Finite Overlap Research Articles

Preparing quantum many-body scar states on quantum computers

Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.

Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction

We theoretically study quantum transport through a quantum dot coupled to Majorana bound states confined at the ends of a topological superconducting nanowire. The topological superconductor forms a loop and is threaded by a tunable magnetic flux, which allows one to control the electron transport in the system. In particular, we investigate phonon-assisted transport properties in the device when the central quantum dot interacts with a single long-wave optical phonon mode. We find that when the two Majorana bound states are unhybridized, the zero-temperature linear conductance has a $2\pi$ periodicity as a function of magnetic flux phase, independent of the electron-phonon interaction, the quantum dot energy, or the finite values of dot-Majorana couplings. For a finite overlap between the Majorana bound states, the linear conductance periodicity generally changes to $4\pi$ either due to a finite electron-phonon coupling strength, or a dot energy level that is tuned away from the Fermi level. Additionally, the differential conductance periodicity changes from $2\pi$ to $4\pi$ when the Majorana bound states hybridize and the electron-phonon coupling is finite. Our results provide insight into transport signatures expected in topological quantum computational platforms that integrate quantum dots as a means for Majorana qubit readout. The energy exchange with an environmental bath, here a single phonon mode, significantly alters the current signatures expected from Majorana modes.

A Data Augmentation Method for Vertical Federated Learning

Federated learning (FL) enables various organizations to jointly train one single model without revealing their private data to each other. The FL can be classified as horizontal federated learning (HFL) and vertical federated learning (VFL) according to the distribution of overlap samples and overlap features in the dataset. VFL allows various organizations to share machine learning based on the overlap samples, each one of which has the same identity. However, VFL suffers from insufficient number of overlap samples among all participants. Hence, the shortage of overlap data results in a worse performance of the global model. In this article, we propose a data augmentation method, FedDA, which is based on the generative adversarial network (GAN) to increase the number of training data. We generate more overlap data by learning the features of finite overlap data and many locally existing nonoverlap data, which expand the availability for training the overlap dataset. A series of experiments were executed on both MNIST and CIFAR-10. The results show that FedDA can efficiently utilize nonoverlap samples to enhance the effect of the data augmentation. It can generate high-quality overlap samples and expand the set of overlap samples. Thus, when the VFL is short of overlap samples, FedDA can provide abundant training data to improve the performance of the VFL model.

Investigations into growth of whistlers with energy of energetic electrons

Runaway electrons have great significance in fusion plasmas as they are considered to be responsible for the excitation of instabilities and for damage to the first wall components. The threshold for the generation of the runaway electron population in tokamaks strongly depends on the toroidal magnetic field and bulk electron temperature. The presence of these runaway electrons with a critical density and magnetic field value are correlated with the magnetosonic whistler activity. The Rosenbluth condition applies to the destabilization of upper hybrid modes, that remains mostly stable in large-scale tokamaks like Joint European Tokamakand International Thermonuclear Experimental reactor. On the other hand, whistlers with a frequency in the lower hybrid range are more likely to be destabilized in a lower magnetic field and temperature, along with the whistlers’ excitation threshold. The process of destabilization of whistlers by energetic electrons thus has a finite overlap between fusion and basic plasma devices, and the outcome from the latter can be scalable to fusion machines. We report that in the linear large volume plasma device, the destabilization of quasi-longitudinal whistlers, driven by the reflected particles from the mirror, takes place in the bulk plasma region i.e. away from the mirror in the energetic belt region, and follows the frequency ordering of . Our explanation involves an alternate limit of quasi-linear analysis, commonly employed for recovering the instability threshold of runaways scattering off whistlers in fusion plasmas, and the growth rate due to the reflected particle is proportional to the inverse square root of electron temperature, where the reflected particle fraction is (Sharma and Vlahos 1984 Astrophys. J. 280 405). The measurements required to obtain the energy scaling of runaway electrons with whistler instability are critical for large devices but remain scarce. We have emphasized the analytic correlation between the two regimes in these investigations.

