Deterministic Phase Research Articles

Topological spin-orbit-coupled fermions beyond rotating wave approximation

The realization of spin–orbit-coupled ultracold gases has driven a wide range of research and is typically based on the rotating wave approximation (RWA). By neglecting the counter-rotating terms, RWA characterizes a single near-resonant spin–orbit (SO) coupling in a two-level system. Here, we propose and experimentally realize a new scheme for achieving a pair of two-dimensional (2D) SO couplings for ultracold fermions beyond RWA. This work not only realizes the first anomalous Floquet topological Fermi gas beyond RWA, but also significantly improves the lifetime of the 2D-SO-coupled Fermi gas. Based on pump–probe quench measurements, we observe a deterministic phase relation between two sets of SO couplings, which is characteristic of our beyond-RWA scheme and enables the two SO couplings to be simultaneously tuned to the optimum 2D configurations. We observe intriguing band topology by measuring two-ring band-inversion surfaces, quantitatively consistent with a Floquet topological Fermi gas in the regime of high Chern numbers. Our study can open an avenue to explore exotic SO physics and anomalous topological states based on long-lived SO-coupled ultracold fermions.

Unbiased multivariate multiscale sample entropy

The development of multi-channel data acquisition techniques has provided richer prior information for studying the nonlinear dynamic characteristics of complex systems. However, conventional nonlinear feature extraction algorithms prove unsuitable in the context of multi-channel data. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although the MMSE algorithm generalized the multiscale sample entropy algorithm, presenting a novel method for multidimensional data analysis, it remains deficient in theoretical underpinning and suffers from shortcomings, such as missing cross-channel correlation information and having biased estimation results. In this paper, unbiased multivariate multiscale sample entropy algorithm (UMMSE) is proposed. UMMSE increases the embedding dimension from <i>M</i> to <i>M</i> + <i>p</i>. This increasing strategy facilitates the reconstruction of a deterministic phase space. By virtue of theoretical scrutiny grounded in probability theory and subsequent experimental validation, this paper illustrates the algorithm's effectiveness in extracting inter-channel correlation information through the integration of cross-channel conditional probabilities. The computation of similarities between sample points across different channels is recognized as a potential source of bias and instability in algorithms.Through simulation experiments, this study delineates the parameter selection range for the UMMSE algorithm. Subsequently, diverse simulation signals are employed to showcase the UMMSE algorithm’s efficacy in extracting both within-channel and cross-channel correlation information. Ultimately, this paper demonstrates that the new algorithm has the lowest computational cost compared with traditional MMSE algorithms.

Super-resolution imaging through scattering media based on improved triple correlation recursion and deterministic iterative estimation.

Iterative phase retrieval algorithms are commonly used in computational techniques and optimization methods to obtain the reconstruction of objects hidden behind opaque scattering media. However, these methods are susceptible to converging to incorrect local minima, and the calculation results tend to be unstable. In this paper, a triple-correlation-based super-resolution imaging (TCSI) framework is proposed to achieve single-shot imaging of unknown objects hidden behind the scattering medium. The amplitude spectrum of the object is obtained by a speckle correlation (SC) method. Iterative relaxation recursion (IRR) sufficiently extracts object information from the triple correlation (TC) of the speckle patterns, serving as the prior initial guess for the iterative estimation algorithm (IE) to obtain a deterministic phase spectrum. Blur correction (BC) is then applied to the diffraction-limited image to achieve super-resolution imaging. Experimental results demonstrate that the flexible framework could effectively overcome the influence of speckle resolution and outperform traditional methods in terms of performance. Our approach provides a basis for non-invasively visualizing various samples behind scattering media.

Stability of traveling waves for deterministic and stochastic delayed reaction–diffusion equation based on phase shift

In this paper, we establish the nonlinear orbital stability of the traveling wave solution of deterministic and stochastic delayed reaction–diffusion equation. Employing the deterministic phase shift and establishing a delayed-integral inequality, we obtain the exponential stability of the traveling wave solution for the deterministic delayed reaction–diffusion equation. Applying a stochastic phase shift and time transformation, we then verify that the traveling wave solution of the deterministic equation retain the nonlinear orbital stability when the noise intensity is small enough and the initial value sufficiently closes the traveling wave.

