Research Directions
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Quantum simulation is an exciting frontier of research. Propelled by rapid advances in experimental capabilities, researchers are now close to realizing the long-sought dream of using controllable quantum systems for efficiently simulating the properties of other less controllable quantum systems. Analog quantum simulators like ultracold neutral atoms in optical lattices, polar molecules, trapped ions, and coupled atom-cavity systems provide extremely versatile platforms for tunably realizing a large variety of quantum states and Hamiltonians. On the one hand, these engineered quantum systems hold the key to resolving longstanding questions in condensed matter physics by the direct emulation of canonical models like the Hubbard model. On the other hand, they provide a promising route to realize fundamentally new many-body phases of matter, without any counterpart in other quantum materials. I am interested in exploring emergent phenomena in these unique quantum many-body systems.
I study theoretical problems at the interface of quantum condensed matter physics, quantum information science, and atomic, molecular, and optical (AMO) physics. I employ an eclectic blend of theoretical tools, ranging from analytical techniques like effective field theories, renormalization group, bosonization, and exact solutions to numerical methods like exact diagonalization, density-matrix renormalization group, and cluster expansions. While my primary motivation is to discover fundamental truths about interacting quantum systems, I am also interested in the applications of my results in quantum metrology and quantum information processing.
The first thread of my research revolves around the search for novel quantum phases of matter. I expect this to be an incessant pursuit, with projects inspired from new experimental and theoretical developments. The next thread of my research examines the dynamics of periodically driven quantum systems. These systems can often exhibit richer physics than their static counterparts, and they provide a new knob for quantum emulation. I am primarily interested in investigating new strategies to preserve quantum coherence in these systems for long times. The third theme of my research focuses on the far-from-equilibrium dynamics of quantum many-body systems. This is an exciting scientific endeavor which has attracted the attention of researchers across various communities. I anticipate that in the coming years, a lot of experimental and theoretical efforts would be directed towards addressing fundamental questions in this area. I plan to continue my research in all of these directions in the future. Additionally, I expect that the specific research projects that I will work on would be motivated by current experimental and theoretical developments.
Some of the highlights of my past and ongoing research is given below.
Quantum Phases of Ultracold Matter
Ultracold atomic gases provide a novel laboratory for the simulation of many-body quantum matter. During the course of my doctoral and post-doctoral research, I have investigated the equilibrium phases of Bose-Einstein condensates loaded in low dimensional optical lattices with unconventional geometries. I have considerable analytical and numerical expertise in modeling these systems. The predictions from my work have been experimentally verified by researchers at Hamburg and Berkeley. I have also collaborated with experimentalists at Purdue on the first realization of Bose-Einstein condensation on a synthetic topological Hall cylinder.
Periodically Driven Quantum Systems
A major focus of my research has been the study of periodically driven quantum systems (also known as Floquet systems). Periodic driving provides a powerful tool for the coherent control of quantum and ultracold matter. Floquet systems are remarkably versatile and can be used to realize quantum phases, which are inaccessible in static systems. Conceptually, however, driven systems can be rather problematic. Heating is ubiquitous in these systems and presents a major obstacle to such experiments. I have proposed several routes to evade thermalization in these systems, both in the context of ultracold atomic matter as well as discrete time crystals. These schemes provide a promising pathway to realize long-lived Floquet phases of matter.
More recently, I have investigated novel prethermal phases that can emerge in quasi-periodically driven quantum systems.
Far-from-equilibrium Quantum Dynamics
Rapid progress in the capabilities of quantum emulators has opened up a new direction of research: probing non-equilibrium quantum dynamics. This is a departure from the usual paradigm of investigating systems that are in or near thermal equilibrium. Researchers are now poised to answer fundamental questions about a variety of issues like the quantum origin of thermalization, quantum critical dynamics (where the quasiparticle concept breaks down), and universal dynamics following a quantum quench. Advances in experimental capabilities have also prompted some notable theoretical advances like the eigenstate thermalization hypothesis, the theory of many-body localization, and holographic theories of transport for strongly correlated systems. Non-equilibrium protocols like periodically driving a quantum system have also been used as an important resource for quantum simulation.
I have worked on several projects in this area. In collaboration with Prof. Erich Mueller, I have explored the dynamics of Bose-Einstein recondensation in higher bands of an optical lattice. I have collaborated with Prof. Kaden Hazzard on a study of the collective modes of ultracold fermionic gases with SU(N) symmetry. More recently, I have demonstrated that geometrically frustrated spin chains can host localized many-body eigenstates in the absence of disorder. In another collaboration with Prof. W. Vincent Liu, I have proposed a scheme to realize fast scrambling in quantum spin chains without appealing to holographic duality.
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