Complex Correlation Function Research Articles

Local Readout and Control of Current and Kinetic Energy Operators in Optical Lattices.

Quantum gas microscopes have revolutionized quantum simulations with ultracold atoms, allowing one to measure local observables and snapshots of quantum states. However, measurements so far were mostly carried out in the occupation basis. Here, we demonstrate how all kinetic operators, such as kinetic energy or current operators, can be measured and manipulated with single-bond resolution. Beyond simple expectation values of these observables, the single-shot measurements allow one to access full counting statistics and complex correlation functions. Our work paves the way for the implementation of efficient quantum state tomography and hybrid quantum computing protocols for itinerant particles on a lattice. In addition, we demonstrate how site-resolved programmable potentials enable a spatially selective, parallel readout in different bases as well as the engineering of arbitrary initial states.

Phase retrieval in inverse ghost diffraction using Sagnac interferometer

Ghost diffraction (GD) involves the use of non-local spatial correlations to image objects with light, which has not interacted with them. Here, we propose and experimentally demonstrate a new technique for first-order correlation measurement and retrieval of two-dimensional phase objects in the GD from inversion of the experimentally measured two-point complex correlation function in a first order interferometer. The GD scheme is experimentally implemented by a specially designed experimental setup wherein one of the orthogonal polarization components of the transversely polarized light interacts with the object and the other polarization component of the light remains intact and directly reaches the detector. The Fourier spectrum of the object is encoded into the two-point spatial correlation of these two orthogonal polarization components which is experimentally detected in an interferometer with a radial shearing in the Sagnac geometry. We experimentally demonstrated imaging of spatially varying phase objects and results are presented for three different cases.

Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map

Global correlation analysis is an important technique to quantify both the shape and amplitude differences between two response vectors. In linear dynamic systems, differences between two Frequency Response Functions (FRFs) are quantified as scalar number curves of the Global Shape Criterion (GSC) and the Global Amplitude Criterion (GAC), to represent FRF similarities at different frequencies. From linear to nonlinear, responses are usually obtained at different frequencies to form the Frequency Response Curve (FRC), replacing the FRF for dynamic analysis. Extending the concept of global correlation analysis from linear FRFs to nonlinear FRCs could quantify shape and amplitude similarities between nonlinear models. However, global correlation analysis for multivalued FRCs with a strong nonlinearity is hard to conduct, as strongly nonlinear correlation functions have complex multivalued phenomena with real/fake characteristics. In this paper, the Global Shape Curve Criterion (GSCC) and Global Amplitude Curve Criterion (GACC) are proposed for the correlation analysis of strongly nonlinear FRCs, which can quantify the similarity between two FRCs with different and complex multivalued phenomena. Through the arclength-based separation, multivalued FRCs are separated to single-valued response branches, in order to compute single-valued correlation functions that form the multivalued correlation function. The computed correlations contain the GSCC and GACC, which separately represent shape and amplitude differences between two FRCs at each frequency. The multivalued correlation function is represented as a Correlation-Map (C-MAP) to extract real correlation characteristics, for accurate correlation analysis. The multivalued correlation analysis is first verified on a 3 DOF model with a strong nonlinearity. Differences between the reference and initial multivalued FRCs are successfully quantified as scalar curves and the GACC may be more sensitive than the GSCC on models with a local nonlinearity. Then, the proposed method is further validated on an experimental 3 DOF model. Very complex 15-valued correlation functions between FRCs with different multivalued phenomena are established. Even so, the real correlations are still successfully extracted by the C-MAP. These show the validity and superiority of the proposed method.

Simulation Investigation of Bulk and Surface Properties of Liquid Benzonitrile: Ring Stacking-Assessment and Deconvolution.