Modeling tensile failure of concrete considering multivariate correlated random fields of material parameters

This paper presents a novel approach for modeling the tensile failure of quasi-brittle materials by incorporating a multivariate random field to represent material parameters in the phase field model. The aim is to characterize and propagate uncertainties in the behaviors of materials, taking into account the spatial variability and probabilistic dependence. Copula theory is employed to investigate the probability distributions and dependence configuration of the parameters. The proposed framework combines the generation approach for the multivariate random field with the phase field model, resulting in a complete numerical analysis methodology. The governing equations of the deterministic phase field model for quasi-brittle solids are outlined, followed by a description of the multivariate random field for quasi-brittle media and its uncertainty characterization procedure using copula theory. A numerical approach for generating samples of the multivariate random field is introduced. The numerical analysis procedure for the tensile fracture of concrete is presented, and the effects of material uncertainties on failure patterns and macroscopic responses are discussed. The results demonstrate that the developed methodology effectively captures the random damage and fracture processes in concrete specimens. The interaction between the correlation length of the random field and the characteristic length scale of the phase field significantly influences the probabilistic characteristics of the random responses. The research findings emphasize the importance of determining the correlation length values accurately. This study contributes to the field of structural reliability analysis by providing a comprehensive framework for modeling the stochastic behavior of quasi-brittle materials. The integration of a multivariate random field and copula theory allows for the realistic representation of material uncertainties and their probabilistic dependence. The proposed methodology, combined with the probability density evolution method (PDEM), offers a powerful tool for analyzing and predicting the probabilistic evolution of material behaviors under tensile loading conditions.

Coherent errors and readout errors in the surface code

We consider the combined effect of readout errors and coherent errors, i.e., deterministic phase rotations, on the surface code. We use a recently developed numerical approach, via a mapping of the physical qubits to Majorana fermions. We show how to use this approach in the presence of readout errors, treated on the phenomenological level: perfect projective measurements with potentially incorrectly recorded outcomes, and multiple repeated measurement rounds. We find a threshold for this combination of errors, with an error rate close to the threshold of the corresponding incoherent error channel (random Pauli-Z and readout errors). The value of the threshold error rate, using the worst case fidelity as the measure of logical errors, is 2.6%. Below the threshold, scaling up the code leads to the rapid loss of coherence in the logical-level errors, but error rates that are greater than those of the corresponding incoherent error channel. We also vary the coherent and readout error rates independently, and find that the surface code is more sensitive to coherent errors than to readout errors. Our work extends the recent results on coherent errors with perfect readout to the experimentally more realistic situation where readout errors also occur.

Securing double random phase encoding using deterministic phase masks and Yang-Gu algorithm in Fresnel domain

In this paper, an encryption scheme, based on a double deterministic phase mask and the Yang-Gu algorithm, is proposed. It consists of double random phase encoding and the Yang-Gu algorithm in Fresnel and Fourier transform, respectively. The random phase masks are replaced with deterministic phase masks that are constructed using chaotic logistic and cubic maps. The encrypted image obtained by the scheme in one-way binary modulation is real and more convenient for storage and transmission. The validation of the proposed cryptosystem is carried out using numerical simulations on greyscale images of Man, DICOM and CUH binary images. The proposed scheme is investigated for its robustness through statistical analysis using histograms and correlation plots. The scheme is also tested for its resistance against occlusion, noise and cryptographic attacks. The proposed cryptosystem is found to be highly sensitive to its private key and Fresnel parameters and therefore secure.

Deterministic vortices evolving from partially coherent fields

Optical vortices—lines of zero intensity around which the field phase has a circulating or helical structure—have become important tools for many applications such as imaging, trapping, and communications. It has long been assumed, however, that there is an intrinsic conflict between optical vortices and partial coherence, in that a vortex is a deterministic phase structure, and a partially coherent field has a randomly fluctuating phase. In most cases, a vortex imposed on a partially coherent field evolves into a singularity of the two-point correlation function. We demonstrate, however, that it is possible to construct a beam that has no deterministic vortices in the source plane yet evolves such a deterministic vortex at a specified propagation distance.

Deterministic Quantum Phase Estimation beyond N00N States

The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.

The role of RNA condensation in reducing gene expression noise.

Biomolecular condensates have been shown to play a fundamental role in localizing biochemistry in a cell. RNA is a common constituent with proteins and can determine biophysical properties. Functions of biomolecular condensates are varied including activating, inhibiting, and localizing reactions. Recently it has been proposed that condensates can buffer noise to diminish cell to cell variability. Here we introduce a phenomenological model in which phase separation of mRNAs into RNP droplets can regulate the abundance of the protein these mRNA encode and markedly decreases expression noise. We place particular emphasis on how this mechanism can facilitate efficient transcription by reducing noise even in the limit of infrequent bursts of transcription, by exploiting the physics of concentration dependent, deterministic phase separation threshold. We investigate two biologically relevant scenarios in which phase separation acts to either “buffer” noise by storing mRNA in inert droplets, or “filter” phase separated mRNAs by accelerating their decay, and quantify expression noise as a function of kinetic parameters. In either case the most efficient expression occurs when bursts produce mRNAs close to the phase separation threshold, which we find to be consistent with observations of a RNP-droplet forming cyclin in multinucleate Ashbya gossypii cells. We finally consider the contribution of noise in the phase separation threshold, and exhibit that protein copy number noise can be efficiently suppressed under modest assumptions on the magnitude and time scale of phase separation threshold fluctuations.

