Research Directions

We develop theories in and out of equilibrium to be tested on various quantum information platforms, utilize tensor networks for computationally intensive numerical simulations and currently collaborate with experimental groups in cold atoms and superconducting circuits. We also remotely operate a commercially available Rydberg atom array analog simulator. 

For time-independent and periodically driven quantum systems, spectral statistics have proven powerful to analyze the universal features that originate from the correlations between (quasi-)energy levels. We utilize random matrix theory (RMT) to capture such universal features, and investigate new routes to universality in chaotic systems that can go beyond the RMT. Many-body chaotic systems also (i) thermalize local observables, which is typically explained in the framework of eigenstate thermalization hypothesis, and (ii) scramble information, which is the spread of spatio-temporal correlations across the many-body system and typically probed with out-of-time-order correlators or tripartite mutual information. We study such dynamical processes in quantum many-body systems including random quantum circuits and prototypical condensed matter models to characterize and understand these complex quantum systems better,  and on the quantum simulators to benchmark these NISQ (noisy intermediate scale quantum) era devices. We are currently exploring topics to bridge quantum many-body dynamics and quantum thermodynamics. 

A motivation behind characterizing many-body quantum chaos and its timescales is finding the ways to break ergodicity and stabilize a localized phase of matter. This is not only interesting from a fundamental perspective, but also the localized degrees of freedom in many-body systems could be leveraged to encode and store quantum information. There are different mechanisms to break ergodicity. We currently focus on quantum scarring. Quantum scars, introduced within the context of single-particle billiard model in 1984, are quantum eigenstates with an enhanced probability density around an unstable periodic orbit (UPO) in a chaotic phase space. We have been extending this concept to many-body realm, and utilizing time-dependent variational principle to invoke classical-quantum correspondence in many-body quantum dynamics.

Coupling photonic cavity fields to electronic degrees of freedom in 2D materials introduces an additional control knob to the toolbox of solid-state engineering. Hence the cavity-QED engineering of quantum materials has emerged as a powerful tool to manipulate the phases of quantum matter. We primarily focus on graphene monolayer and its stacks subject to enhanced vacuum fluctuations and apply both analytical and numerical methods to understand the nature of these hybrid systems. We also have a special interest in chiral cavities that can break time-reversal symmetry in quantum materials.