The content and the molecular dynamics (MD) simulation analysis here are inspired by our recent ab initio calculation on benzonitrile (BZN), whereas the present results are to expand and develop macroscopic documentation involving data verification. MD simulations of the bulk liquid BZN in the range of 293–323 K unravel the hydrogen bond (−C≡N···H) formation with strength in the order of ortho-H ≫ meta-H ∼> para-H. The possibility for ortho-Hs to get involved in the formation of two bonds simultaneously confirms each having σ- and π-bonding features. Accordingly, we used vast efforts for structural analysis particularly based on the deconvolution of the corresponding complex correlation functions. Specific angle-dependent correlation functions led to the recognition of the molecular stacking with a strict anti-parallel orientation. The in-plane dimer and trimer also take part in the structural recognition. A singularity, found in the trend of the simulated temperature-dependent viscosity and diffusion coefficient of liquid BZN, is centered at about 313 K and quite fascinatingly emulates the reported experiment viscosity. An interplay between a small change in the trend of density and a large change in the corresponding viscosity is a key factor in supporting the singularity. Deconvolution of the simulation results allows attributing the singularity to structural alteration involving H-bonding of different types and extent. Approaching the range of 308–313 K, an alteration between hydrogen bond formation involving mostly ortho-Hs and mixed ortho-Hs + meta-H is possible and supports the singularity.

Correlation functions of non-Markovian systems out of equilibrium: analytical expressions beyond single-exponential memory

This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g. viscoelastic) fluid environment. Analytical investigations of such systems based on non-Markovian stochastic equations are notoriously difficult. A common approximation is that of a single-exponential memory, corresponding to the introduction of one auxiliary variable coupled to the Markovian dynamics of the main variable. As a generalization, we here investigate a class of ‘toy’ models with altogether three degrees of freedom, giving rise to more complex forms of memory. Specifically, we consider, mainly on an analytical basis, the under- and overdamped motion of a colloidal particle coupled linearly to two auxiliary variables, where the coupling between variables can be either reciprocal or non-reciprocal. Projecting out the auxiliary variables, we obtain non-Markovian Langevin equations with friction kernels and colored noise, whose structure is similar to that of a generalized Langevin equation. For the present systems, however, the non-Markovian equations may violate the fluctuation–dissipation relation as well as detailed balance, indicating that the systems are out of equilibrium. We then study systematically the connection between the coupling topology of the underlying Markovian system and various autocorrelation functions. We demonstrate that already two auxiliary variables can generate surprisingly complex (e.g. non-monotonic or oscillatory) memory and correlation functions. Finally, we show that a minimal overdamped model with two auxiliary variables and suitable non-reciprocal coupling yields correlation functions resembling those describing hydrodynamic backflow in an optical trap.

Характеристики обнаружения когерентной системы селекции движущихся целей при рассогласовании параметров квадратурных каналов.

ntroduction. Operation of adaptive system of moving targets selection is considered, which is represented by single intermittent subtractor with coherent accumulator, which is tuned in frequency. System of moving targets selection is made in the form of two quadrature channels, in which high-frequency passive interference and signal from moving object are converted to video frequency with subsequent rejection, accumulation and comparison with threshold level. Setting the task. Investigation of the effect of the inevitable in practice amplitude and phase misalignments of quadrature channel parameters on the detection characteristics of the adaptive selection system of moving targets. Method. Method of complex variable is used, in which passive interference and signal from moving object at input and output of adaptive selection system of moving targets are presented in the form of pair of real components shifted in phase by ninety degrees. Results. Models of passive interference and signal from moving object are presented taking into account possible in practice amplitude and phase mismatches of quadrature channels parameters. The structure of the processing device is shown, which includes a series-connected generator of quadrature components of passive interference and a signal from a moving object, an adaptive cutting filter in the form of a single intermittent subtraction circuit with a frequency-tuned rejection zone, an adaptive coherent accumulator and a threshold device. Expressions are obtained for complex correlation functions of passive interference and signal from moving object at output of coherent accumulator taking into account inevitable amplitude and phase mismatches of quadrature channels parameters. Dependencies of probability of correct detection of signal from moving object against the background of passive interference from value of deviation of transmission coefficients of quadrature channels and phase mismatch of reference voltages for different values of average frequency of spectral density of passive interference are calculated and constructed. Conclusion. Significant dependence of probability of correct detection of signal from moving object on average frequency of spectral density of passive interference, as well as amplitude and phase mismatches of quadrature channels parameters is shown.

