research
Driven and hybrid quantum matter - non-equilibrium, topology, and entanglement as resources.
I study driven and hybrid quantum matter at the interface of AMO and condensed-matter physics. The overarching goal is to turn the non-equilibrium, topological, and entanglement structure of quantum systems into a resource for quantum sensing, engineered quantum materials, and quantum information.
My approach combines large-scale many-body numerics (exact diagonalization (ED), Floquet ED, and DMRG / tensor-network methods) with the construction of minimal analytical models that isolate the essential physics. I also develop open-source Julia tooling for the symbolic and operator-algebra work this requires (see software).
A central object is the one-period Floquet evolution
\[U(T)=\mathcal{T}\exp\!\Bigl(-\tfrac{i}{\hbar}\int_0^T H(t)\,dt\Bigr), \qquad H_{\mathrm{eff}}=\tfrac{i\hbar}{T}\log U(T)\approx H_0+\tfrac{1}{\Omega}[H_{-1},H_{+1}]+\cdots,\]and its effective generator $H_{\mathrm{eff}}$ organized in powers of the drive frequency $\Omega$.
1. Non-equilibrium & Floquet engineering
Periodically driving a quantum system reorganizes its spectrum into quasienergy bands that need not exist in any equilibrium counterpart. In driven rotors, the angular-momentum basis acts as an angular-momentum lattice, letting us port band-topology concepts verbatim. Responses follow from band geometry, with Chern numbers
\[\nu=\tfrac{1}{2\pi}\int_{\mathrm{BZ}}\operatorname{Tr}\,\mathcal{F}[\mathcal{A}]\]when applicable. On laser-kicked molecules this lattice picture reveals Dirac cones protected by symmetry, whose topological charges control inter-band transport and leave measurable fingerprints in alignment/orientation correlators $\langle\cos\theta\rangle,\langle\cos^2\theta\rangle$. See topological charges in kicked molecules.
2. Topology of hybrid light–matter systems
Cavity and chiral-light coupling can reshape topology without an external drive. We established the bulk-boundary correspondence for graphene in a chiral cavity: every light-matter-interaction-induced gap hosts unidirectional chiral edge currents set by the band Chern number, and a universal scaling governs their dispersion, localization length, and photon distribution - a blueprint for tunable chiral channels in quantum-optical devices. See hybrid light-matter boundaries of graphene.
For multi-gap rotor Floquet systems, braiding of band degeneracies reshapes topology across gaps. These phases are characterized by frame / Euler-class structure and non-Abelian charges; nodal lines acquire quaternion-valued charges that flip under braiding, underlying anomalous multi-gap behavior on the angular-momentum lattice. See anomalous multi-gap topology.
3. Entanglement & driven-dissipative protocols
I also work on the entanglement structure of highly excited eigenstates. For local Hamiltonians with anti-commuting symmetries, extensive zero-energy nullspaces allow construction of low-entropy eigenstates with area-law scaling, connecting to many-body scars. See area-law eigenstates from nullspaces.
On the driven-dissipative side, an ensemble of polar molecules in a microwave cavity generates collective rotational-photonic cat states through a cavity Kerr nonlinearity emerging from virtual multilevel transitions, extending light-matter cat-state physics to collective molecular rotations. See collective rotational cat states.
Earlier work
Earlier I studied coupled superfluidity in 2D Bose mixtures, where inter-species vortex binding modifies BKT physics and schematically RG flows
\[\tfrac{dK_i^{-1}}{dl}\sim y_i^2+\lambda y_1y_2,\qquad \tfrac{dy_i}{dl}\sim (2-\pi K_i)\,y_i+\cdots\]predict correlated criticality and shifted transition temperatures. See coupled 2D superfluids.
Beyond quantum matter, I explored how interactions between climate/eco “tipping elements” reshape thresholds and produce cascades in networks governed by
\[\dot x_i=f_i(x_i,\mu_i)+\sum_j K_{ij}\,g_{ij}(x_j),\]informing compound-risk assessments. See cascading tipping dynamics. I also examined classical analogs of dynamical localization by discretizing phase space in kicked-rotor maps, clarifying the minimal ingredients for transport suppression. See classical localization.
Prefer the papers? See publications. The computational backbone of this work is collected in software.