Local Phase Difference Research Articles

Dynamic tunable nonreciprocal single-photon scattering mediated by a giant atom assisted with a time-modulated cavity

Nonreciprocal single-photon scattering in a one-dimensional waveguide coupled to a giant two-level atom assisted with a time-modulated single-mode cavity is investigated. The analytic expressions of the single-photon scattering amplitudes are derived by using an effective Floquet Hamiltonian in real space. The scattering characteristics are discussed detail in both the Markovian and the non-Markovian regimes, and the corresponding conditions for achieving perfect nonreciprocal single-photon transmission are obtained. In the Markovian regime, a frequency-tunable single-photon diode with an ideal transmission contrast ratio can be realized by adjusting the frequency of the cavity mode, the local coupling phase difference, and the accumulated phase between the two coupling points. Furthermore, the influence of the intrinsic energy dissipations on the photon transport is discussed in detail. It is found that the dissipations of the cavity and the giant atom affect discriminatively the nonreciprocal single-photon scattering process. In the non-Markovian regime, the influence of the non-Markovian retarded effect induced by the time delay on the nonreciprocal single-photon scattering is discussed in detail. The results reveal that, although the retarded effect leads to a complex nonreciprocal scattering spectrum, dynamic tunable perfect nonreciprocal transmission with more abundant physical phenomena suitable for photons with different frequencies within a larger range can also be achieved. Such a nonreciprocal single-photon device can be used as an elementary unit for various quantum information processing and may have potential applications in quantum network engineering.

Local phase-constrained convolutional autoencoder network for identifying multivariate geochemical anomalies

Autoencoder is a powerful tool for identifying multivariate geochemical anomalies. However, existing autoencoder-based geochemical anomaly detection methods primarily rely on a global reconstruction error (e.g., mean square error) to define the lower limit of geochemical anomalies, neglecting the common, local structure information of geochemical data. This limitation inevitably results in the decreased accuracy of geochemical anomaly identification. This study proposed a local Phase-Constrained Convolutional AutoEncoder network (PC-CAE) for the identification of multivariate geochemical anomalies. Initially, we employed a local Fourier transform to extract phase information from both the original and the reconstructed data. Subsequently, a convolutional autoencoder network was utilized to learn the latent representation of geochemical background, using the local phase difference between the original and reconstructed data to preserve the local data structure related to geology setting. Additionally, an adaptive weighting strategy was employed to mitigate the overfitting issue. The training samples with high reconstruction errors were finally identified as anomalies. We tested the validity of PC-CAE using the stream sediment geochemical dataset collected in the Jiaodong gold province, Eastern China. The results demonstrated that PC-CAE outperforms existing convolutional autoencoder network and spectrum–area multifractal model in identifying multivariate geochemical anomalies associated with Au mineralization.

Phase unwrapping for phase imaging using the plug-and-play proximal algorithm.

Phase unwrapping (PU) is essential for various scientific optical applications. This process aims to estimate continuous phase values from acquired wrapped values, which are limited to the interval (-π,π]. However, the PU process can be challenging due to factors such as insufficient sampling, measurement errors, and inadequate equipment calibration, which can introduce excessive noise and unexpected phase discontinuities. This paper presents a robust iterative method based on the plug-and-play (PnP) proximal algorithm to unwrap two-dimensional phase values while simultaneously removing noise at each iteration. Using a least-squares formulation based on local phase differences and reformulating it as a partially differentiable equation, it is possible to employ the fast cosine transform to obtain a closed-form solution for one of the subproblems within the PnP framework. As a result, reliable phase reconstruction can be achieved even in scenarios with extremely high noise levels.

Phase engineering of anomalous Josephson effect derived from Andreev molecules

A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.

Active XY model on a substrate: Density fluctuations and phase ordering.

We explore the generic long-wavelength properties of an active XY model on a substrate, consisting of a collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation, and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it displays generalized quasi-long-range order (QLRO): It shows phase ordering which is generically either logarithmically stronger than the conventional QLRO found in its equilibrium limit, together with "miniscule number fluctuations," or logarithmically weaker than QLRO along with "giant number fluctuations," showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short-range phase order are found, characterized by the presence or absence of stable clusters of finite sizes. In a surprising connection, the hydrodynamic theory for this model also describes the fluctuations in a Kardar-Parisi-Zhang (KPZ) surface with a conserved species on it, or an active fluid membrane with a finite tension, without momentum conservation and a conserved species living on it. This implies the existence of stable fluctuating surfaces that are only logarithmically smoother or rougher than the Edward-Wilkinson surface at two dimensions (2D) can exist, in contrast to the 2D pure KPZ-like "rough" surfaces.