Wolf phase tomography (WPT) of transparent structures using partially coherent illumination

In 1969, Emil Wolf proposed diffraction tomography using coherent holographic imaging to extract 3D information from transparent, inhomogeneous objects. In the same era, the Wolf equations were first used to describe the propagation correlations associated with partially coherent fields. Combining these two concepts, we present Wolf phase tomography (WPT), which is a method for performing diffraction tomography using partially coherent fields. WPT reconstruction works directly in the space–time domain, without the need for Fourier transformation, and decouples the refractive index (RI) distribution from the thickness of the sample. We demonstrate the WPT principle using the data acquired by a quantitative-phase-imaging method that upgrades an existing phase-contrast microscope by introducing controlled phase shifts between the incident and scattered fields. The illumination field in WPT is partially spatially coherent (emerging from a ring-shaped pupil function) and of low temporal coherence (white light), and as such, it is well suited for the Wolf equations. From three intensity measurements corresponding to different phase-contrast frames, the 3D RI distribution is obtained immediately by computing the Laplacian and second time derivative of the measured complex correlation function. We validate WPT with measurements of standard samples (microbeads), spermatozoa, and live neural cultures. The high throughput and simplicity of this method enables the study of 3D, dynamic events in living cells across the entire multiwell plate, with an RI sensitivity on the order of 10−5.

Measurement of Pure States of Light in the Orbital-Angular-Momentum Basis Using Nine Multipixel Image Acquisitions

The existing techniques for measuring high-dimensional pure states of light in the orbital angular momentum (OAM) basis either involve a large number of single-pixel data acquisitions and substantial postselection errors that increase with dimensionality, involve substantial loss, or require interference with a reference beam of known phase. Here, we propose an interferometric technique that can measure an unknown pure state using only nine multipixel image acquisitions without involving postselection, loss, or a separate reference beam. The technique essentially measures two complex correlation functions of the input field and then employs a recursive postprocessing algorithm to infer the state. We experimentally demonstrate the technique for pure states up to dimensionality of 25, reporting a mean fidelity greater than $90\mathrm{%}$ up to 11 dimensions. Our technique can significantly improve the performance of OAM-based information processing applications.

Stochastic complex transmittance screens for synthesizing general partially coherent sources.

We develop a method to synthesize any partially coherent source (PCS) with a genuine cross-spectral density (CSD) function using complex transmittance screens. Prior work concerning PCS synthesis with complex transmittance screens has focused on generating Schell-model (uniformly correlated) sources. Here, using the necessary and sufficient condition for a genuine CSD function, we derive an expression, in the form of a superposition integral, that produces stochastic complex screen realizations. The sample autocorrelation of the screens is equal to the complex correlation function of the desired PCS. We validate our work by generating, in simulation, three PCSs from the literature-none has ever been synthesized using stochastic screens before. Examining planar slices through the four-dimensional CSD functions, we find the simulated results to be in excellent agreement with theory, implying successful realization of all three PCSs. The technique presented herein adds to the existing literature concerning the generation of PCSs and can be physically implemented using a simple optical setup consisting of a laser, spatial light modulator, and spatial filter.

Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble

In these proceedings we summarise how the determinantal structure for the conditional overlaps among left and right eigenvectors emerges in the complex Ginibre ensemble at finite matrix size. An emphasis is put on the underlying structure of orthogonal polynomials in the complex plane and its analogy to the determinantal structure of $k$-point complex eigenvalue correlation functions. The off-diagonal overlap is shown to follow from the diagonal overlap conditioned on $k\geq2$ complex eigenvalues. As a new result we present the local bulk scaling limit of the conditional overlaps away from the origin. It is shown to agree with the limit at the origin and is thus universal within this ensemble.

