We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals, metamaterials and 2D materials, by utilizing the Dirac-Maxwell correspondence. We start by exploring the vacuum where the reciprocal momentum space of both Maxwell’s equations and the massless Dirac equation (Weyl equation) possess a magnetic monopole. The critical distinction is the nature of magnetic monopole charges, which are integer valued for photons but half-integer for electrons. This inherent difference is directly tied to the spin and ultimately connects to the bosonic or fermionic behavior. We also show the presence of photonic Dirac strings, which are line singularities in the underlying Berry gauge potential. While the results in vacuum are intuitively expected, our central result is the application of this topological Dirac-Maxwell correspondence to 2D photonic (bosonic) materials, as opposed to conventional electronic (fermionic) materials. Intriguingly, within dispersive matter, the presence of photonic Dirac monopoles is captured by nonlocal quantum Hall conductivity–i.e., a spatiotemporally dispersive gyroelectric constant. For both 2D photonic and electronic media, the nontrivial topological phases emerge in the context of massive particles with broken time-reversal symmetry. However, the bulk dynamics of these bosonic and fermionic Chern insulators are characterized by spin-1 and spin-½ skyrmions in momentum space, which have fundamentally different interpretations. This is exemplified by their contrasting spin-1 and spin-½ helically quantized edge states. Our work sheds light on the recently proposed quantum gyroelectric phase of matter and the essential role of photon spin quantization in topological bosonic phases.

Topological phases of matter arise in distinct fermionic and bosonic flavors. The fundamental differences between them are encapsulated in their rotational symmetries—the spin. Although spin quantization is routinely encountered in fermionic topological edge states, analogous quantization for bosons has proven elusive. To this end, we develop the complete electromagnetic continuum theory characterizing 2+1D topological bosons, taking into account their intrinsic spin and orbital angular momentum degrees of freedom. We demonstrate that spatiotemporal dispersion (momentum and frequency dependence of linear response) captures the matter-mediated interactions between bosons and is a necessary ingredient for topological phases. We prove that the bulk topology of these 2+1D phases is manifested in transverse spin-1 quantization of the photon. From this insight, we predict two unique bosonic phases—one with even parity C = ±2 and one with odd C = ±1. To understand the even parity phase C = ±2, we introduce an exactly solvable model utilizing nonlocal optical Hall conductivity and reveal a single gapless photon at the edge. This unidirectional photon is spin-1 helically quantized, immune to backscattering, defects, and exists at the boundary of the C = ±2 bosonic phase and any interface-even vacuum. The contrasting phenomena of transverse quantization in the bulk, but longitudinal (helical) quantization on the edge is addressed as the quantum gyroelectric effect. We also validate our bosonic Maxwell theory by direct comparison with the supersymmetric Dirac theory of fermions. To accelerate the discovery of such bosonic phases, we suggest two probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy-loss spectroscopy and cold atom near-field measurement of nonlocal optical Hall conductivity.

In (2+1)-dimensional materials, nonlocal topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries (e.g., time reversal T2=+1). Additionally, they support topologically protected spin-1 edge states, which are fundamentally different than spin-12 and pseudo-spin-12 edge states arising in fermionic and pseudofermionic systems. The striking feature of the edge state is that all electric and magnetic field components vanish at the boundary, in stark contrast to analogs of Jackiw-Rebbi domain wall states. This surprising open boundary solution of Maxwell's equations, dubbed the quantum gyroelectric effect [Phys. Rev. A 98, 023842 (2018)], is the supersymmetric partner of the topological Dirac edge state where the spinor wave function completely vanishes at the boundary. The defining feature of such phases is the presence of temporal and spatial dispersion in conductivity (the linear response function). In this paper, we generalize these topological electromagnetic phases beyond the continuum approximation to the exact lattice field theory of a periodic atomic crystal. To accomplish this, we put forth the concept of microscopic photonic band structure of solids, analogous to the traditional theory of electronic band structure. Our definition of topological invariants utilizes optical Bloch modes and can be applied to naturally occurring crystalline materials. For the photon propagating within a periodic atomic crystal, our theory shows that besides the Chern invariant C∈Z, there are also symmetry-protected topological (SPT) invariants ν∈ZN which are related to the cyclic point group CN of the crystal ν=CmodN. Due to the rotational symmetries of light R(2π)=+1, these SPT phases are manifestly bosonic and behave very differently from their fermionic counterparts R(2π)=−1 encountered in conventional condensed-matter systems. Remarkably, the nontrivial bosonic phases ν≠0 are determined entirely from rotational (spin-1) eigenvalues of the photon at high-symmetry points in the Brillouin zone. Our work accelerates progress toward the discovery of bosonic phases of matter where the electromagnetic field within an atomic crystal exhibits topological properties.

Chern-Simons theories have been very successful in explaining integer and fractional quantum Hall phases of matter, topological insulators, and Weyl semimetals. However, it remains an open question as to whether Chern-Simons theories can be adapted to topological photonics. We develop a viscous Maxwell-Chern-Simons theory to capture the fundamental physics of a topological electromagnetic phase of matter. We show the existence of a unique spin-1 skyrmion in the viscous Hall fluid arising from a photonic Zeeman interaction in momentum space. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of photon spin-1 quantization in identifying new phases of matter.