Magnetization dynamics in a Majorana-wire–quantum-dot setup

We theoretically study the quench dynamics of the local magnetization in a hybrid Majorana-wire--quantum-dot system coupled to external leads. In order to thoroughly understand the origin of the dot magnetization dynamics, we consider either normal metal or ferromagnetic electrodes. In the first case, the magnetization arises exclusively from the proximity to the topological superconductor hosting Majorana zero-energy modes and the associated development of an induced exchange field. We predict a nonmonotonic dependence of the dot's magnetization in the odd-occupation regime and show that the dynamics is governed by the magnitude of the coupling to Majorana wire. However, when the system is coupled to ferromagnetic leads, the ferromagnet and Majorana contributions to the effective exchange field are competing with each other and reveal a nontrivial dynamical behavior. As a result, the time-dependent magnetization can undergo multiple sign changes preceding the relaxation to a new thermal value. We also identify the transport regime, where fine tuning of the coupling to Majorana wire within a narrow range allows one to manipulate the magnetic state of the system. The effect of spin polarization of the leads and influence of the finite overlap between the Majorana edge modes are also examined. Moreover, we analyze the quench in the energy of the quantum dot orbital level and demonstrate that the rather straightforward charge dynamics can disguise nontrivial time evolution of the magnetization. Finally, we compare predicted dynamics with results obtained for quantum dot coupled to spin-polarized fermionic bound state instead of Majorana zero-energy mode.

Continuous Hue-Based Self-Calibration of a Smartphone Spectrometer Applied to Optical Fiber Fabry-Perot Sensor Interrogation.

Smartphone-based optical spectrometers allow the development of a new generation of portable and cost-effective optical sensing solutions that can be easily integrated into sensor networks. However, most commonly the spectral calibration relies on the external reference light sources which have known narrow spectral lines. Such calibration must be repeated each time the fiber and diffraction grating holders are removed from the smartphone and reattached. Moreover, the spectrometer wavelength scale can drift during the measurement because of the smartphone temperature fluctuations. The present work reports on a novel spectral self-calibration approach, based on the correspondence between the light wavelength and the hue features of the spectrum measured using a color RGB camera. These features are caused by the nonuniformity of camera RGB filters’ responses and their finite overlap, which is a typical situation for RGB cameras. Thus, the wavelength scale should be externally calibrated only once for each smartphone spectrometer and can further be continuously verified and corrected using the proposed self-calibration approach. An ability of the plug-and play operation and the temperature drift elimination of the smartphone spectrometer was experimentally demonstrated. Conducted experiments involved interrogation of optical fiber Fabry-Perot interferometric sensor and demonstrated a nanometer-level optical path difference resolution.

Majorana-Kondo interplay in T-shaped double quantum dots

The transport behavior of a double quantum dot side-attached to a topological superconducting wire hosting Majorana zero-energy modes is studied theoretically in the strong correlation regime. It is shown that Majorana modes can leak to the whole nanostructure, giving rise to a subtle interplay between the two-stage Kondo screening and the half-fermionic nature of Majorana quasiparticles. In particular, the coupling to the topological wire is found to reduce the effective exchange interaction between the two quantum dots in the absence of normal leads. Interestingly, it also results in an enhancement of the second-stage Kondo temperature when the normal leads are attached. Moreover, it is shown that the second stage of the Kondo effect can become significantly modified in one of the spin channels due to the interference with the Majorana zero-energy mode, yielding the low-temperature conductance equal to $G=G_0/4$, where $G_0 = 2e^2/h$, instead of $G=0$ in the absence of the topological superconducting wire. We also identify a nontrivial spin-charge ${\rm SU}(2)$ symmetry present in the system at a particular point in parameter space, despite lack of the spin nor charge conservation. Finally, we discuss the consequences of a finite overlap between two Majorana modes, as relevant for short Majorana wires.