Controlling Andreev Bound States with the Magnetic Vector Potential.

Tunneling spectroscopy measurements are often used to probe the energy spectrum of Andreev bound states (ABSs) in semiconductor-superconductor hybrids. Recently, this spectroscopy technique has been incorporated into planar Josephson junctions (JJs) formed in two-dimensional electron gases, a potential platform to engineer phase-controlled topological superconductivity. Here, we perform ABS spectroscopy at the two ends of planar JJs and study the effects of the magnetic vector potential on the ABS spectrum. We show that the local superconducting phase difference arising from the vector potential is equal in magnitude and opposite in sign at the two ends, in agreement with a model that assumes localized ABSs near the tunnel barriers. Complemented with microscopic simulations, our experiments demonstrate that the local phase difference can be used to estimate the relative position of localized ABSs separated by a few hundred nanometers.

Abdominopelvic MR to CT registration using a synthetic CT intermediate.

Accurate coregistration of computed tomography (CT) and magnetic resonance (MR) imaging can provide clinically relevant and complementary information and can serve to facilitate multiple clinical tasks including surgical and radiation treatment planning, and generating a virtual Positron Emission Tomography (PET)/MR for the sites that do not have a PET/MR system available. Despite the long‐standing interest in multimodality co‐registration, a robust, routine clinical solution remains an unmet need. Part of the challenge may be the use of mutual information (MI) maximization and local phase difference (LPD) as similarity metrics, which have limited robustness, efficiency, and are difficult to optimize. Accordingly, we propose registering MR to CT by mapping the MR to a synthetic CT intermediate (sCT) and further using it in a sCT‐CT deformable image registration (DIR) that minimizes the sum of squared differences. The resultant deformation field of a sCT‐CT DIR is applied to the MRI to register it with the CT. Twenty‐five sets of abdominopelvic imaging data are used for evaluation. The proposed method is compared to standard MI‐ and LPD‐based methods, and the multimodality DIR provided by a state of the art, commercially available FDA‐cleared clinical software package. The results are compared using global similarity metrics, Modified Hausdorff Distance, and Dice Similarity Index on six structures. Further, four physicians visually assessed and scored registered images for their registration accuracy. As evident from both quantitative and qualitative evaluation, the proposed method achieved registration accuracy superior to LPD‐ and MI‐based methods and can refine the results of the commercial package DIR when using its results as a starting point. Supported by these, this manuscript concludes the proposed registration method is more robust, accurate, and efficient than the MI‐ and LPD‐based methods.

Phase-resolved visualization of radio-frequency standing waves in superconducting spiral resonator for metamaterial applications

Superconducting microcircuits and metamaterials are promising candidates for use in new generation cryogenic electronics. Their functionality is largely justified by the macroscopic distribution of electromagnetic fields in arranged unit cells, rather than by the microscopic properties of composite materials. We present a new method for visualizing the spatial structure of penetrating microwaves with microscopic resolution in planar superconducting macroscopic resonators as the most important circuit-forming elements of modern microelectronics. This method uses a low-temperature laser scanning microscope that examines the phase (i.e., direction) and amplitude of local radio-frequency currents versus the two-dimensional coordinates of the superconducting resonant structure under test. Phase-sensitive contrast is achieved by synchronizing the intensity-modulated laser radiation with the resonant harmonics of the microwave signal passing through the sample. In this case, the laser-beam-induced loss in the illuminated area will strongly depend on the local phase difference between the RF carrier signal and the spatially temporal structure of the focused laser oscillation. This approach eliminates the hardware limitations of the existing technique of radio-frequency microscopy and brings the phase-sensitive demodulation mode to the level necessary for studying the physics of superconducting metamaterials. The advantage of the presented method over the previous method of RF laser scanning micros-copy is demonstrated by the example of the formation of standing waves in a spiral superconducting Archimedean resonator up to the 38th eigenmode resonance.

Phase Gradients and Anisotropy of the Suprachiasmatic Network: Discovery of Phaseoids.

Biological neural networks operate at several levels of granularity, from the individual neuron to local neural circuits to networks of thousands of cells. The daily oscillation of the brain's master clock in the suprachiasmatic nucleus (SCN) rests on a yet to be identified network of connectivity among its ∼20,000 neurons. The SCN provides an accessible model to explore neural organization at several levels of organization. To relate cellular to local and global network behaviors, we explore network topology by examining SCN slices in three orientations using immunochemistry, light and confocal microscopy, real-time imaging, and mathematical modeling. Importantly, the results reveal small local groupings of neurons that form intermediate structures, here termed "phaseoids," which can be identified through stable local phase differences of varying magnitude among neighboring cells. These local differences in phase are distinct from the global phase relationship, namely that between individual cells and the mean oscillation of the overall SCN. The magnitude of the phaseoids' local phase differences is associated with a global phase gradient observed in the SCN's rostral-caudal extent. Modeling results show that a gradient in connectivity strength can explain the observed gradient of phaseoid strength, an extremely parsimonious explanation for the heterogeneous oscillatory structure of the SCN.