Plume Current Change by Seawall Construction for a Harbor Development in South Korea

Kim, M.-J.; Kim, C.-S.; Choi, B.-J., and Lee, S.-H., 2018. Plume Current Change by Seawall Construction for a Harbor Development in South Korea. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 126–130. Coconut Creek (Florida), ISSN 0749-0208.The present study investigates the effects of a seawall construction on the nearfield plume dispersal and surface circulation in the west coast of Korea where the Saemangeum tide dike (33 km long) had been constructed from 1993 to 2006 to reclaim the wide tidal flat in the riverine estuary. The plume water has since flowed out by the gate operation from the two sluices (11 km apart) in the southern dike to the offshore, which altered source location of the plume in the coastal sea. Recently a 3.5 km long seawall was constructed at 4 km offshore from the northern sluice. The changes of the plume current and surface circulation near the newly constructed seawall were examined using data set of High Frequency Radar-derived current (HFR-current), wind and sluice-outflow velocity in summer 2010 (before the seawall construction) and summer 2014 (under the seawall construction). It was found that construction of seawall evidently changed tidal plume dispersal pattern and nearfield distribution of monthly-mean plume current. Complex correlation and Empirical Orthogonal Function (EOF) analyses on the subinertial surface current, wind, and sluice-outflow velocity in summer 2010 and summer 2014 revealed that wind and outflow velocity are dominant factors controlling variations of the plume extension and coastal current.

Polarization modulation for imaging behind the scattering medium.

We propose and experimentally demonstrate a technique, based on polarization modulation, for imaging of the polarization discriminating object hidden behind a scattering medium. This is realized by making use of the relation between the complex correlation function of the randomly scattered orthogonal polarization components in the far field and polarized source structure at the scattering plane. Full use of a polarimetric parameter at the scattering plane is realized in the object plane reconstruction behind the scattering medium using a backpropagation approach. To demonstrate application of the technique, imaging of two different objects lying behind the scattering media is presented.

Inference for interacting linear waves in ordered and random media

A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We investigate systems with both deterministic and quenched disordered couplings on two extreme topologies: complete and sparse graphs. To match further applications in optics also complex couplings and external fields are considered and general inference formulas are derived for real and imaginary parts of Hermitian coupling matrices from real and imaginary parts of complex correlation functions. The whole procedure is, eventually, tested on numerically generated correlation functions and local magnetizations by means of Monte Carlo simulations.

Higher spin entanglement entropy

In this paper, we develop a perturbation formulation to calculate the single interval higher spin R$\acute{e}$nyi and entanglement entropy for two dimensional conformal field theory with $\mathcal{W}_{\infty}(\lambda)$ symmetry. The system is at finite temperature and is deformed by higher spin chemical potential. We manage to compute higher spin R$\acute{e}$nyi entropy with various spin deformations up to order $\mathcal{O}(\mu^2)$. For spin 3 deformation, we calculate exact higher spin R$\acute{e}$nyi entropy up to $\mathcal{O}(\mu^4)$. When $\lambda=3$, in the large $c$ limit, we find perfect match with tree level holographic higher spin entanglement entropy up to order $\mu^4$ obtained by the Wilson line prescription. We also find quantum corrections to higher spin entanglement entropy which is beyond tree level holographic results. The quantum correction is universal at order $\mu^4$ in the sense that it is independent of $\lambda$. Our computation relies on a multi-valued conformal map from $n$-sheeted Riemann surface $\mathcal{R}_n$ to complex plane and correlation functions of primary fields on complex plane. The method can be applied to general conformal field theories with $\mathcal{W}$ symmetry.

Physical and Statistical Properties of the Complex Monopulse Ratio

Angular glint gives rise to random pointing errors, which can deteriorate the direction-of-arrival (DOA) estimation accuracy. In monopulse radars the glint manifests itself through a complex valued process known as the complex monopulse ratio (CMR). Physical and statistical properties of the glint are considered. It is proposed to use the Poynting vector formalism for the CMR physical interpretation. The complex probability density function (pdf) and correlation function of CMR are derived.