A chiral absorber of light can emit spin-polarized (circularly polarized) thermal radiation based on Kirchhoff’s law which equates spin-resolved emissivity with spin-resolved absorptivity for reciprocal media at thermal equilibrium. No such law is known for nonreciprocal media. In this work, we discover three spin-resolved Kirchhoff’s laws of thermal radiation applicable for both reciprocal and nonreciprocal planar media. In particular, these laws are applicable to multi-layered or composite slabs of generic bianisotropic material classes which include (uniaxial or biaxial) birefringent crystals, (gyrotropic) Weyl semimetals, magnetized semiconductors, plasmas, ferromagnets and ferrites, (magnetoelectric) topological insulators, metamaterials and multiferroic media. We also propose an experiment to verify these laws using a single system of doped indium antimonide (InSb) thin film in an external magnetic field. Furthermore, we reveal a surprising result that the planar slabs of all these material classes can emit partially circularly polarized thermal light without requiring any surface patterning, and identify planar configurations which can experience nontrivial thermal optomechanical forces and torques upon thermal emission into the external environment at lower temperature (nonequilibrium). Our work also provides a new fundamental insight of detailed balance of angular momentum (in addition to energy) of equilibrium thermal radiation, and paves the way for practical functionalities based on thermal radiation using nonreciprocal bianisotropic materials.

Spin and orbital angular momentum of light plays a central role in quantum nanophotonics as well as topological electrodynamics. Here, we show that the thermal radiation from finite-size bodies comprising nonreciprocal magneto-optical materials can exert a spin torque even in global thermal equilibrium. Moving beyond the paradigm of near-field heat transfer, we calculate near-field radiative angular momentum transfer between finite-size nonreciprocal objects by combining Rytov's fluctuational electrodynamics with the theory of optical angular momentum. We prove that a single magneto-optical cubic particle in nonequilibrium with its surroundings experiences a torque in the presence of an applied magnetic field (T-symmetry breaking). Furthermore, even in global thermal equilibrium, two particles with misaligned gyrotropy axes experience equal-magnitude torques with opposite signs which tend to align their gyrotropy axes parallel to each other. Our results are universally applicable to semiconductors like InSb (magnetoplasmas) as well as Weyl semimetals which exhibit the anomalous Hall effect (gyrotropic) at infrared frequencies. Our work paves the way towards near-field angular momentum transfer mediated by thermal fluctuations for nanoscale devices.

Circularly polarized light can be obtained by using either polarization conversion or structural chirality. Here we reveal a fundamentally unrelated mechanism of generating circularly polarized light using coupled nonequilibrium sources. We show that thermal emission from a compact dimer of subwavelength, anisotropic antennas can be highly circularly polarized when the antennas are at unequal temperatures. Furthermore, the handedness of emitted light is flipped upon interchanging the temperatures of the antennas, thereby enabling reconfigurability of the polarization state lacked by most circularly polarized light sources. We describe the fundamental origin of this mechanism using rigorous fluctuational electrodynamic analysis and further provide practical examples for its experimental implementation. Apart from the technology applications in reconfigurable devices, communication, and sensing, this work motivates new inquiries of angular-momentum-related thermal-radiation phenomena using thermal nonequilibrium, without applying magnetic field.

The interplay of photon spin and orbital angular momentum (OAM) in the optical fiber (one-dimensional waveguide) has recently risen to the forefront of quantum nanophotonics. Here, we introduce the fermionic dual of the optical fiber, the Dirac wire, which exhibits unique electronic spin and OAM properties arising from confined solutions of the Dirac equation. The Dirac wires analyzed here represent cylindrical generalizations of the Jackiw-Rebbi domain wall and the minimal topological insulator, which are of significant interest in spintronics. We show the unique longitudinal spin arising from electrons confined to propagation in a wire, an effect that is fundamentally prohibited in planar geometries. Our work sheds light on the universal spatial dynamics of electron spin in confined geometries and the duality between electronic and photonic spin.

A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing
localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect
translational symmetry in both directions. Similarly, Wannier functions that respect time-reversal symmetry
cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been
enlightening and was recently extended to topological crystalline insulators which include obstructions tied to
space-group symmetries. In this paper, we introduce a class of two-dimensional topological materials known
as optical N-insulators that possess obstructions to construct localized molecular polarizabilities. The optical
N-invariant N ∈ Z is the winding number of the atomistic susceptibility tensor χ and counts the number of
singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the
optical band structure of the material—the eigenvectors of the susceptibility tensor—which constitutes the
collection of optical Bloch functions. The localized basis of these eigenvectors is optical Wannier functions
which characterize the molecular polarizabilities at different lattice sites. We prove that in a nontrivial optical
phase N = 0, such a localized polarization basis is impossible to construct. Utilizing the mathematical machinery
of K theory, these optical N-phases are refined further to account for the underlying crystalline symmetries of
the material, generating a complete classification of the topological electromagnetic phase of matter.

High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas that are necessary for qubit operation, initialization, and readout, also cause detrimental effects by enhancing fluctuations of electromagnetic fields. Therefore, evanescent wave Johnson noise (EWJN) caused by near-field thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decoherence of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a macroscopic quantum electrodynamics theory of EWJN to account for the dynamics of two spin qubits interacting with metallic circuitry. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two-spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) the silicon quantum dot system and (b) nitrogen-vacancy centers in diamond. Finally, we introduce a Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics, and open quantum systems to suppress the effects of near-field thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity.