Linear Coupling Research Articles

Squeezing-enhanced quantum sensing with quadratic optomechanics

Cavity optomechanical (COM) sensors, enhanced by quantum squeezing or entanglement, have become powerful tools for measuring ultra-weak forces with high precision and sensitivity. However, these sensors usually rely on linear COM couplings, a fundamental limitation when measurements of the mechanical energy are desired. Very recently, a giant enhancement of the signal-to-noise ratio was predicted in a quadratic COM system. Here we show that the performance of such a system can be further improved surpassing the standard quantum limit by using quantum squeezed light. Our approach is compatible with available engineering techniques of advanced COM sensors and provides new opportunities for using COM sensors in tests of fundamental laws of physics and quantum metrology applications.

Exploring Magnetic Attributes: Borospherene-Like and Buckminsterfullerene-Like Lattices in Monte Carlo Simulations

This study explores the magnetic properties of Borospherene-like and Buckminsterfullerene-like lattices using Monte Carlo simulation, revealing novel behaviors. The dependency of blocking temperature (T B ) on external magnetic field strength (H), linear coupling interaction (J), and biquadratic coupling interaction (K) was studied and compared between the two lattice types. Additionally, the evolution of coercive field (H C ) with J and K parameters for both lattice types was analyzed. This study highlights the unique magnetic responses of these lattices and their potential applications in magnetic research and nanotechnology.

Simulating magnetism in Borospherene-like nanostructure: a Monte Carlo exploration

ABSTRACT This study employs a Monte Carlo approach to investigate the magnetic properties and thermal behaviour of the Borospherene-like nanostructure, yielding insightful information. The analysis delves into the blocking temperature (TB ) concerning external magnetic field (H), biquadratic coupling interaction (K), linear coupling interaction (JSS ), and crystal field (Δ). Results highlight the impact of JSS , K, and |Δ| on coercive field (Hc) and hysteresis loop. A distinct magnetisation plateau is observed at |Δ|=−5, underscoring the crucial roles of JSS , K, and |Δ| in dynamic magnetic behaviour. The current research provides a comprehensive understanding of the system's magnetic dynamics, offering valuable insights for potential applications in nanotechnology.

Dynamics of non–identical coupled Chialvo neuron maps

We study numerically the dynamics of low–dimensional ensembles of discrete neuron models - Chialvo maps. We are focused on choosing the autonomous map parameters corresponding to the invariant curve. We consider two cases of coupling organization: (i) via a nonlinear function of models; (ii) linear coupling, which is an analog of electrical neuron interaction. For the first case, the possibility of invariant curve doublings and the emergence of quasi-periodicity within Arnold tongues as a result of the secondary Neimark-Sacker bifurcation are found. For the second case, we discover an area of three-frequency quasi-periodicity for the case of two neurons. It arises softly as a result of quasi-periodic Hopf bifurcation. We demonstrate a set of resonant two-frequency regimes tongues embedded in this area and bounded by lines of saddle-node bifurcations of invariant curves. For ensemble of three linearly coupled maps, four-frequency quasi-periodicity becomes possible with a built-in system of tongues of three-frequency regimes (tori). We discuss the effect of noise and the evolution of “noise quasi-periodic” regimes, resonant regimes of this type and bifurcations of invariant tori with increasing of noise intensity.

Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics.

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.

Mean-Field Ring Polymer Rates Using a Population Dividing Surface.

Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

High power, broadband, coaxial to microstrip bi‐directional coupler in the VHF/UHF band

AbstractBroadband couplers consist usually of multiple coupled lines that are each a quarter wave‐length long. Herein, in contrast to conventional methods, a short length of a microstrip line is coupled to a coaxial line. The length of the coupled microstrip line is small compared to the wavelength at the lowest operating frequency. The coupling is weak and the microstrip line is λ/8 at the highest operating frequency. The proposed structure resembles a pair of coupled lines with a linear coupling response. The coupling exhibits a slope of 6 dB/octave over multi‐octave bandwidth. The microstrip line is connected to a lumped element compensating network at the coupled port. The compensating network is a low‐pass circuit with a slope of −6 dB/octave. The power handling of the coupler is high due to the coaxial line and the weakly coupled microstrip line. Electromagnetic simulations and analytical formulations are presented. The broadband coupler handles nearly 1 kW of input power. Due to the weak coupling of the microstrip‐coaxial coupler, the lumped element circuit needs to handle <1.5 W. A high‐power coupler has been fabricated for the frequency range of 30 to 500 MHz. It exhibits a coupling response of 56 ± 0.4 dB.

