Zubin Jacob gives invited talk at Rice University quantum seminar “New directions in quantum sensing: Photonic spin density and atomistic topological electrodynamics”.

Nitrogen vacancy (NV) centers in diamond have emerged as promising room temperature quantum sensors for probing condensed matter phenomena ranging from spin liquids, 2D magnetic materials ,and magnons to hydrodynamic flow of current. Here, we propose and demonstrate that the nitrogen-vacancy center in diamond can be used as a quantum sensor for detecting the photonic spin density. We exploit a single spin qubit on an atomic force microscope tip to probe the spinning field of an incident Gaussian light beam. The spinning field of light induces an effective static magnetic field in the single spin qubit probe. We perform room-temperature sensing using Bloch sphere operations driven by a microwave field (XY8 protocol). This nanoscale quantum magnetometer can measure the local polarization of light in ultra-subwavelength volumes. We also put forth a rigorous theory of the experimentally measured phase change using the NV center Hamiltonian and perturbation theory involving only virtual photon transitions. The direct detection of the photonic spin density at the nanoscale using NV centers in diamond opens interesting quantum metrological avenues for studying exotic phases of photons, nanoscale properties of structured light as well as future on-chip applications in spin quantum electrodynamics (sQED)

We also propose to identify and search for atomistic topological electrodynamic phases of matter using quantum sensing. Over the past three decades, graphene has become the prototypical platform for discovering unique phases of topological matter. Both the Chern C∈Z and quantum spin Hall υ∈Z2 insulators were first predicted in graphene, which led to a veritable explosion of research in topological materials. We introduce a new topological classification of two-dimensional matter – the optical N-phases N∈Z. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor χ. We verify N= 2 in graphene with the underlying physical mechanism being repulsive Hall viscosity. An experimental probe, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, is proposed to demonstrate this repulsion. To conclude, we develop topological circulators by exploiting gapless edge plasmons that are immune to back-scattering and navigate sharp defects with impunity. Our work indicates the optical N-invariant is a universal property that captures topological electrodynamic physics beyond graphene.

**See also:**Atomistic Topological Electrodynamics