Todd Van Mechelen

Purdue University West Lafayette

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Zubin Jacob

Purdue University West Lafayette

Sathwik Bharadwaj

Purdue University West Lafayette

Wenbo Sun

Purdue University West Lafayette

Ashwin K. Boddeti

Purdue University West Lafayette

Robert-Jan Slager

University of Manchester

Rajib Rahman

UNSW Sydney

Farhad Khosravi

University of Alberta

Farid Kalhor

Purdue University West Lafayette

Adrián Buganza Tepole

Purdue University West Lafayette

H. P. Urbach

Delft University of Technology

Cooperative Institutions

Purdue University West Lafayette

University of Alberta

University of Tehran

Stanford University

Intel (United States)

Tata Institute of Fundamental Research

University of Cambridge

Harvard University

UNSW Sydney

Delft University of Technology

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Quantum gyroelectric effect: Photon spin-1 quantization in continuum topological bosonic phases

Physical review. A/Physical review, A (2018)

Todd Van Mechelen Zubin Jacob

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 $C=\pm 2$ and one with odd $C=\pm 1$. To understand the even parity phase $C=\pm 2$, we introduce an exactly solvable model utilizing non-local 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 $C=\pm 2$ 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 gyro-electric effect (QGEE). 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 new probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy loss spectroscopy and cold atom near-field measurement of non-local optical Hall conductivity.

Parity (physics)

10.1103/physreva.98.023842

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Citations (47)

Optical N-invariant of graphene’s viscous Hall fluid

Conference on Lasers and Electro-Optics (2021)

Todd Van Mechelen Zubin Jacob

We introduce a new topological classification of two-dimensional matter related to its optical properties. Graphene’s viscous Hall fluid is the first candidate of this topological electromagnetic phase of matter with the underlying physical mechanism being Hall viscosity.

Viscous liquid

10.1364/cleo_qels.2021.fw2o.2

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Topological edge plasmons in graphene's viscous Hall fluid

Bulletin of the American Physical Society (2021)

Wenbo Sun Todd Van Mechelen Ashwin K. Boddeti Adrián Buganza Tepole Hadiseh Alaeian

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Universal spin-momentum locking of evanescent waves

Conference on Lasers and Electro-Optics (2016)

Todd Van Mechelen Zubin Jacob

We show the existence of an inherent handedness (spin) of evanescent-electromagnetic-waves which is fundamentally locked to the direction of propagation (momentum). It is universal and accompanies evanescent waves in total internal reflection, waveguides/fibers and surface-states.

Reflection

Spin wave

Momentum (technical analysis)

Waveguide

10.1364/cleo_qels.2016.fw1d.6

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Citations (33)

Unidirectional Maxwellian Spin Waves

Conference on Lasers and Electro-Optics (2020)

Todd Van Mechelen Zubin Jacob

We develop a unified perspective of unidirectional topological edge waves in non-reciprocal media. We focus on the inherent role of photonic spin in non-reciprocal gyroelectric media, ie. magnetized metals or magnetized insulators.

Reciprocal

Spin wave

Topological insulator

10.1364/cleo_qels.2020.fm2b.2

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Citations (1)

Photon spin-1 quantization in continuum topological bosonic phases

arXiv (Cornell University) (2018)

Todd Van Mechelen Zubin Jacob

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 revelation, we predict two unique bosonic phases - one with even parity $C=\pm 2$ and one with odd $C=\pm 1$. To understand the even parity phase $C=\pm 2$, we introduce an exactly solvable model utilizing non-local 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 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 gyrotropic effect (QGE). 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 new probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy loss spectroscopy and cold atom near-field measurement of non-local optical Hall conductivity.

Parity (physics)

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Photonic Dirac Monopole: Spin-1 Quantization

arXiv (Cornell University) (2018)

Todd Van Mechelen Zubin Jacob

We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals and metamaterials, by utilizing the Dirac-Maxwell correspondence. We show that even in vacuum, 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. We prove that 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. Our work sheds light on the recently proposed spin-1 bosonic phase of matter and the fundamental role of photon spin quantization in topological bosonic phases.

Helical Dirac fermion

Massless particle

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Role of Radial Charges on the Angular Momentum of Electromagnetic Fields: Spin- 3/2 Light

Physical Review Letters (2018)

Omar El Gawhary Todd Van Mechelen H. P. Urbach

Electromagnetic fields carry a linear and an angular momentum, the first being responsible for the existence of the radiation pressure and the second for the transfer of torque from electromagnetic radiation to matter. The angular momentum is considered to have two components, one due to the polarization state of the field, usually called spin angular momentum (SAM), and one due to the existence of topological azimuthal charges in the field phase profile, which leads to the orbital angular momentum (OAM). These two contributions to the total angular momentum of an electromagnetic field appear, however, to not be independent of each other, something which is described as spin-orbit coupling. Understanding the physics of this coupling has kept scientists busy for decades. Very recently it has been shown that electromagnetic fields necessarily carry also invariant radial charges that, as discussed in this Letter, play a key role in the angular momentum. Here we show that the total angular momentum consists in fact of three components: one component only dependent on the spin of the field, another dependent on the azimuthal charges carried by the field, and a third component dependent on the spin and the radial charges contained in the field. By properly controlling the number and coupling among these radial charges it is possible to design electromagnetic fields with a desired total angular momentum. Remarkably, we also discover fields with no orbital angular momentum and a spin angular momentum typical of spin-3/2 objects, irrespective of the fact that photons are spin-1 particles.

Angular momentum operator

10.1103/physrevlett.121.123202

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Citations (11)

Exploiting universal nonlocal dispersion in optically active materials for spectro-polarimetric computational imaging

eLight (2024)

Xueji Wang Todd Van Mechelen Sathwik Bharadwaj M. Roknuzzaman Fanglin Bao

Abstract Recent years have seen significant advancements in exploring novel light-matter interactions such as hyperbolic dispersion within natural crystals. However, current studies have predominantly concentrated on local optical response of materials characterized by a dielectric tensor without spatial dispersion. Here, we investigate the nonlocal response in optically-active crystals with screw symmetries, revealing their lossless, super-dispersive properties compared to traditional optical response functions. We leverage this universal nonlocal dispersion, i.e. the dispersion of optical rotatory power, to explore a novel spectral de-multiplexing scheme compared to conventional gratings, prisms and metasurfaces. We design and demonstrate an ‘Nonlocal-Cam’ - a camera that exploits nonlocal dispersion through sampling of polarized spectral states and the application of computational spectral reconstruction algorithms. The Nonlocal-Cam captures information in both laboratory and outdoor field experiments which is unavailable to traditional intensity cameras - the spectral texture of polarization. Merging the fields of nonlocal electrodynamics and computational imaging, our work paves the way for exploiting nonlocal optics of optically active materials in a variety of applications, from biological microscopy to physics-driven machine vision and remote sensing.

10.1186/s43593-024-00078-2

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Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity

arXiv (Cornell University) (2023)

Wenbo Sun Todd Van Mechelen Sathwik Bharadwaj Ashwin K. Boddeti Zubin Jacob

Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant has been proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, fundamentally different from the Chern and Z2 invariants. In this paper, we introduce the topologically protected edge excitation -- optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit fundamentally different dispersion relations, stability, and edge profiles from the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum-classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of repulsive Hall viscosity and opens practical applications of topological electromagnetic phases of two-dimensional materials.

Topological insulator

10.48550/arxiv.2307.00218

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