Robust Controller Synthesis and Analysis in Inverter-Dominant Droop-Controlled Islanded Microgrids

This work investigates the problem of controller design for the inverters in an islanded microgrid. Robust μ-synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and share power among them, respectively. The designed controllers alleviate the need for additional sensors to measure the states of the system by relying only on output feedback. It is shown that the designed μ-synthesis controller properly damps resonant oscillations, and its performance is robust to the control-loop time delay and parameter uncertainties. The stability of a droop-controlled islanded microgrid including multiple distributed generation (DG) units is analyzed by linearizing the nonlinear power flow model around the nominal operating point and applying theorems from linear algebra. It is indicated that the droop controller stabilizes the microgrid system with dominantly inductive tie-line impedances for all values of resistive-inductive loads, while for the case of resistive-capacitive loads the stability is conditioned on an upper bound on the load susceptances. The robust performance of the designed μ-synthesis controller is studied analytically, compared with the similar analysis in an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control (benchmark) framework, and verified by simulations for a four DG benchmark microgrid. Furthermore, the robustness of the droop controllers is analyzed by Monte Carlo simulations in the presence of local voltage fluctuations and phase differences among neighboring DGs.

A topological Josephson junction platform for creating, manipulating, and braiding Majorana bound states

As part of the intense effort toward identifying platforms in which Majorana bound states can be realized and manipulated to perform qubit operations, we propose a topological Josephson junction architecture that achieves these capabilities and which can be experimentally implemented. The platform uses conventional superconducting electrodes deposited on a topological insulator film to form networks of proximity-coupled lateral Josephson junctions. Magnetic fields threading the network of junction barriers create Josephson vortices that host Majorana bound states localized in the junction where the local phase difference is an odd multiple of π, i.e. attached to the cores of the Josephson vortices. This enables us to manipulate the Majorana states by moving the Josephson vortices, achieving functionality exclusive to these systems in contrast to others, such as those composed of topological superconductor nanowires. We describe protocols for: (1) braiding localized Majorana states by exchange, (2) controlling the separation and hence the coupling of adjacent localized Majorana states to effect non-Abelian rotations via hybridization of the Majorana modes, and (3) reading out changes in the non-local parity correlations induced by such operations. These schemes utilize current pulses and local magnetic field pulses to control the location of vortices, and measurements of the Josephson current–phase relation to reveal the presence of the Majorana bound states. Finally, we present brief discussions of readout schemes and viable experimental settings for realizing the platform.

Single-ion addressing via trap potential modulation in global optical fields

To date, individual addressing of ion qubits has relied primarily on local Rabi or transition frequency differences between ions created via electromagnetic field spatial gradients or via ion transport operations. Alternatively, it is possible to synthesize arbitrary local one-qubit gates by leveraging local phase differences in a global driving field. Here we report individual addressing of 40Ca+ ions in a two-ion crystal using axial potential modulation in a global gate laser field. We characterize the resulting gate performance via one-qubit randomized benchmarking, applying different random sequences to each co-trapped ion. We identify the primary error sources and compare the results with single-ion experiments to better understand our experimental limitations. These experiments form a foundation for the universal control of two ions, confined in the same potential well, with a single gate laser beam.

SWI processing using a local phase difference modulated venous enhancement filter with noise compensation

Susceptibility weighted imaging (SWI) involves post-processing of gradient echo images which are sensitive to the spatial variations in magnetic susceptibility. The aim of this study is to develop an automated filtering scheme to enhance the contrast-to-noise ratio (CNR) and blooming on SWI. Here, the high-pass filtering for SWI processing is designed by applying a weighting function to the neighboring phase differences to enhance the susceptibility-related (SuR) contrast. This is accomplished by summing the neighboring phase differences, weighted with a scaled and shifted error function of the phase difference. Besides using the filter weights of this weighted high-pass (WHP) filter to minimize the filtering artefacts using a filter scale parameter, the CNR is further increased by introduction of the neighborhood-based noise compensation weights into the filtering process. These weights are deduced from the channel phase distribution, conditioned on the channel magnitude and noise variance. Using in vivo SWI data acquired at 1.5 T (16 nos.) and 3.0 T (30 nos.), the magnitude SWI processed using the noise compensated WHP (WHPC) filter is shown to provide an average CNR improvement of 68.40% over that of a homodyne high-pass (HHP) filter. Two tailed t-tests performed separately for different field strengths, show significant differences (p < 0.001) between mean separations of phase masks generated from the WHPC and HHP filtered phase images. In conclusion, the WHPC filter, tuned by the mean separation of the phase mask, enhances the SuR contrast of magnitude SWI for evaluation of mild cognitive impairments, brain tumor and hemorrhagic stroke.

