Quantum Geometry and Topology
The electronic behavior of solids is governed not only by their energy spectrum but also by the geometric and topological properties of their Bloch wavefunctions – the quantum states in a crystal lattice. Topology, measured by Berry curvature and Chern number, dictates the presence of topological modes which are protected against perturbations, such as edge currents in quantum anomalous Hall insulators. By contrast, quantum geometry, quantified by measures like the quantum metric tensor (or Fubini-Study metric), describes the local structure of these Bloch states in momentum space. This “distance” between states encodes crucial information, such as a band’s spatial spread, its entanglement with remote bands, and the strength and polarization of optical transitions.
Schematic of Bloch wavefunctions varying as a function of crystal momentum
Fascinating questions arise at the intersection of quantum geometry and strong electron-electron interactions. A classic example is the Mott insulator, where strong Coulomb repulsion localizes charges in a partially filled band, making the system insulating despite band theory predicting metallic behavior. This localization typically relies on electrons occupying well-defined, compact orbitals, often described by Wannier functions—real-space orbitals constructed from Bloch states. However, this picture is made more complicated in the presence of non-trivial topology and quantum geometry, as they impose fundamental limits on how localized these Wannier orbital can be, leading to unresolved theoretical challenges. Such regimes are now experimentally accessible, notably in moiré materials. These systems host nearly flat bands where the kinetic energy is quenched, allowing Coulomb interactions and non-trivial quantum metric effects to dominate and yielding exotic phases such as fractional Chern insulators. Our group investigates the interplay between Mott localization and the delocalizing influence of quantum geometry and topology, as well as how quantum geometry shapes the response of strongly correlated systems to light [arXiv:2303.01597].
Light-Matter Coupling
Coupling materials to electromagnetic fields provides a valuable way to control and probe quantum matter. We are interested in the interplay between light-matter coupling and strong correlations in quantum materials. This is especially interesting for systems with nontrivial band geometry (see Quantum Geometry and Topology section), where the structure of Bloch wave functions enables fundamentally new optical responses in the presence of electron-electron interactions.
Schematic of engineering light-induced metastable triplet superconductors or probing competing odd-parity instabilities in conventional superconductors
In terms of control, we have studied the problem of accessing metastable correlated phases using ultrafast light pulses in the terahertz regime in [Nat Commun 15, 1776 (2024)]. For centrosymmetric superconductors with strong spin-orbit coupling, we proposed a scheme for accessing metastable triplet-pairing states starting from a conventional singlet-pairing state by optically driving a Bardasis-Schrieffer mode.
Schematic of contributions to optical conductivity scaling due to interband scattering
We also investigate novel optical responses in interacting systems enabled by quantum geometry. In such systems, electronic correlations couple the electromagnetic field to the changing character of Bloch wavefunctions, generating a novel form of light-matter interaction. This can dramatically alter the low-frequency optical properties of quantum materials. For example, this leads to a finite optical absorption for correlated metals in parabolic bands [arXiv:2504.11428], where such a response is typically assumed to vanish.
Cavity QED
The strong coupling regime of photons and quantum materials inside optical cavities has emerged as an exciting environment for manipulating states of matter with light, but not much is known about how the cavity-embedded materials affect the properties of light. By solving quantum optical input-output relations for many-body systems, our group has studied the impact to the statistics of photons transmitted through such cavities [arXiv:2411.08964]. We explain a process that we call a many-body photon blockade, in which nonlinearities introduced to the photons by interacting with cavity-embedded materials causes a tendency for transmitted photons to bunch or antibunch, as seen in coincidence measurements. This process can serve as a probe of material properties and light-induced changes to the material. In addition, we explore ways in which this process can be leveraged as a source for the efficient generation of quantum light, such as single photons or entangled pairs, with potential applications for photon-based computation and quantum sensing.
Non-Equilibrium Dynamics
Open Quantum Systems
Every quantum system is open in the sense that it has coupling to its surroundings. Often times this coupling is small enough to be negligible. For example in defining the electronic and magnetic ordering of 2D materials one tends not to think about gain and loss processes, where gaining electrons from an insulating substrate or from the air seems far fetched. Nevertheless there are scenarios where one needs to consider gain and loss: for example when a system is connected to a battery/leads current can enter and leave the system [Phys. Rev. B 50, 5528 (1994)]. Another natural platform where gain and loss is pivotal is in optical cavities, as we discuss in the Light-Matter Coupling section.
Relaxing the assumption that the substrate is insulating can have profound effects for a 1D or 2D material on top of the substrate. As we showed in [Phys. Rev. B 106, 161109 (2022)], placing a material on a substrate can generate flat bands with long quasiparticle lifetimes that could be promising to realize interaction driven physics. In [npj Quantum Materials 9, 104 (2024)] we developed a general formalism to probe the responses of these open quantum systems with applications to fermionic, bosonic, and spin systems. Finally, open quantum systems reach into the realm of devices simulating quantum physics where in [Phys. Rev. B 108, 104310 (2023)] we considered the statistical mechanics of quantum circuits.
Floquet Engineering
Tailoring the properties of quantum materials on demand is a central goal of condensed matter physics. Over the past decade, Floquet engineering has emerged as a pathway to modulate material properties on ultrafast timescales. Here a strong drive, such as an intense laser pulse, is used to coherently tune quantum states. We are especially interested in Floquet engineering strongly correlated materials. For example, we investigate how driving can stabilize novel phases such as quantum spin liquids [Nat Commun 8, 1192 (2017), Phys. Rev. Research 4, L032036 (2022), arXiv:2412.03777] and alter optical responses in Mott insulators [forthcoming work]. This work is motivated by and in close collaboration with several experimental groups.