Monica Allen: Information-theoretic Entropy Imaging of Quantum Matter
Date: THURSDAY, October 29th, 2026
Location: Elings Hall, 1601
Time: 12:30 PM
Information-theoretic entropy imaging of quantum matter
Abstract: Microscopy has made states of matter visible as spatial objects, revealing where domains nucleate, how phase boundaries move, and when conducting pathways connect. Yet quantitative measures of this organization remain limited. In this talk, I will discuss two new approaches that extend the information accessible through microscopy of quantum materials. First, I will describe layer-resolved microwave impedance microscopy, a technique that images quantum electronic states on individual atomic planes within van der Waals heterostructures at temperatures down to 50 mK. Applied to double- layer graphene, this technique reveals how charge disorder varies between layers and how electrostatic screening influences fragile fractional quantum Hall states.
I will then turn from resolving spatial structure to quantifying its complexity. Drawing upon the toolbox of information theory, I will introduce "entropy imaging," an approach that uses lossless data compression to quantify spatial complexity, predictability, and order in real-space images of quantum materials. Repeated motifs can be encoded compactly, while less predictable patterns require longer descriptions. In graphene, this technique reveals a pronounced maximum in spatial complexity near the quantum Hall critical point, where isolated conducting regions evolve into an extended network. A disordered Hofstadter model reproduces this behavior, and the same framework tracks fractional quantum Hall transitions and resolves fractional puddles. Together, these results illustrate how combining new forms of microscopy with information-theoretic analysis can reveal the spatial organization underlying quantum phenomena.
Bio: Monica Allen is an Assistant Professor of Physics at the University of California, San Diego. Her research combines scanning probe microscopy, electronic transport, and nanofabrication to investigate correlated and topological states in quantum materials. Her group develops microwave imaging techniques that operate at millikelvin temperatures to visualize electronic phases and their spatial organization. She received her B.A. and Ph.D. in Physics from Harvard University and was a Karel Urbanek Postdoctoral Fellow in Applied Physics at Stanford University before joining UC San Diego. She is a recipient of the NSF CAREER Award and the Air Force Office of Scientific Research Young Investigator Award.