Phase-based block matching applied to motion estimation with unconventional beamforming strategies

A phase-based block matching method adapted to motion estimation with unconventional beamforming strategies is presented. The unconventional beamforming technique used allows us to obtain 2-D RF images with axial and lateral modulations. Based on these images, we propose a method that uses phase images instead of amplitude images. This way of proceeding allows us to provide an analytical solution to the local displacement estimation so that no minimization of a classical cost function is used for the local estimation. For this reason, the local estimator is directly applied to signals, without the need to process a complex cross-correlation function, as is done with most of the phase shift estimators. In this paper, the method is applied to elastography. Results with simulated data show that a downsampling of axial and lateral modulated signals leads to very little change in the accuracy and in the spatial resolution of the proposed method. For example, for decimation factors of 2 in the axial direction and of 4 in the lateral direction, the mean axial absolute error is 3 mum. The same estimation with original images provides a mean axial error of 0.7 microm. The accuracy of the lateral motion is unchanged in this case. The accuracy of our method with downsampled signals is an important issue in the purpose of a real-time implementation. With experimental data, for the same level of estimation error, classical block matching using the maximum of cross correlation as a local estimator requires images that are 36 times larger (in number of pixels) and consequently a computational time roughly 10 times longer. Our phase block matching is also shown to provide 10 percent less error than a motion estimation method based on seeking the zero of the complex correlation function phase. Finally, it is shown that given the separability of the local estimator that we propose, our method can be applied on both n-D signals and classical RF ultrasound images. The phase block matching method presented was implemented in real time on an ultrasound research scanner.

Analytic Estimation of Subsample Spatial Shift Using the Phases of Multidimensional Analytic Signals

In this correspondence, a method of analytic subsample spatial shift estimation based on an a priori n-D signal model is proposed. The estimation uses the linear phases of n analytic signals defined with the multidimensional Hilbert transform. This estimation proposes: i) an analytic solution to the n-D shift estimation and ii) an estimation without processing complex cross-correlation function or cross-spectra between signals contrary to most phase shift estimators. The method provides better performance in estimating subsample shifts than two classical estimators, one using the maximum of cross-correlation function and the other seeking the zero of the complex correlation function phase. Two delay estimators using the in-phase and quadrature-phase components of signals are also compared to our estimator. Like most estimators using the complex signal phases, the estimator proposed herein presents the advantage of unaltered accuracy when low sampled signals are used. Moreover, we show that this method can be applied to motion tracking with ultrasound images. Thus, included in a block-based motion estimation method and tested with ultrasound data, this estimator provides an analytical solution to the translation estimation problem.

Correlation function-based finite-difference time-domain method for simulating ultrashort pulse propagation. I. Formalism

A finite-difference time-domain formalism for simulating coherent linear pulse propagation is presented that incorporates a medium response described by any two-time energy gap correlation function. Two algorithms, for real and complex correlation functions, are developed to evaluate the electric polarization through explicit treatment of the density matrix for a two-level system. The coherence relaxation terms in the resulting finite-differenced Maxwell–Liouville equations depend on integrals over the energy gap fluctuation correlation function. The algorithms are used to simulate ultrashort mid-infrared pulse propagation through optically dense samples of HDO in liquid D2O as a demonstration of their performance and flexibility. These algorithms represent a first step toward the goal of incorporating complicated material responses into the full-field simulation of nonlinear pulse propagation and nonlinear optical spectroscopy.

Modified Phased Tracking Method for Measurement of Change in Thickness of Arterial Wall

In this study, the change in thickness of the arterial wall caused by the heartbeat was measured by the phased tracking method [IEEE Trans. UFFC. 43 (1996) 791] for noninvasive assessment of the regional elasticity of the arterial wall. In the phased tracking method, the change in thickness of the arterial wall is obtained from the difference between displacements of two points set along an ultrasonic beam. The displacement during the pulse repetition interval is determined by the phase of the complex correlation between the quadrature modulated ultrasonic waves. For suppressing noise components, the complex correlation function is spatially averaged in the region, which corresponds to the ultrasonic wavelength. However, spatial averaging of displacements is not desirable for measurement of the change in thickness, because the change in thickness is caused by the spatial inhomogeneity of displacements. In this paper, the phased tracking method was modified for direct estimation of the change in thickness without spatial averaging of displacements.

Top Chern Classes of Universal Bundles on the Complex Projective Plane and Correlation Functions of Asymptotically Free SYM N=2 QFT

Top Chern Classes of Universal Bundles on the Complex Projective Plane and Correlation Functions of Asymptotically Free SYM N=2 QFT