Particle-like States Research Articles

Soliton confinement in a quantum circuit

Confinement of topological excitations into particle-like states - typically associated with theories of elementary particles - are known to occur in condensed matter systems, arising as domain-wall confinement in quantum spin chains. However, investigation of confinement in the condensed matter setting has rarely ventured beyond lattice spin systems. Here we analyze the confinement of sine-Gordon solitons into mesonic bound states in a perturbed quantum sine-Gordon model. The latter describes the scaling limit of a one-dimensional, quantum electronic circuit (QEC) array, constructed using experimentally-demonstrated QEC elements. The scaling limit is reached faster for the QEC array compared to spin chains, allowing investigation of the strong-coupling regime of this model. We compute the string tension of confinement of sine-Gordon solitons and the changes in the low-lying energy spectrum. These results, obtained using the density matrix renormalization group method, could be verified in a quench experiment using state-of-the-art QEC technologies.

Resurgence, conformal blocks, and the sum over geometries in quantum gravity

In two dimensional conformal field theories the limit of large central charge plays the role of a semi-classical limit. Certain universal observables, such as conformal blocks involving the exchange of the identity operator, can be expanded around this classical limit in powers of the central charge c. This expansion is an asymptotic series, so — via the same resurgence analysis familiar from quantum mechanics — necessitates the existence of non-perturbative effects. In the case of identity conformal blocks, these new effects have a simple interpretation: the CFT must possess new primary operators with dimension of order the central charge. This constrains the data of CFTs with large central charge in a way that is similar to (but distinct from) the conformal bootstrap. We study this phenomenon in three ways: numerically, analytically using Zamolodchikov’s recursion relations, and by considering non-unitary minimal models with large (negative) central charge. In the holographic dual to a CFT2, the expansion in powers of c is the perturbative loop expansion in powers of ћ. So our results imply that the graviton loop expansion is an asymptotic series, whose cure requires the inclusion of new saddle points in the gravitational path integral. In certain cases these saddle points have a simple interpretation: they are conical excesses, particle-like states with negative mass which are not in the physical spectrum but nevertheless appear as non-manifold saddle points that control the asymptotic behaviour of the loop expansion. This phenomenon also has an interpretation in SL(2, ℝ) Chern-Simons theory, where the non-perturbative effects are associated with the non-Teichmüller component of the moduli space of flat connections.

Mechanism of Skyrmion Attraction in Chiral Magnets near the Ordering Temperatures

Isolated chiral skyrmions are investigated within the phenomenological Dzyaloshinskii model near the ordering temperatures of quasi-two-dimensional chiral magnets with Cnv symmetry and three-dimensional cubic helimagnets. In the former case, isolated skyrmions (IS) perfectly blend into the homogeneously magnetized state. The interaction between these particle-like states, being repulsive in a broad low-temperature (LT) range, is found to switch into attraction at high temperatures (HT). This leads to a remarkable confinement effect: near the ordering temperature, skyrmions exist only as bound states. This is a consequence of the coupling between the magnitude and the angular part of the order parameter, which becomes pronounced at HT. The nascent conical state in bulk cubic helimagnets, on the contrary, is shown to shape skyrmion internal structure and to substantiate the attraction between them. Although the attracting skyrmion interaction in this case is explained by the reduction of the total pair energy due to the overlap of skyrmion shells, which are circular domain boundaries with the positive energy density formed with respect to the surrounding host phase, additional magnetization "ripples" at the skyrmion outskirt may lead to attraction also at larger length scales. The present work provides fundamental insights into the mechanism for complex mesophase formation near the ordering temperatures and constitutes a first step to explain the phenomenon of multifarious precursor effects in that temperature region.

Edge reconstruction and emergent neutral modes in integer and fractional quantum Hall phases

This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the ν = 2/5 phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counter-propagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particle-like phases at ν = 1, 1/3, and 2/5 as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorder-induced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases and could explain the absence of anyonic interference in electronic Mach-Zehnder setups.

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

The presence of “upstream” modes, moving against the direction of charge current flow in the fractional quantum Hall (FQH) phases, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here, we report noise measurements at the edges of FQH states realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at length, L = 4 μm and 10 μm away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for “hole-conjugate” FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remains independent of length, which matches our theoretical analysis demonstrating the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems.