Efficient Aperture Fill Time Correction for Wideband Sparse Array Using Improved Variable Fractional Delay Filters.

To solve the problem of aperture fill time (AFT) for wideband sparse arrays, variable fractional delay (VFD) FIR filters are applied to eliminate linear coupling between spatial and time domains. However, the large dimensions of the filter coefficient matrix result in high system complexity. To alleviate the computational burden of solving VFD filter coefficients, a novel multi-regultion minimax (MRMM) model utilizing the sparse representation technique has been presented. The error function is constrained by the introduction of L2-norm and L1-norm regularizations within the minimax criterion. The L2-norm effectively resolves the problems of overfitting and non-unique solutions that arise in the sparse optimization of traditional minimax (MM) models. Meanwhile, the use of multiple L1-norms enables the optimal design of the smallest sub-filter number and order of the VFD filter. To solve the established nonconvex model, an improved sequential-alternating direction method of multipliers (S-ADMM) algorithm for filter coefficients is proposed, which utilizes sequential alternation to iteratively update multiple soft-thresholding problems. The experimental results show that the optimized VFD filter reduces system complexity significantly and corrects AFT effectively in a wideband sparse array.

Existence of Viscosity Solutions for Weakly Coupled Cooperative Parabolic Systems with Fully Nonlinear Principle Part

In this paper, the existence of viscosity solutions for weakly coupled, degenerate, and cooperative parabolic systems is studied in a bounded domain. In particular, we consider the viscosity solutions of parabolic systems with fully nonlinear degenerated principal symbol and linear coupling part. The maximum principle theorem is given as well.

Superradiant instability of charged extremal black holes in Einstein-Born-Infeld gravity

We study charged scalar perturbations of charged extremal black holes in Einstein-Born-Infeld theory. Our numerical results indicate that these black holes all suffer from superradiant instability by the unstable quasi-bound states, regardless how small the coupling constant is. We therefore provide a new example that the superradiant stability of the Reissner-Nordström black hole is a fine-tuned result, as in the case when it is embedded in the STU supergravity model. The work is also motivated by the weak gravity conjecture since at the linear coupling constant level, the theory belongs to a subsect of four-derivative corrections in the effective field theory. Our results appear to support the notion that the black holes do decay when gravity is weaker by the correction, but the decaying halftime requires nonlinear effects and cannot be seen at the level of linear coupling constant. The full nonlinear effects also indicate that the black holes can decay even when gravity is stronger.

Enhancement and manipulation of nonreciprocity via dissipative coupling

Classical and quantum nonreciprocity have important applications in information processing due to their special one-way controllability for physical systems. In this paper we investigate the nonreciprocal transmission and quantum correlation by introducing the dissipative coupling into a linear coupling system consisting of two microdisk resonators. Our research results demonstrate that even in the case of a stationary resonator, dissipative coupling can effectively induce nonreciprocity within the system. Moreover, the degree of nonreciprocity increases with the dissipative coupling strength. Importantly, the phase shift between the dissipative coupling and coherent coupling serves as a critical factor for controlling both nonreciprocal transmision and one-way quantum steering. Consequently, the introduction of dissipative coupling not only enhances the nonreciprocal transmission and nonreciprocal quantum correlation but also enables on-demand manipulation of nonreciprocity. This highlights dissipation as an effective means for manipulating classical and quantum nonreciprocity, thus playing a favorable role in chiral quantum networks.

On the higher-order smallest ring-star network of Chialvo neurons under diffusive couplings.

