Research

My research in high-energy theoretical physics focuses on aspects of quantum gravity and holographic duality, a deep correspondence between two quantum field theories that initially seem to have very little to do with each other. On one side is a theory of quantum gravity living in a "bulk" spacetime of negative curvature called anti-de Sitter space. On the other side is a non-gravitational quantum field theory, usually with conformal symmetry, that lives on the boundary of the bulk spacetime. Here is a brief introduction to gravitational holography.

The case of 3D gravity is special: 3D spacetimes are very rigid, and pure gravity looks trivial in 3 dimensions. But upon quantization, one finds a rich variety of nontrivial effects, many of which are not fully understood. Meanwhile, the 2D boundary theory inherits an infinite set of symmetries from the bulk: here one can say and do much more than is possible in higher dimensions. My work focuses on using the 2D boundary theory and its bulk dual to better understand a toy model of quantum gravity and to extract general lessons for fundamental physics.

Holography with Conical Defects

Probing heavy states with light fields; or, In Search of Lost Temperature

In holography, the Hawking-Page phase transition describes the thermodynamic stability of black holes: it allows a thermal gas to suddenly nucleate a black hole above a certain threshold energy. To study the transition from below the threshold, one can mimic a black hole by placing a massive particle in the bulk. Not quite heavy enough to have an event horizon, such particles nevertheless bends the space around it into a cone-shaped geometry. These conical defects begin to act very much like black holes as their mass approaches the black hole threshold.

By measuring the dynamical and statistical correlations between a light "probe" field and the conical defect, one learns a great deal about the transition. Together with David Berenstein and Frazier Li, I studied these correlations both in the bulk and on the boundary. We were able to match predictions from both the bulk and boundary theories, which predict that long-range correlations of the light field are suppressed as the defect becomes more massive.

I am currently working on extending what we've done in various directions. More updates to come soon!

Causality in Holography

A wild goose chase to save causality and learn how the bulk is encoded on the boundary

Causality is the property of physical theories that prevents information from traveling faster than light. Because of how bulk information about particles and light rays is encoded on the boundary, it may look as though the boundary allows faster-than-light communication. The animation shows a particle "dragging" its boundary description, a subregion of the boundary (maroon), faster than a light ray (green) sent along the boundary to keep pace.

In a paper with my advisor David Berenstein (see also my talk), I proved that I proved that this effect arises due to the nonlocality inherent in the boundary description of the bulk physics: quantum information on the boundary is delocalized in such a way that it can jump across the boundary with infinite speed, without really being at any one point. Disaster is averted because at least one of the two boundary light signals always manages to stay inside the boundary subregion as it moves, preserving causal contact. Our work verifies that bulk and boundary causality are equivalent, rules out superluminal travel, and sheds new light on the holographic encoding of information.

Ultracold Molecules

Building the Coolest Atomic and Molecular Optics Lab in New York City

As an undergraduate at Columbia University, I worked on experimental AMO physics in Prof. Sebastian Will's group. The WillLab studies quantum gases of atoms and molecules cooled to nanokelvin temperatures, where they form Bose-Einstein condensates (BECs) that display quantum behavior on macroscopic scales. The lab has the tools to manipulate the quantum states of individual atoms, to tune their interactions, and to perform quantum simulations with the capacity to answer major questions in many-body physics. The lab synthesizes BECs of sodium (Na) and cesium (Cs), and brings them together to form Na-Cs mixtures and dipolar NaCs molecules. The lab also uses programmable arrays of optical tweezers to laser-cool, position, and manipulate individual strontium atoms. These platforms provide insight into strongly correlated quantum phases and other exotic states of matter.

I joined Prof. Will's group in the lab's early days, so much of my work went towards building the lab. I built diode lasers, aligned spectroscopy cells, did lots of soldering, and designed home-built components using CAD and a 3D printer. My first major project was to simulate and design the Zeeman slower that cools Na atoms and passes them to a MOT. I also wrote the Python code for an early version of our imaging and data analysis software. The code instructed a camera to take a sequence of absorption images of an ultracold gas cloud, fitted the data to a Gaussian model for the cloud's density, and computed the cloud's temperature and phase-space density. During my time with the group, I also gave a talk on FM spectroscopy and wrote my undergraduate thesis on the Hubbard model.