Field-driven metamorphoses of isolated skyrmions within the conical state of cubic helimagnets

Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. Deep physical relations and common physical features of a large variety of very different solitonic states in these systems arise from the mathematical similarity of phenomenological equations. During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for the experimental investigation of topological solitons and the understanding of their nonsingular field configurations. This is directly related to the discovery of particle-like chiral skyrmions, which are also considered as promising ingredients for technological applications. Here we introduce a paradigm of facile skyrmionic networks with mutually orthogonal orientations of constituent isolated skyrmions. On the one hand, such networks are envisioned as a novel concept of spintronic devices based, e.g., on gapless skyrmion motion along each other, and are presumably responsible for precursor phenomena near the ordering temperatures of bulk cubic helimagnets. In particular, we demonstrate an interconversion between mutually orthogonal skyrmions: horizontal skyrmions may swirl into an intermediate spring-like state and subsequently squeeze into vertical skyrmions with both polarities. On the other hand, skyrmion tubes are considered as building blocks for particle-like states with more involved internal structure. A family of target-skyrmions, which includes a so far overlooked type with a multiple topological charge, is formed owing to the tendency to minimize the interaction energy between vertical and horizontal skyrmions. The conical phase serves as a suitable background for considered skyrmion evolution. It substantializes the attracting skyrmion-skyrmion interaction in the skyrmionic networks, shapes their internal structure, and guides the nucleation processes. Alternatively, intricate textural changes of isolated skyrmions result not only in the structural deformations of a host conical state, but may lead to the formation of an exotic skyrmion order with pairs of merons being the core of the game. Generically, the fundamental insights provided by this work emphasize a three-dimensional character of skyrmion metamorphoses and can also be extended to three-dimensional solitons, such as hopfions.

Optical emission from light-like and particle-like excitons in monolayer transition metal dichalcogenides

Several monolayer transition metal dichalcogenides (TMDs) are direct band gap semiconductors and potentially efficient emitters in light emitting devices. Photons are emitted when strongly bound excitons decay radiatively, and accurate models of such excitons are important for a full understanding of the emission. Importantly, photons are emitted in directions uniquely determined by the exciton center of mass momentum and with lifetimes determined by the exciton transition matrix element. The exciton band structures of two-dimensional hexagonal materials, including TMDs, are highly unusual with coexisting particle- and light-like bands. The latter is non-analytic with emission selection rules essentially opposite to the particle-like states, but has been ignored in analyses of TMD light emission so far. In the present work, we analyse the temperature and angular dependence of light emission from both exciton species and point out several important consequences of the unique exciton band structure. Within a first-principles Density-Functional-Theory+Bethe-Salpeter-Equation framework, we compute exciton band structures and optical matrix elements for the important TMDs MoS2, MoSe2, WS2, and WSe2. At low temperature, only the particle-like band is populated and our results agree with previous work. However, at slightly elevated temperatures, a significant population of the light-like band leads to modified angular emission patterns and lifetimes. Clear experimental fingerprints are predicted and explained by a simple four-state model incorporating spin-orbit as well as intervalley exchange coupling.

Energy Relaxation in Edge Modes in the Quantum Hall Effect.

Studies of energy flow in quantum systems complement the information provided by common conductance measurements. The quantum limit of heat flow in one-dimensional ballistic modes was predicted, and experimentally demonstrated, to have a universal value for bosons, fermions, and fractionally charged anyons. A fraction of this value is expected in non-Abelian states; harboring counterpropagating edge modes. In such exotic states, thermal-energy relaxation along the edge is expected, and can shed light on their topological nature. Here, we introduce a novel experimental setup that enables a direct observation of thermal-energy relaxation in chiral 1D edge modes in the quantum Hall effect. Edge modes, emanating from a heated reservoir, are partitioned by a quantum point contact (QPC) constriction, which is located at some distance along their path. The resulting low frequency noise, measured downstream, allows determination of the "effective temperature" of the edge mode at the location of the QPC. An expected, prominent energy relaxation was found in hole-conjugate states. However, relaxation was also observed in particlelike states, where heat is expected to be conserved. We developed a model, consisting of distance-dependent energy loss, which agrees with the observations; however, we cannot exclude energy redistribution mechanisms, which are not accompanied with energy loss.

