All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer

spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there

exist open questions on the quantized description of the spin of the gauge field particle—the photon. Using quantum field theory, we discover the quantum operators for the spin angular momentum (SAM) SM = (1/c) d3xπ × A and orbital angular momentum (OAM) LM = −(1/c) d3xπμx × ∇Aμ of the photon, where πμ is the conjugate canonical momentum of the gauge field Aμ. We also reveal a perfect symmetry between the angular momentum commutation relations for Dirac fields and Maxwell fields. We derive the well-known OAM and SAM of classical electromagnetic fields from the above-defined quantum operators. Our work shows that the spin and OAM operators commute, which is important for simultaneously observing and separating the SAM and OAM. The correct commutation relations of orbital and spin angular momentum of the photon have applications in quantum optics, topological photonics as well as nanophotonics and can be extended in the future for the spin structure of nucleons.

# Publications

## 2022

Thermal radiation is traditionally an incoherent radiative signal, where the radiated heat is highly unpolarized, spectrally broad, and omnidirectional. The recent extensive interests in thermal photonics focus on tailoring the temporal coherence (spectrum) and spatial coherence (directivity) of thermal radiation. Here, we investigate the photon spin characteristics of the radiation excited by thermal fluctuations using a symmetrybroken metasurface. Utilizing spin-polarized angle-resolved thermal emission spectroscopy (SPARTES), we explicitly show when both mirror- and inversion- symmetries are broken, the summation of spin-angular momentum projected on wavevectors, namely the optical helicity, can be non-vanishing even without applying a magnetic field. We find the photon spin and the energy-momentum dispersion of thermal radiation can be effectively tailored through symmetry engineering. Our results firmly suggest the symmetry-based strategy provides a general pathway for comprehensively controlling the temporal, spatial, and especially spin coherence of thermal radiation.

Generation of local magnetic field at the nanoscale is desired for many applications such as spinqubit-based quantum memories. However, this is a challenge due to the slow decay of static magnetic fields. Here, we demonstrate photonic spin density (PSD) induced effective static magnetic field for an ensemble of nitrogen-vacancy (NV) centers in bulk diamond. This locally induced magnetic field is a result of coherent interaction between the optical excitation and the NV centers. We demonstrate an optically induced spin rotation on the Bloch sphere exceeding 10 degrees which has potential applications in all optical coherent control of spin qubits.

Optical N-insulators: Topological obstructions to optical Wannier functions in the atomistic susceptibility tensor

”. Physical Review Research, 4, 2.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.

Germanium is typically used for solid-state electronics, fiber-optics, and infrared applications, due to its semiconducting behavior at optical and infrared wavelengths. In contrast, here we show that the germanium displays metallic nature and supports propagating surface plasmons in the deep ultraviolet (DUV) wavelengths, that is typically not possible to achieve with conventional plasmonic metals such as gold, silver, and aluminum. We measure the photonic band spectrum and distinguish the plasmonic excitation modes: bulk plasmons, surface plasmons, and Cherenkov radiation using a momentum-resolved electron energy loss spectroscopy. The observed spectrum is validated through the macroscopic electrodynamic electron energy loss theory and first-principles density functional theory calculations. In the DUV regime, intraband transitions of valence electrons dominate over the interband transitions, resulting in the observed highly dispersive surface plasmons. We further employ these surface plasmons in germanium to design a DUV radiation source based on the Smith-Purcell effect. Our work opens a new frontier of DUV plasmonics to enable the development of DUV devices such as metasurfaces, detectors, and light sources based on plasmonic germanium thin films.

Quantum Machine Learning (QML) is an emerging research area advocating the use of quantum computing for advancement in machine learning. Since the discovery of the capability of Parametrized Variational Quantum Circuits (VQC) to replace Artificial Neural Networks, they have been widely adopted to different tasks in Quantum Machine Learning. However, despite their potential to outperform neural networks, VQCs are limited to small scale applications given the challenges in scalability of quantum circuits. To address this shortcoming, we propose an algorithm that compresses the quantum state within the circuit using a tensor ring representation. Using the input qubit state in the tensor ring representation, single qubit gates maintain the tensor ring representation. However, the same is not true for two qubit gates in general, where an approximation is used to have the output as a tensor ring representation. Using this approximation, the storage and computational time increases linearly in the number of qubits and number of layers, as compared to the exponential increase with exact simulation algorithms. This approximation is used to implement the tensor ring VQC. The training of the parameters of tensor ring VQC is performed using a gradient descent based algorithm, where efficient approaches for backpropagation are used. The proposed approach is evaluated on two datasets: Iris and MNIST for the classification task to show the improved accuracy using more number of qubits. We achieve a test accuracy of 83.33% on Iris dataset and a maximum of 99.30% and 76.31% on binary and ternary classification of MNIST dataset using various circuit architectures. The results from the IRIS dataset outperform the results on VQC implemented on Qiskit, and being scalable, demonstrates the potential for VQCs to be used for large scale Quantum Machine Learning applications.