Deformable and breakable DEM particle clusters for modelling compression of plastic and brittle porous materials — Model and structure properties

A new framework for DEM modelling of deformable and breakable particles is presented. In our approach, real-life particles are modelled as agglomerates (or clusters) of many DEM particles forming spherical clumps and interacting via a linear elasto-plastic force. Such interaction provides a finite equilibrium overlap, resulting in mechanically stable clusters after agglomeration. Since inter-particles bonds are elastic, clusters can be used to model particles or structures that can deform elastically, plastically or break. Different clusters can bond as well, providing the basis for modelling complex particle agglomeration. The framework is described, and key structural properties of clusters are defined and analytically related to DEM components packing and their material properties. These relations are numerically validated showing a very good agreement, enabling clusters to be designed with a precise structure. Applications of this model range from particle deformation and breakage to porous structures, from soil mechanics to die compaction and tableting.

Wide-Range Band-Gap Tuning and High Electrical Conductivity in La- and Pb-Doped SrSnO3 Epitaxial Films.

Perovskite oxide SrSnO3 has attracted considerable attentions recently due to its high carrier mobility and high transparency. Here, we experimentally and theoretically investigated the effects of La and Pb doping on the microstructure, band gaps, and electrical properties of SrSnO3 epitaxial thin films. X-ray diffraction analysis showed that the in-plane lattice constants of Pb-doped SrSnO3 (SrSn1-xPbxO3, x = 0-1, SSPO) films increased from 4.053 to 4.178 Å with the increase in Pb doping content. High-resolution transmission electron microscopy images revealed that SSPO films were coherently grown on LaAlO3(001) substrates. The optical band-gap values were considerably decreased gradually from 4.43 to 2.16 eV with Pb doping content while maintaining high optical transmittance in the visible wavelength range. Density functional theory calculations showed that the narrowing of band gap was attributed to a finite overlap between Pb 6s and Sn 5s orbitals around the bottom of the conduction band. As doping with 5% La in SSPO films, the electrical conductivity was improved greatly, and transport properties were investigated through temperature-dependent resistivity and Hall measurements. A lowest room-temperature resistivity of 0.5 mΩ cm and a maximum mobility of 39.9 cm2/Vs were observed in 5% La in the SSPO film at x = 1. Such wide-range tuning of the band gaps and excellent electrical properties of La- and Pb-doped SrSnO3 epitaxial thin films may provide promising applications in optoelectronic devices.

Spectroscopic Contrast of Diarylethene Molecules on Octanethiol Monolayer

We present a systematic scanning tunneling microscopy (STM) study of bias-dependent imaging of disulfur diarylethene (2S-DE) molecules on octanethiol (C8) monolayer at room temperature. In a rigid confinement of the C8 matrix, we did not observe any significant variation in the appearance of the 2S-DE. On the contrary, a reversal in the apparent height of the 2S-DE was present when the molecule was situated on a gold vacancy island. We attributed this finding to the presence of a new electronic state that became accessible for a tunneling event. In addition, the C8 surface structure underwent a reversible phase transformation from root 3 x root 3 R30 degrees hexagonal to c(4x2) square superlattice when the bias voltage was reduced from -825 mV to -425 mV or vice versa. Under a finite bias voltage, an appreciable topographic variation of the 2S-DE signature was demonstrated for the first time. This finding can be ascribed to a finite overlap of the associated wave functions that occurred between the tip state and the 2S-DE molecular energy level. We believe that physical insight on the bias-dependent imaging of organic molecules on solid surface is important towards the advancement of molecular electronics-based devices.

Multi-scale simulation method for electroosmotic flows

Electroosmotic transport in micro-and nano- channels has important applications in biological and engineering systems but is difficult to model because nanoscale structure near surfaces impacts flow throughout the channel. We develop an efficient multi-scale simulation method that treats near-wall and bulk subdomains with different physical descriptions and couples them through a finite overlap region. Molecular dynamics is used in the near-wall subdomain where the ion density is inconsistent with continuum models and the discrete structure of solvent molecules is important. In the bulk region the solvent is treated as a continuum fluid described by the incompressible Navier-Stokes equations with thermal fluctuations. A discrete description of ions is retained because of the low density of ions and the long range of electrostatic interactions. A stochastic Euler-Lagrangian method is used to simulate the dynamics of these ions in the implicit continuum solvent. The overlap region allows free exchange of solvent and ions between the two subdomains. The hybrid approach is validated against full molecular dynamics simulations for different geometries and types of flows.