Observation of a topological insulator Dirac cone reshaped by non-magnetic impurity resonance

The massless Dirac electrons found at topological insulator surfaces are thought to be influenced very little by weak, non-magnetic disorder. However, a resonance effect of strongly perturbing non-magnetic impurities has been theoretically predicted to change the dispersion and physical nature of low-energy quasiparticles, resulting in unique particle-like states that lack microscopic translational symmetry. Here we report the direct observation of impurities reshaping the surface Dirac cone of the model three-dimensional topological insulator bismuth selenide. A pronounced kink-like dispersion feature is observed in disorder-enriched samples, and found to be closely associated with the anomaly caused by impurity resonance in the surface state density of states, as observed by dichroic angle-resolved photoemission spectroscopy. The experimental observation of these features, which closely resemble theoretical predictions, has significant implications for the properties of topological Dirac cones in applied scenarios that commonly feature point-defect disorder at surfaces or interfaces.

BMS symmetry, soft particles and memory

In this work, we revisit unitary irreducible representations of the Bondi–Metzner–Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of supermomenta in addition to 4-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing 4-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.

High energy density spots and production of kink–antikink pairs in particle collisions

Creation of solitons as kink–antikink pairs from particles is investigated, in the ϕ4 model. Particle-like states are simulated by two widely separated identical wave trains which are propagated toward collision point from both sides in a trivial background. The maximal energy density that can be achieved in the collisions of the particle-like wave trains is investigated numerically for different wave train parameters. Maximum energy and number of kink–antikink pairs created after the collision is calculated and the relation between them are studied. It is shown numerically that, if the number of created kink–antikink pairs are N, the maximal energy density should be at least equal to N2∕2.

Seeing Wave-Particle Superposition with Cavity Input-Output Process

We present an experimental protocol to implement quantum delay-choice experiment in the context of cavity input-output process. In our protocol, the single-atom is employed as ancillary qubit to test the wave-particle feature of a single photon. With the cavity input-output process, we show that the controlled phase shift gate between single-atom and single-photon can be naturally used to generate the controlled Hadamard gate, which thus allows us to construct the quantum circuit for realizing the quantum delay-choice experiment. We also demonstrate the photonic wavelike and particlelike states can be simultaneously observed in our platform. Our protocol may open a new prospect using cavity quantum electrodynamics system to study some counterintuitive fundamental phenomenons in quantum mechanics.

A spin dynamics approach to solitonics

In magnetic materials a variety of non-collinear ground state configurations may emerge as a result of competition among exchange, anisotropy, and dipole-dipole interaction, yielding magnetic states far more complex than those of homogenous ferromagnets. Of particular interest in this study are particle-like configurations. These particle-like states, e.g., magnetic solitons, skyrmions, or domain walls, form a spatially localised clot of magnetic energy. In this paper we address topologically protected magnetic solitons and explore concepts that potentially might be relevant for logical operations and/or information storage in the rapidly advancing filed of solitonics (and skyrmionics). An ability to easily create, address, and manipulate such structures is among the prerequisite forming a basis of “-onics technology”, and is investigated in detail here using numerical and analytical tools.

New type of stable particlelike states in chiral magnets.

We present a new type of thermodynamically stable magnetic state at interfaces and surfaces of chiral magnets. The state is a soliton solution of micromagnetic equations localized in all three dimensions near a boundary, and it contains a singularity but nevertheless has finite energy. Both features combine to form a quasiparticle state for which we expect unusual transport and dynamical properties. It exhibits high thermal stability and thereby can be considered as a promising object for fundamental research and practical applications in spintronic devices. We identified the range of existence of such particlelike states in the thickness dependent magnetic phase diagram for helimagnet films and analyzed its stability in comparison with the isolated skyrmion within the conical phase. We provide arguments that such a state can be found in different B20-type alloys, e.g., Mn_{1-x}Fe_{x}Ge, Mn_{1-x}Fe_{x}Si, Fe_{1-x}Co_{x}Si.

Remote creation of hybrid entanglement between particle-like and wave-like optical qubits

The wave-particle duality of light has led to two different encodings for optical quantum information processing. Several approaches have emerged based either on particle-like discrete-variable states, e.g. finite-dimensional quantum systems, or on wave-like continuous-variable states, e.g. infinite-dimensional systems. Here, we demonstrate the first measurement-induced generation of entanglement between optical qubits of these different types, located at distant places and connected by a lossy channel. Such hybrid entanglement, which is a key resource for a variety of recently proposed schemes, including quantum cryptography and computing, enables to convert information from one Hilbert space to the other via teleportation and therefore connect remote quantum processors based upon different encodings. Beyond its fundamental significance for the exploration of entanglement and its possible instantiations, our optical circuit opens the promises for heterogeneous network implementations, where discrete and continuous-variable operations and techniques can be efficiently combined.

