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DOE OSTI2021

On restricting first order form of gauge theories to one-loop order

Highlights: • We prove the equivalence of the first and second-order formalism. • We use Lagrange multiplier fields to limit radiative effects to one-loop order. • We prove that the quantized theory is both renormalizable and unitary. The first order form of the Yang–Mills and Einstein–Hilbert actions are quantized, and it is shown how Green’s functions computed using the first and the second order form of these theories are related. Next we show how by use of Lagrange multiplier fields (LM), radiative effects beyond one-loop order can be eliminated. This allows one to compute Green’s functions exactly without loss of unitarity. The consequences of this restriction on radiative effects are examined for the Yang–Mills and Einstein–Hilbert actions. In these two gauge theories, we find that the quantized theory is both renormalizable and unitary once the LM field is used to eliminate effects beyond one-loop order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Quadrupole topological photonic crystals

Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell’s equations for a gyromagnetic photonic crystal (PhC) through a double-band-inversion process. The quadrupole moment is quantized by the simultaneous presence of crystalline symmetry and broken time-reversal symmetry, which is confirmed using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands and the expectation value of the quadrupole operator. Furthermore, we reveal the boundary manifestations of quadrupole phases as quantized edge polarizations and fractional corner charges. The latter are the consequence of a filling anomaly of energy bands as first predicted in electronic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Giant topological longitudinal circular photo-galvanic effect in the chiral multifold semimetal CoSi

The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light’s polarization, known as the circular photo-galvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material parameters and the incident frequency. In this work, we perform terahertz emission spectroscopy with tunable photon energy from 0.2 –1.1 eV in the chiral topological semimetal CoSi. We identify a large longitudinal photocurrent peaked at 0.4 eV reaching ~550 μ A/V 2 , which is much larger than the photocurrent in any chiral crystal reported in the literature. Using first-principles calculations we establish that the peak originates only from topological band crossings, reaching 3.3 ± 0.3 in units of the quantization constant. Our calculations indicate that the quantized circular photo-galvanic effect is within reach in CoSi upon doping and increase of the hot-carrier lifetime. The large photo-conductivity suggests that topological semimetals could potentially be used as novel mid-infrared detectors.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Linear and nonlinear optical responses in the chiral multifold semimetal RhSi

Chiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and nonlinear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of different kinds of multifold fermions. The characteristic features of the CPGE, which displays a sign change at 0.4 eV and a large non-quantized response peak of around 160 μA/V 2 at 0.7 eV, are explained by assuming that the chemical potential crosses a flat hole band at the Brillouin zone center. Our theory predicts that, in order to observe a quantized CPGE in RhSi, it is necessary to increase the chemical potential as well as the quasiparticle lifetime. More broadly, our methodology, especially the development of the broadband terahertz emission spectroscopy, could be widely applied to study photogalvanic effects in noncentrosymmetric materials and in topological insulators in a contact-less way and accelerate the technological development of efficient infrared detectors based on topological semimetals.

Materials Science↗

DOE OSTI2022

Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl 3

The honeycomb magnet α-RuCl 3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κ xy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κ xy on α-RuCl3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κ xy /T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. In conclusion, the bosonic character is incompatible with half-quantization of κ xy /T.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Metamaterial-based theoretical description of light scattering by metallic nano-hole array structures

We have experimentally and theoretically investigated the light-matter interaction in metallic nano-hole array structures. The scattering cross section spectrum was measured for three samples each having a unique nano-hole array radius and periodicity. Each measured spectrum had several peaks due to surface plasmon polaritons. The dispersion relation and the effective dielectric constant of the structure were calculated using transmission line theory and Bloch's theorem. Using the effective dielectric constant and the transfer matrix method, the surface plasmon polariton energies were calculated and found to be quantized. Using these quantized energies, a Hamiltonian for the surface plasmon polaritons was written in the second quantized form. Working with the Hamiltonian, a theory of scattering cross section was developed based on the quantum scattering theory and Green's function method. For both theory and experiment, the location of the surface plasmon polariton spectral peaks was dependant on the array periodicity and radii of the nano-holes. Good agreement was observed between the experimental and theoretical results. It is proposed that the newly developed theory can be used to facilitate optimization of nanosensors for medical and engineering applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Multinucleon structure and dynamics via quantum computing

We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero Hamiltonian matrix elements of the many-nucleon system. With our Fock-state based input model, we show how to implement the sparse matrix simulation algorithms to calculate the dynamics of the second-quantized many-nucleon Hamiltonian. Based on the dynamics simulation methods, we also present the methodology for structure calculations of the many-nucleon system. In this work, we provide an explicit circuit design of our input model of the second-quantized Hamiltonian within a direct encoding scheme that maps the occupation of each available single-particle state in the many-nucleon state to the state of specific qubit in a quantum register. Here, we analyze our method and provide the asymptotic cost in computing resources for structure and dynamics calculations of many-nucleon systems. For pedagogical purposes, we demonstrate our input model with two model problems in restricted model spaces.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators

Gapless helical edge modes are a hallmark of the quantum spin Hall effect. Protected by time-reversal symmetry, each edge contributes a quantized zero-temperature conductance quantum G 0 ≡ e 2 /h. However, the experimentally observed conductance in WT e2 decreases below G 0 per edge already at edge lengths around 100 nm, even in the absence of explicit time-reversal breaking due to an external field or magnetic impurities. Here we show how a time-reversal breaking excitonic condensate with a spin-spiral order that can form in WT e2 leads to the breakdown of conductance quantization. We perform Hartree-Fock calculations to compare time-reversal breaking and preserving excitonic insulators. Using these mean-field models we demonstrate via quantum transport simulations that weak nonmagnetic disorder reproduces the edge length scaling of resistance observed in the experiments. We complement this by analysis in the Luttinger liquid picture, shedding additional light on the mechanism behind the quantization breakdown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers

Fractional Chern insulators (FCI) with fractionally quantized Hall conductance at fractional fillings and an extended quantum anomalous Hall (EQAH) crystal with an integer quantized Hall conductance over an extended region of doping were recently observed in pentalayer graphene. One particularly puzzling observation is the transition between the EQAH and FCI regimes, driven either by temperature or electrical current. Here, in this study, we propose a scenario to understand these transitions based on the topologically protected gapless edge modes that are present in both the FCI and EQAH phases and should be most relevant at temperature scales below the energy gap. Our consideration is based on the simple assumption that the edge velocity in FCI is smaller than that in EQAHE and thus contributes to a higher entropy. We further argue that domains with opposite fractionally quantized Hall conductance are ubiquitous in the devices due to disorder, which gives rise to a network of edge modes. The velocity of the edge modes between domains is further reduced due to edge reconstruction. The edge velocity can also be reduced by current when the occupation of the edge mode approaches the gap edge. The edge entropy therefore drives the transition from EQAH to FCI either by temperature or current at a nonzero temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Perturbative quantum evolution of the gravitational state and dressing in general backgrounds

This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the Hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a “gauge-invariant canonical quantization,” which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green’s functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary Hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti–de-Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Exploration of thermal counterflow in He II using particle tracking velocimetry

Flow visualization using particle image velocimetry (PIV) and particularly particle tracking velocimetry (PTV) has been applied to thermal counterflow in He II for nearly two decades now, but the results remain difficult to interpret because tracer particle motion can be influenced by both the normal fluid and superfluid components of He II as well as the quantized vortex tangle. For instance, in one early experiment it was observed (using PTV) that tracer particles move at the normal fluid velocity v n , while in another it was observed (using PIV) that particles move at v n /2. Besides the different visualization methods, the range of applied heat flux investigated by these experiments differed by an order of magnitude. To resolve this apparent discrepancy and explore the statistics of particle motion in thermal counterflow, we apply the PTV method to a wide range of heat flux at a number of different fluid temperatures. In our analysis, we introduce a scheme for analyzing the velocity of particles presumably moving with the normal fluid separately from those presumably influenced by the quantized vortex tangle. Our results show that for lower heat flux there are two distinct peaks in the streamwise particle velocity probability density function (PDF), with one centered at the normal fluid velocity v n (named G2 for convenience) while the other is centered near v n /2 (G1). For higher heat flux there is a single peak centered near v n /2 (G3). Using our separation scheme, we show quantitatively that there is no size difference between the particles contributing to G1 and G2. We also show that nonclassical features of the transverse particle velocity PDF arise entirely from G1, while the corresponding PDF for G2 exhibits the classical Gaussian form. The G2 transverse velocity fluctuation, backed up by second sound attenuation in decaying counterflow, suggests that large-scale turbulence in the normal fluid is absent from the two-peak region. We offer a brief discussion of the physical mechanisms that may be responsible for our observations, revealing that G1 velocity fluctuations may be linked to fluctuations of quantized vortex line velocity, and suggest a number of numerical simulations that may reveal the underlying physics in detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Growth, characterization, and Chern insulator state in MnBi 2⁢ Te 4 via the chemical vapor transport method

As the first intrinsic antiferromagnetic topological insulator, MnBi 2 Te 4 has provided a platform to investigate the interplay of band topology and magnetism as well as the emergent phenomena arising from such an interplay. Here we report the chemical-vapor-transport (CVT) growth and characterization of MnBi 2 Te 4 , as well as the observation of the field-induced quantized Hall conductance in 6-layer devices. Through comparative studies between our CVT-grown and flux-grown MnBi 2 Te 4 via magnetic, transport, scanning tunneling microscopy, and angle-resolved photoemission spectroscopy measurements, we find that CVT-grown MnBi 2 Te 4 is marked with higher Mn occupancy on the Mn site, slightly higher Mn Bi antisites, smaller carrier concentration, and a Fermi level closer to the Dirac point. Furthermore, a 6-layer device made from the CVT-grown sample shows by far the highest mobility of 2500 cm 2 V s in MnBi 2 Te 4 devices with the quantized Hall conductance appearing at 1.8 K and 8 T. Furthermore, our study provides a route to obtain high-quality single crystals of MnBi 2 Te 4 that are promising to make superior devices and realize emergent phenomena, such as the layer Hall effect and quantized anomalous Hall effect, etc.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Chaotic roots of the modular multiplication dynamical system in Shor's algorithm

Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an integrable system, which is paradoxical from the viewpoint of quantum chaos, given that the classical limit of the modular multiplication operator is a highly chaotic system that occupies the “maximally random” Bernoulli level of the classical ergodic hierarchy. In this work, we approach this apparent paradox from a quantum dynamical systems viewpoint, and consider whether signatures of ergodicity and chaos may indeed be encoded in such an “integrable” quantization of a chaotic system. We show that Shor's modular multiplication operator, in specific cases, can be written as a superposition of quantized 𝐴-baker's maps exhibiting more typical signatures of quantum chaos and ergodicity. This work suggests that the integrability of Shor's modular multiplication operator may stem from the interference of other “chaotic” quantizations of the same family of maps, and paves the way for deeper studies on the interplay of integrability, ergodicity, and chaos in and via quantum algorithms.

Dynamical systems↗

DOE OSTI2016

Coherent scattering of an atom in the field of a standing wave under conditions of initial quantum correlation of subsystems

Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Lion Cub: Minimizing Communication Overhead in Distributed Lion

Communication overhead is a key challenge in distributed deep learning, especially on slower Ethernet intercon nects, and given current hardware trends, communication is likely to become a major bottleneck. While gradient compression techniques have been explored for SGD and Adam, the Lion optimizer has the distinct advantage that its update vectors are the output of a sign operation, enabling straightforward quantization. However, simply compressing updates for communication and using techniques like majority voting fails to lead to end-to-end speedups due to inefficient communication algorithms and reduced convergence. We analyze three factors critical to distributed learning with Lion: optimizing communication methods, identifying effective quantization methods, and assessing the necessity of momentum synchronization. Our findings show that quantization techniques adapted to Lion and selective momentum synchronization can significantly reduce communication costs while maintaining convergence. We combine these into Lion Cub, which enables up to 5x speedups in end-to-end training compared to Lion. This highlights Lion’s potential as a communication-efficient solution for distributed training.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Can We Detect the Quantum Nature of Weak Gravitational Fields?

A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted to find solutions to this deep riddle, an alternative path built upon the idea that experimental evidence could determine whether gravity is quantized has been decades in the making. The possibility of an experimental answer to the question of the quantization of gravity is of renewed interest in the era of gravitational wave detectors. We review and investigate an important subset of phenomenological quantum gravity, detecting quantum signatures of weak gravitational fields in table-top experiments and interferometers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Methods and apparatuses for self-generating fault-tolerant keys in spread-spectrum systems

Self-generating fault-tolerant keys for use in spread-spectrum systems are disclosed. At a communication device, beacon signals are received from another communication device and impulse responses are determined from the beacon signals. The impulse responses are circularly shifted to place a largest sample at a predefined position. The impulse responses are converted to a set of frequency responses in a frequency domain. The frequency responses are shuffled with a predetermined shuffle scheme to develop a set of shuffled frequency responses. A set of phase differences is determined as a difference between an angle of the frequency response and an angle of the shuffled frequency response at each element of the corresponding sets. Each phase difference is quantized to develop a set of secret-key quantized phases and a set of spreading codes is developed wherein each spreading code includes a corresponding phase of the set of secret-key quantized phases.

42 ENGINEERING↗

DOE OSTI2015

Light-front representation of chiral dynamics in peripheral transverse densities

The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed light-front time. At peripheral transverse distances b = O(M_pi^{-1}) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). We represent the leading-order chiral EFT results for the peripheral transverse densities as overlap integrals of chiral light-front wave functions, describing the transition of the initial nucleon to soft pion-nucleon intermediate states and back. The new representation (a) explains the parametric order of the peripheral transverse densities; (b) establishes an inequality between the spin-independent and -dependent densities; (c) exposes the role of pion orbital angular momentum in chiral dynamics; (d) reveals a large left-right asymmetry of the current in a transversely polarized nucleon and suggests a simple interpretation. The light-front representation enables a first-quantized, quantum-mechanical view of chiral dynamics that is fully relativistic and exactly equivalent to the second-quantized, field-theoretical formulation. It relates the charge and magnetization densities measured in low-energy elastic scattering to the generalized parton distributions probed in peripheral high-energy scattering processes. The method can be applied to nucleon form factors of other operators, e.g. the energy-momentum tensor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