## 2021

Non-reciprocal energy transfer through the Casimir effect

”. Nature Nanotechnology.One of the fundamental predictions of quantum mechanics is the occurrence of random fluctuations in a vacuum caused by zero-point energy. Remarkably, quantum electromagnetic fluctuations can induce a measurable force between neutral objects, known as the Casimir effect^{1}, and it has been studied both theoretically^{2,3} and experimentally^{4-9}. The Casimir effect can dominate the interaction between microstructures at small separations and is essential for micro-and nanotechnologies^{10,11}. It has been utilized to realize nonlinear oscillation^{12}, quantum trapping^{13}, phonon transfer^{14,15,} and dissipation dilution^{16}. However, a non-reciprocal device based on quantum vacuum fluctuations remains an unexplored frontier. Here we report quantum-vacuum-mediated non-reciprocal energy transfer between two micromechanical oscillators. We parametrically modulate the Casimir interaction to realize a strong coupling between the two oscillators with different resonant frequencies. We engineer the system's spectrum such that it possesses an exceptional point^{17-20} in the parameter space and explore the asymmetric topological structure in its vicinity. By dynamically changing the parameters near the exceptional point and utilizing the non-adiabaticity of the process, we achieve non-reciprocal energy transfer between the two oscillators with high contrast. Our work demonstrates a scheme that employs quantum vacuum fluctuations to regulate energy transfer at the nanoscale and may enable functional Casimir devices in the future.

**See also:**Quantum

Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the tradeoff between the entropy of hidden cause and conditional mutual information of observed variables to develop a scalable algorithmic approach for inferring causality in the presence of latent confounders (common causes) in quantum systems. As an application, we consider a system of three entangled qubits and transmit the second and third qubits over separate noisy quantum channels. In this model, we validate that the first qubit is a latent confounder and the common cause of the second and third qubits. In contrast, when two entangled qubits are prepared and one of them is sent over a noisy channel, there is no common confounder. We also demonstrate that the proposed approach outperforms the results of classical causal inference for Tubingen database when the variables are classical by exploiting quantum dependence between variables through density matrices rather than joint probability distributions. Thus, the proposed approach unifies classical and quantum causal inference in a principled way.

We numerically demonstrate that a planar slab made of magnetic Weyl semimetal (a class of topological materials) can emit high-purity circularly polarized (CP) thermal radiation over a broad mid- and long-wave infrared wavelength range for a significant portion of its emission solid angle. This effect fundamentally arises from the strong infrared gyrotropy or nonreciprocity of these materials, which primarily depends on the momentum separation between Weyl nodes in the band structure. We clarify the dependence of this effect on the underlying physical parameters and highlight that the spectral bandwidth of CP thermal emission increases with increasing momentum separation between the Weyl nodes. We also demonstrate, using the recently developed thermal discrete dipole approximation (TDDA) computational method, that finite-size bodies of magnetic Weyl semimetals can emit spectrally broadband CP thermal light, albeit over smaller portion of the emission solid angle compared to the planar slabs. Our work identifies unique fundamental and technological prospects of magnetic Weyl semimetals for engineering thermal radiation and designing efficient CP light sources.

Long-Range Dipole-Dipole Interactions in a Plasmonic Lattice

”. Nano letters, 22, Pp. 22–28.Spontaneous emission of quantum emitters can be enhanced by increasing the local density of optical states, whereas engineering dipole–dipole interactions requires modifying the two-point spectral density function. Here, we experimentally demonstrate long-range dipole–dipole interactions (DDIs) mediated by surface lattice resonances in a plasmonic nanoparticle lattice. Using angle-resolved spectral measurements and fluorescence lifetime studies, we show that unique nanophotonic modes mediate long-range DDI between donor and acceptor molecules. We observe significant and persistent DDI strengths for a range of densities that map to ∼800 nm mean nearest-neighbor separation distance between donor and acceptor dipoles, a factor of ∼100 larger than free space. Our results pave the way to engineer and control long-range DDIs between an ensemble of emitters at room temperature.