Assembly of bipolar microtubule structures by passive cross-linkers and molecular motors.

During cell division, sister chromatids are segregated by the mitotic spindle, a bipolar assembly of interdigitating antiparallel polar filaments called microtubules. The spindle contains the midzone, a stable region of overlapping antiparallel microtubules, that is essential for maintaining bipolarity. Although a lot is known about the molecular players involved, the mechanism underlying midzone formation and maintenance is still poorly understood. We study the interaction of polar filaments that are cross-linked by molecular motors moving directionally and by passive cross-linkers diffusing along microtubules. Using a particle-based stochastic model, we find that the interplay of motors and passive cross-linkers can generate a stable finite overlap between a pair of antiparallel polar filaments. We develop a mean-field theory to study this mechanism in detail and investigate the influence of steric interactions between motors and passive cross-linkers on the overlap dynamics. In the presence of interspecies steric interactions, passive cross-linkers mimic the behavior of molecular motors and stable finite overlaps are generated even for non-cross-linking motors. Finally, we develop a mean-field theory for a bundle of aligned polar filaments and show that they can self-organize into a spindlelike pattern. Our work suggests possible ways as to how cells can generate spindle midzones and control their extensions.

HETEROGENEOUS SYSTEMS IN DIMENSIONS: LOWER SPECTRUM

The lower part of the spectrum of the Helmholtz equation for a heterogeneous system in a finite region in $d$ dimensions, where the solutions to the corresponding homogeneous system are known, can be systematically approximated by means of iterative methods. These methods only require the specification of an arbitrary ansatz and converge to the desired solution, regardless of the strength of the inhomogeneities, provided the ansatz has a finite overlap with it. In this paper, different boundary conditions at the borders of the domain are assumed, and some applications are used to illustrate the methods.

Thermoelectric effect in the Kondo dot side-coupled to a Majorana mode

We investigate the linear thermoelectric response of an interacting quantum dot side-coupled by one of two Majorana modes hosted by a topological superconducting wire. We employ the numerical renormalization group technique to obtain the thermoelectrical conductance L in the Kondo regime while the background temperature T, the Majorana-dot coupling Γ m , and the overlap e m between the two Majorana modes are tuned. We distinguish two transport regimes in which L displays different features: the weak- (Γ m T K ) regimes, where T K is the Kondo temperature. For an infinitely long nanowire where the Majorana modes do not overlap (e m = 0), the thermoelectrical conductance in the weak-coupling regime exhibits a peak at T ~ Γ m <T K . This peak is ascribed to the anti-Fano resonance between the asymmetric Kondo resonance and the zero-energy Majorana bound state. In the strong-coupling regime, on the other hand, the Kondo-induced peak in L is affected by the induced Zeeman splitting in the dot. For finite but small overlap (0 <e m <Γ m ), the interference between the two Majorana modes restores the Kondo effect in a smaller energy scale Γ′ m and gives rise to an additional peak in Γ ~ Γ′ m, whose sign is opposite to that at T ~ Γ m . In the strong-coupling regime this additional peak can cause a non-monotonic behavior of L with respect to the dot gate. Finally, in order to identify the fingerprint of Majorana physics, we compare the Majorana case with its counterpart in which the Majorana bound states are replaced by a (spin-polarized) ordinary bound state and find that the thermoelectric features for finite e m are the genuine effect of the Majorana physics.

Exact overlaps in the Kondo problem.

It is well known that the ground states of a Fermi liquid with and without a single Kondo impurity have an overlap that decays as a power law of the system size, expressing the Anderson orthogonality catastrophe. Ground states with two different values of the Kondo couplings have, however, a finite overlap in the thermodynamic limit. This overlap, which plays an important role in quantum quenches for impurity systems, is a universal function of the ratio of the corresponding Kondo temperatures, which is not accessible using perturbation theory or the Bethe ansatz. Using a strategy based on the integrable structure of the corresponding quantum field theory, we propose an exact formula for this overlap, which we check against extensive density matrix renormalization group calculations.

