.g., SiC or diamond. In my two recent first-author papers [1,2], we develop protocols to guide experimentalists toward the generation of such states. I have also supported research [3] that provides a geometrical framework for visualizing driving fields used for dynamically corrected single-qubit operation.
During this postdoc, I have also worked on problems in topological insulators, specifically on the question of how spinful impurities lift the topological protection of edge modes by breaking time-reversal symmetry and thus give rise to backscattering. We have published two long papers addressing this question [4,5]. In my first-author paper [4], I showed how the symmetries of the system can be leveraged to dramatically simplify the problem analytically, thereby exponentially reducing the difficulty of obtaining the eigenstates while retaining the full quantum degrees of freedom of the impurities. This allowed me to solve the transport problem numerically for a large number of impurities, and to then use a scaling analysis to extrapolate the results to the mesoscopic systems encountered experimentally [4].
During my graduate studies with my PhD advisor, Prof. Sudip Chakravarty, I investigated topologically nontrivial phases of matter, and the effects of disorder at the quantum scale. In Ref. [6] we explored the phase diagram of a chiral superconductor with longer-ranged interactions, characterizing the behavior near magnetic flux vortices, and, in particular, identifying the presence (and number) of Majorana modes. In another paper [7] we recognized that, because charge density wave order in the under-doped regime cuprates breaks translation and a \(\mathbb{Z}_2\) symmetry, the charge order can be treated with an Ising model. Following this thread through a sophisticated numerical simulation, we were able to identify a novel non-Fermi liquid, and provide constraints to models describing the pseudogap regime.
My postdoctoral work has been in a significantly different field than
my doctorate work, and I have enjoyed the transition. I consider some of
my key strengths to be the breadth of research problems I have tackled,
my analytical mathematical abilities, and my sophisticated computational
expertise. As a result of this skillset I am very comfortable and
interested in exploring new areas of condensed matter and quantum
information science, as well as combining the two.