Polarization Filtering and Phase Controlling Metasurfaces Based on a Metal-Insulator-Metal Grating

Metasurfaces used in the manipulation of light beams have attracted growing interests owing to their unique electromagnetic properties in the subwavelength regime. However, most previously demonstrated single-layer metasurfaces are normally designed to realize one-fold function of either polarization or phase manipulation and suffer from low cross-polarization conversion efficiency and high-background, especially for transmissive metasurfaces. Here, a metasurface based on metal-insulator-metal (MIM) subwavelength grating is proposed to simultaneously achieve polarization filtering and phase controlling. The transmission coefficient reaches up to 78.9% and the polarization extinction ratio (ER = 20*log(T TM /T TE) is larger than 16.1 dB. A local abrupt phase difference covering 0–2π is introduced into transmitted light with the polarization direction vertical to the grating by artificially tailoring the geometrical parameters of MIM grating. Furthermore, background-free wavefront control and high-purity radial/azimuthal polarization are realized by the metasurfaces based on the MIM grating. This flexible and high-efficient scheme of full control wavefront and polarization promises an unprecedented progress of spatial vectorial beams modulation and enable the realization of novel optical components.

Non-stationary local thermoacoustic phase relationships in a gas turbine combustor

A framework is presented for analyzing the local instantaneous phase difference between non-stationary heat release rate and pressure oscillations that is appropriate for use in high-pressure liquid-fueled combustors. High-speed OH* chemiluminescence images were used as a qualitative marker of the heat release rate, from which the local phase shift relative to the pressure was calculated using the Hilbert transform technique. Two types of behavior were observed during time sequences with constant amplitude pressure oscillations. For the first behavior, a region with out-of-phase pressure and heat release rate oscillations moved upstream along the nozzle shear layer towards the nozzle. For the second behavior, transitions occurred between out-of-phase oscillations in a region along the centerline and a toroidal region close to the nozzle. For time periods with increasing amplitude pressure fluctuations, in-phase heat release rate and pressure oscillations developed throughout the upstream portion of the combustor. These in-phase oscillations could extend along the burner centerline and towards the downstream portion of the combustor. This behavior is reversed during time periods with decreasing amplitude pressure oscillations; the upstream portion of the combustor transitions to featuring regions with out-of-phase oscillations.

Scale-Free Navigational Planning by Neuronal Traveling Waves.

Spatial navigation and planning is assumed to involve a cognitive map for evaluating trajectories towards a goal. How such a map is realized in neuronal terms, however, remains elusive. Here we describe a simple and noise-robust neuronal implementation of a path finding algorithm in complex environments. We consider a neuronal map of the environment that supports a traveling wave spreading out from the goal location opposite to direction of the physical movement. At each position of the map, the smallest firing phase between adjacent neurons indicate the shortest direction towards the goal. In contrast to diffusion or single-wave-fronts, local phase differences build up in time at arbitrary distances from the goal, providing a minimal and robust directional information throughout the map. The time needed to reach the steady state represents an estimate of an agent’s waiting time before it heads off to the goal. Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map. In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

Quantum dynamics of local phase differences between reservoirs of driven interacting bosons separated by simple aperture arrays

We present a derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3 + 1)D microscopic model with local U(1) gauge symmetry. We show that inclusion of local chemical potential and driving velocity fields as a gauge field allows derivation of the hydrodynamic equations of motion for the driven macroscopic phase differences across simple aperture arrays. For a single aperture, the current–phase equation for driven flow contains sinusoidal, linear and current-bias contributions. We compute the renormalization group (RG) beta function of the periodic potential in the effective action for small tunneling amplitudes and use this to analyze the temperature dependence of the low-energy current–phase relation, with application to the transition from linear to sinusoidal current–phase behavior observed in experiments by Hoskinson et al (2006 Nature Phys. 2 23–6) for liquid 4He driven through nanoaperture arrays. Extension of the microscopic theory to a two-aperture array shows that interference between the microscopic tunneling contributions for individual apertures leads to an effective coupling between apertures which amplifies the Josephson oscillations in the array. The resulting multiaperture current–phase equations are found to be equivalent to a set of equations for coupled pendula, with microscopically derived couplings.