Multiple chiral topological states in liquid crystals from unstructured light beams

It is shown experimentally that unstructured light beams can generate a wealth of distinct metastable defect structures in thin films of chiral liquid crystals. Various kinds of individual chiral topological states are obtained as well as dimers and trimers, which correspond to the entanglement of several topological unit cells. Self-assembled nested assemblies of several metastable particle-like topological states can also be formed. Finally, we propose and experimentally demonstrate an opto-electrical approach to generate tailor-made architectures.

Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography

The aim of the present paper is to explain and accurately calculate the missing dark energy density of the cosmos by scaling the Planck scale and using the methodology of the relatively novel discipline of cosmic crystallography and Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation. Following this road we arrive at a modified version of Einstein’s energy mass relation E = mc2 which predicts a cosmological energy density in astonishing accord with the WMAP and supernova measurements and analysis. We develop non-constructively what may be termed super symmetric Penrose fractal tiling and find that the isomorphic length of this tiling is equal to the self affinity radius of a universe which resembles an 11 dimensional Hilbert cube or a fractal M-theory with a Hausdorff dimension where. It then turns out that the correct maximal quantum relativity energy-mass equation for intergalactic scales is a simple relativistic scaling, in the sense of Weyl-Nottale, of Einstein’s classical equation, namely EQR = (1/2)(1/) moc2 = 0.0450849 mc2 and that this energy is the ordinary measurable energy density of the quantum particle. This means that almost 95.5% of the energy of the cosmos is dark energy which by quantum particle-wave duality is the absolute value of the energy of the quantum wave and is proportional to the square of the curvature of the curled dimension of spacetime namely where and is Hardy’s probability of quantum entanglement. Because of the quantum wave collapse on measurement this energy cannot be measured using our current technologies. The same result is obtained by involving all the 17 Stein spaces corresponding to 17 types of the wallpaper groups as well as the 230-11=219 three dimensional crystallographic group which gives the number of the first level of massless particle-like states in Heterotic string theory. All these diverse subjects find here a unified view point leading to the same result regarding the missing dark energy of the universe, which turned out to by synonymous with the absolute value of the energy of the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation while ordinary energy is the energy of the quantum particle into which the Hawking-Hartle wave collapse at cosmic energy measurement. In other words it is in the very act of measurement which causes our inability to measure the “Dark energy of the quantum wave” in any direct way. The only hope if any to detect dark energy and utilize it in nuclear reactors is future development of sophisticated quantum wave non-demolition measurement instruments.

Probing the states of nucleons in exotic nuclei

Many of the most exotic neutron-proton asymmetric nuclei are produced in relatively small numbers in high-energy fragmentation reactions. They are produced as fast secondary beams with energies of 100 MeV per nucleon or more. Developments made and recent results that both exploit and assess fast one- and two-nucleon removal reactions from such secondary beams are reviewed. This includes very recent work that interfaces the sudden, eikonal reaction models used with more ab-initio nuclear structure inputs. The potential use of neutron pick-up reactions to study particle-like states in exotic nuclei is also outlined.

Oscillon Resonances and Creation of Kinks in Particle Collisions

We present a numerical study of the process of production of kink-antikink pairs in the collision of particlelike states in the one-dimensional ϕ4 model. It is shown that there are 3 steps in the process: The first step is to excite the oscillon intermediate state in the particle collision, the second step is a resonance excitation of the oscillon by the incoming perturbations, and, finally, the soliton-antisoliton pair can be created from the resonantly excited oscillon. It is shown that the process depends fractally on the amplitude of the perturbations and the number of perturbations. We also present the effective collective coordinate model for this process.

Fuzzy knot theory interpretation of Yang–Mills instantons and Witten’s 5-Brane model

A knot theory interpretation of ‘tHooft’s instanton based on hyperbolic volume, crossing numbers and exceptional Lie symmetry groups is given. Subsequently it is shown that although instantons and particle-like states of Heterotic super strings may appear to be different concepts, on a very deep fuzzy level they are not.