Atomic Insight into the Successive Antiferroelectric-Ferroelectric Phase Transition in Antiferroelectric Oxides.

Antiferroelectrics characterized by voltage-driven reversible transitions between antiparallel and parallel polarity are promising for cutting-edge electronic and electrical power applications. Wide-ranging explorations revealing the macroscopic performances and microstructural characteristics of typical antiferroelectric systems have been conducted. However, the underlying mechanism has not yet been fully unraveled, which depends largely on the atomistic processes. Herein, based on atomic-resolution transmission electron microscopy, the deterministic phase transition pathway along with the underlying lattice-by-lattice details in lead zirconate thin films was elucidated. Specifically, we identified a new type of ferrielectric-like dipole configuration with both angular and amplitude modulations, which plays the role of a precursor for a subsequent antiferroelectric to ferroelectric transformation. With the participation of the ferrielectric-like phase, the phase transition pathways driven by the phase boundary have been revealed. We provide new insights into the consecutive phase transformation in low-dimensional lead zirconate, which thus would promote potential antiferroelectric-based multifunctional devices.

Non-linear time series analysis of Parkinsonian tremor signals

Nonlinear time series analysis of Parkinsonian tremor signals involves exploring the complex dynamics and nonlinear interactions within the tremor signals to gain insights into the underlying physiological processes. By applying advanced analytical techniques, researchers aim to uncover hidden patterns, chaotic behavior, and self-organization within the signals, which can provide valuable information for the diagnosis and monitoring of Parkinson's disease. The vibrational phenomena studied in this work regards the arm and forearm vibration with the purpose to detect and recognize the dynamic properties and correlations of onset of pathological tremor in patients affected by Parkinson disease. Experimental data measured by patients will be analyzed using multiscale recursive analysis methodologies through the TISEAN package (1). Recurrence plot analysis is a method that visually represents the recurrent patterns and dependencies within a time series and helps to identify important features such as deterministic dynamics, periodicity, and phase relationships (2,3).

A novel image encryption mechanism based on umbrella map and Yang-Gu algorithm

A novel image encryption algorithm based on nonlinear discrete chaotic umbrella map and Yang-Gu mixture amplitude-phase retrieval algorithm in fractional Fourier domain is proposed in this paper. Here in the proposed mechanism the input image is encrypted with a deterministic phase mask and later subjected to fractional Fourier transform. Thereafter, for scrambling the pixels of transformed image the umbrella map is utilized. The umbrella map along with providing a broader range of control parameters also enhances the key space. Scrambled image is further encoded with additional deterministic phase mask before subjecting it to another level of fractional Fourier transform. The phase truncated portion of the resultant image is used as an input to the Yang-Gu mixture amplitude-phase retrieval algorithm in the Fourier domain. The encrypted image attained by one-way binary modulation is real-valued, which makes it more appropriate for storage and transmission. Comprehensive statistical and attack analysis of the proposed scheme has been carried out. Sensitivity analysis of the scheme to various keys and crucial parameters has also been done. The results demonstrate the robustness and efficacy of the proposed mechanism. The exceptional resistance to noise attacks makes it suitable for use in extremely noisy channels and real valued cipher image is more convenient to store and transmit.

Speckle suppression of cylindrical holography using deterministic gradient update

Cylindrical holography has gained a lot of attention in recent years because of its large field of view. However, with the introduction of random phases into the object surface to achieve a large field of view, the reconstruction quality of a phase-only cylindrical hologram is severely degraded by the speckle noise. In this paper, a deterministic gradient update is proposed for the speckle suppression of cylindrical holography. The proposed method is an optimization method for phase-only cylindrical hologram generation. The optimized hologram is achieved by iteratively updating the phase-only hologram by adding the deterministic gradient phase to the previous phase. The deterministic gradient phase is calculated by the previous phase and the gradient loss, which is the gradient difference between the images of the reconstruction and the object. The key to our proposed method is how to deal with the derivation of the complex numbers involved in the reconstruction process. Different from traditional speckle suppression methods such as cylindrical self-diffraction iteration, our proposed method deterministically gives the direction of phase optimization, which makes the reconstruction quality better. The effectiveness of our proposed method is verified by numerical simulation. Our proposed method performs well on images with different resolutions, especially high-resolution images such as 4K. The reconstructed image via our method can reach 30 dB, which improves the quality of the reconstructed image by 10 dB compared to traditional speckle suppression methods.