Assessment of the dynamic interactions between heart rate and arterial pressure by the cross time–frequency analysis

In this study, a framework for the characterization of the dynamic interactions between RR variability (RRV) and systolic arterial pressure variability (SAPV) is proposed. The methodology accounts for the intrinsic non-stationarity of the cardiovascular system and includes the assessment of both the strength and the prevalent direction of local coupling. The smoothed pseudo-Wigner–Ville distribution (SPWVD) is used to estimate the time–frequency (TF) power, coherence, and phase-difference spectra with fine TF resolution. The interactions between the signals are quantified by time-varying indices, including the local coupling, phase differences, time delay, and baroreflex sensitivity (BRS). Every index is extracted from a specific TF region, localized by combining information from the different spectra. In 14 healthy subjects, a head-up tilt provoked an abrupt decrease in the cardiovascular coupling; a rapid change in the phase difference (from 0.37 ± 0.23 to −0.27 ± 0.22 rad) and time delay (from 0.26 ± 0.14 to −0.16 ± 0.16 s) in the high-frequency band; and a decrease in the BRS (from 23.72 ± 7.66 to 6.92 ± 2.51 ms mmHg−1). In the low-frequency range, during a head-up tilt, restoration of the baseline level of cardiovascular coupling took about 2 min and SAPV preceded RRV by about 0.85 s during the whole test. The analysis of the Eurobavar data set, which includes subjects with intact as well as impaired baroreflex, showed that the presented methodology represents an improved TF generalization of traditional time-invariant methodologies and can reveal dysfunctions in subjects with baroreflex impairment. Additionally, the results also suggest the use of non-stationary signal-processing techniques to analyze signals recorded under conditions that are usually supposed to be stationary.

Entropic inequalities in classical and quantum domains

Different kinds of entropy associated with probability distribution functions characterizing the system state in classical and quantum domains are reviewed. Shannon entropy and Rényi entropy are discussed. The notion of tomographic entropy determined by the probability distribution in the phase space of the classical system and by the density operator of the quantum system is considered. Inequalities for the tomographic entropies in classical and quantum domains are studied, and a difference in the form of these inequalities in corresponding domains is suggested as a test to clarify the classicality and quantumness of the system state in quantum optics experiments. A new bound for tomographic entropy (ln πe)Φ(θ) depending on the local oscillator phase difference in homodyne photon detection experiments is discussed.

Quantifying tidal signatures of the benthic nepheloid layer in Gaoping Submarine Canyon in Southern Taiwan

The benthic nepheloid layer (BNL) has been observed in the head region of the Gaoping/Kaoping Submarine Canyon (KPSC) throughout a year. The top of the BNL could be as high as 100 m above the canyon floor in which the suspended sediment concentration (SSC) could be as high as 30 mg/l. In the BNL, sand-sized particles comprise the largest size-class in the suspended sediment population. Based on three one-month time series observations near the canyon floor of along-canyon velocity, water temperature, and the volume concentration (VC) of clay, very-fine-to-medium silt, coarse silt and sand size-classes in 2000, 2002, and 2004, the BNL is strongly modulated by the tides at semidiurnal, diurnal, quarter, and sixth diurnal and spring-neap frequencies. In the course of a semidiurnal tidal cycle, the flood (up-canyon) current brings colder water from the seaward part of the canyon causing the SSC and the thickness of the BNL to increase. The SSC immediately near the canyon floor also increases in response to the maximum flood and ebb currents of the M 2 tide. The tidal-to-total energy ratio (ER) of the along-canyon flow is between 70–80%, and between 50–80% among the suspended sediment of clay, very-fine-to-medium silt, coarse silt and sand size-classes. The M 2 is the most important tidal constituent in the temporal variations of along-canyon flow, water temperature, and the VC of the four size-classes. The local phase differences between the forcing (velocity), and the responses (temperature and VC) at the M 2 frequency show distinct phase-lock that suggests patterns of standing and progressive internal tides. Suspended sediments in the BNL also respond to the M 2 forcing in a coherent fashion. Suspended sediment movements are strongly affected by nonlinear processes as indicated by the elevated values of the amplitude ratio of M 4/M 2 of the suspended sediment size-classes comparing to that of the flow. The cross-canyon geometry and the slope of the submarine canyon floor affect the propagation of the barotropic and internal tides, which in turn, affect the nonlinearity generation in the BNL.