Signatures of Majorana States in Electron Transport through a Quantum Dot Coupled to a Topological Wire

We consider theoretically a system composed of a quantum dot coupled to a topological superconducting wire. The dot, being in Coulomb blockade (CB) regime, is additionally coupled to the leads, allowing standard transport measurements. The topological wire hosts Majorana states at its ends, which, as we show, characteristically modifies conductance through the dot. An unpaired Majorana state in the wire causes a unique temperature dependence of zero bias conductance vs. gate voltage. It decreases in-between CB peaks and on the sides of the peaks from the plateau at ∼ e2/2h when temperature increases. At the same time conductance increases at the CB peak positions. It is accompanied by zero bias anomaly in differential conductance. For finite overlap of Majorana states in the wire the zero bias anomaly disappears. Instead, two characteristic Fano resonances of opposite symmetry appear, positioned mirror-symmetrically with respect to zero bias.

Magnetic breakdown in an array of overlapping Fermi surfaces

We develop a theoretical framework for a magnetic breakdown in an array of circular two-dimensional bands with a finite overlap of neighboring Fermi surfaces due to the presence of a presumably weak periodic potential, and apply the obtained results to the electron bands in carbon honeycomb structures of doped graphene and intercalated graphite compounds. In contrast to the standard treatment, inaugurated more than fifty years ago by Slutskin and Kadigrobov, with electron semiclassical trajectories encircling significantly overlapping Fermi surfaces, we examine a configuration in which bands are related in a way that the Fermi surfaces only slightly overlap, forming internal band pockets with areas of the size comparable to the area of the quantum magnetic flux for a given external magnetic field. Such band configuration has to be treated quantum mechanically. The calculation leads to the results for magnetic breakdown coefficients comprising an additional large factor with respect to the standard results, proportional to the ratio of the Fermi energy and the cyclotron energy. Also, these coefficients show oscillating dependence on energy, as well as on the wave number of periodic potential. Both mentioned elements enable the adjustment of the preferred wave vector of possible magnetic breakdown induced density wave instability at the highest possible critical temperature.

Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnetCoNb2O6

We present experimental and theoretical evidence that an interesting quantum many-body effect -- quasi-particle breakdown -- occurs in the quasi-one-dimensional spin-1/2 Ising-like ferromagnet CoNb$_2$O$_6$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of CoNb$_2$O$_6$ and determine the exchange parameters of this model by fitting the calculated single particle dispersion to the one observed experimentally in applied transverse magnetic fields. We present high-resolution inelastic neutron scattering measurements of the single particle dispersion which observe "anomalous broadening" effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for non-zero matrix elements for decay by breaking the $\mathbb{Z}_2$ spin inversion symmetry of the Hamiltonian.

Transport in two-dimensional disordered semimetals.

We theoretically study transport in two-dimensional semimetals. Typically, electron and hole puddles emerge in the transport layer of these systems due to smooth fluctuations in the potential. We calculate the electric response of the electron-hole liquid subject to zero and finite perpendicular magnetic fields using an effective medium approximation and a complementary mapping on resistor networks. In the presence of smooth disorder and in the limit of a weak electron-hole recombination rate, we find for small but finite overlap of the electron and hole bands an abrupt upturn in resistivity when lowering the temperature but no divergence at zero temperature. We discuss how this behavior is relevant for several experimental realizations and introduce a simple physical explanation for this effect.

Conservation laws protect dynamic spin correlations from decay: Limited role of integrability in the central spin model

Mazur's inequality renders statements about persistent correlations possible. We generalize it in a convenient form applicable to any set of linearly independent constants of motion. This approach is used to show rigorously that a fraction of the initial spin correlations persists indefinitely in the isotropic central spin model unless the average coupling vanishes. The central spin model describes a major mechanism of decoherence in a large class of potential realizations of quantum bits. Thus the derived results contribute significantly to the understanding of the preservation of coherence. We will show that persisting quantum correlations are not linked to the integrability of the model, but caused by a finite operator overlap with a finite set of constants of motion.