Quantitative comparison of the mean–return-time phase and the stochastic asymptotic phase for noisy oscillators

Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean–return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.

Improving security by utilizing hybrid deterministic phase mask and orthogonal encoding

Improving security by utilizing hybrid deterministic phase mask and orthogonal encoding

Single-cycle all-fiber frequency comb

Single-cycle pulses with deterministic carrier-envelope phase enable the study and control of light-matter interactions at the sub-cycle timescale, as well as the efficient generation of low-noise multi-octave frequency combs. However, current single-cycle light sources are difficult to implement and operate, hindering their application and accessibility in a wider range of research. In this paper, we present a single-cycle 100 MHz frequency comb in a compact, turn-key, and reliable all-silica-fiber format. This is achieved by amplifying 2 $\mu$m seed pulses in heavily-doped Tm:fiber, followed by cascaded self-compression to yield 6.8 fs pulses with 215 kW peak power and 374 mW average power. The corresponding spectrum covers more than two octaves, from below 700 nm up to 3500 nm. Driven by this single-cycle pump, supercontinuum with 180 mW of integrated power and a smooth spectral amplitude between 2100 and 2700 nm is generated directly in silica fibers. To broaden applications,few-cycle pulses extending from 6 $\mu$m to beyond 22 $\mu$m with long-term stable carrier-envelope phase are created using intra-pulse difference frequency, and electro-optic sampling yields comb-tooth-resolved spectra. Our work demonstrates the first all-fiber configuration that generates single-cycle pulses, and provides a practical source to study nonlinear optics on the same timescale.

The critical role of hot carrier cooling in optically excited structural transitions

The hot carrier cooling occurs in most photoexcitation-induced phase transitions (PIPTs), but its role has often been neglected in many theoretical simulations as well as in proposed mechanisms. Here, by including the previously ignored hot carrier cooling in real-time time-dependent density functional theory (rt-TDDFT) simulations, we investigated the role of hot carrier cooling in PIPTs. Taking IrTe2 as an example, we reveal that the cooling of hot electrons from the higher energy levels of spatially extended states to the lower energy levels of the localized Ir–Ir dimer antibonding states strengthens remarkably the atomic driving forces and enhances atomic kinetic energy. These two factors combine to dissolute the Ir–Ir dimers on a timescale near the limit of atomic motions, thus initiating a deterministic kinetic phase transition. We further demonstrate that the subsequent cooling induces nonradiative recombination of photoexcited electrons and holes, leading to the ultrafast recovery of the Ir–Ir dimers observed experimentally. These findings provide a complete picture of the atomic dynamics in optically excited structural phase transitions.

On Asymptotic Efficiency of the M2M4 Signal-to-Noise Estimator for Deterministic Complex Sinusoids.

The moment-based signal-to-noise (SNR) estimator was proposed for a complex sinusoidal signal with a deterministic but unknown phase corrupted by additive Gaussian noise by Sekhar and Sreenivas. The authors studied its performances only through numerical examples and concluded that the proposed estimator is asymptotically efficient and exhibits finite sample super-efficiency for some combinations of signal and noise power. In this paper, we derive the analytical asymptotic performances of the proposed SNR estimator, and we show that, contrary to what it has been concluded by Sekhar and Sreenivas, the proposed estimator is neither (asymptotically) efficient nor super-efficient. We also show that when dealing with deterministic signals, the covariance matrix needed to derive asymptotic performances must be explicitly derived as its known general form for random signals cannot be extended to deterministic signals. Numerical examples are provided whose results confirm the analytical findings.

Macroscopically entangled light fields

A novel method of macroscopically entangled light-pair generation is presented for a quantum laser using randomness-based deterministic phase control of coherent light in a coupled Mach–Zehnder interferometer (MZI). Unlike the particle nature-based quantum correlation in conventional quantum mechanics, the wave nature of photons is applied for collective phase control of coherent fields, resulting in a deterministically controllable nonclassical phenomenon. For the proof of principle, the entanglement between output light fields from a coupled MZI is examined using the Hong-Ou-Mandel-type anticorrelation technique, where the anticorrelation is a direct evidence of the nonclassical features in an interferometric scheme. For the generation of random phase bases between two bipartite input coherent fields, a deterministic control of opposite frequency shifts results in phase sensitive anticorrelation, which is a macroscopic quantum feature.