Network dynamical systems with higher-order interactions are a current trending topic, pervasive in many applied fields. However, our focus in this work is neurodynamics. We numerically study the dynamics of the smallest higher-order network of neurons arranged in a ring-star topology. The dynamics of each node in this network is governed by the Chialvo neuron map, and they interact via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through multi-body interactions. We deploy the higher-order coupling strength as the primary bifurcation parameter. We start by analyzing our model using standard tools from dynamical systems theory: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of disparate chaotic attractors. We also observe an interesting route to chaos from a fixed point via period-doubling and the appearance of cyclic quasiperiodic closed invariant curves. Furthermore, we numerically observe the existence of codimension-1 bifurcation points: saddle-node, period-doubling, and Neimark-Sacker. We also qualitatively study the typical phase portraits of the system, and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure, respectively. Finally, we study the synchronization behavior among the neurons using the cross correlation coefficient and the Kuramoto order parameter. We conjecture that unfolding these patterns and behaviors of the network model will help us identify different states of the nervous system, further aiding us in dealing with various neural diseases and nervous disorders.

Causalized Convergent Cross Mapping and Its Implementation in Causality Analysis.

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications.

The interacting vacuum and tensions: A comparison of theoretical models

We analyse three interacting vacuum dark energy models with the aim of exploring whether the H0 and σ8 tensions can be simultaneously resolved in such models. We present the first ever derivation of the covariant gauge-invariant perturbation formalism for the interacting vacuum scenario, and, for the sub-class of geodesic cold dark matter models, connect the evolution of perturbation variables in this approach to the familiar cosmological observables. We show how H0 and σ8 evolve in three interacting vacuum models: firstly, a simple linear coupling between the vacuum and cold dark matter; secondly, a coupling which mimics the behaviour of a Chaplygin gas; and finally a coupling which mimics the Shan–Chen fluid dark energy model. We identify, if any, the regions of parameter space which would correspond to a simultaneous resolution of both tensions in these models. When constraints from observational data are added, we show how all the models described are constrained to be close to their ΛCDM limits.

Strain and piezoelectric control of electronic and photonic properties of p − n diodes

Piezoelectricity is a well-known effect in a vast number of technologically important insulators and semiconductors and exists in 20 out of the 32 three-dimensional crystal classes. The piezoelectric effect is the driving mechanism behind several classical sensors and transmitters, and also most recently, in many nanodevices. Zhong Lin Wang coined the fields piezotronics and piezo-phototronics where the piezoelectric effect plays a dominant role. Piezoelectricity couples in a linear fashion mechanical strain to electrical fields and vice versa. In solids, there is another linear coupling between strain and the electric potential, known as the deformation potential effect. While linear in its coupling nature, this effect does not require the solid to be non-centrosymmetric in contrast to the piezoelectric effect. Moreover, the deformation potential effect is quantitatively huge and leads to changes in the conduction and valence band edges of III–V and II–VI materials of, typically, 50–100 meV in the presence of 1 % strain. Therefore, the deformation potential effect is essential to determine the electronic and photonic properties of bulk and nanostructure semiconductors in the presence of strain. In this work, we compute the relative importance of piezoelectricity and the deformation potential effect in the presence of lattice mismatch and external strain. We choose p − n junctions of ZnO/GaN structures but anticipate that the general conclusions can be carried over to other material structures. The main result of the present work is that both the inclusion of the deformation potential effect and piezoelectricity is crucial to correctly compute the effect of strain on p − n junction current–voltage curves and photonic properties. In our analysis of wurtzite heterostructures, the spontaneous polarization effect is also included but this effect appears to play a minor role for electronic and photonic properties.

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

Model reduction for an internally damped n-particle chain in a potential well under polyharmonic excitation

The study focuses on the model reduction of an internally damped chain of particles confined within a weakening potential well subjected to polyharmonic excitation to investigate the chain’s escape dynamics. The chain features strong linear coupling between particles and nonnegligible viscous damping forces arising from their relative motion. The potential well is modeled to have no energy dissipation, which means that damping arises solely from the internal interactions among particles and not from their motion through a resisting medium. Polyharmonic excitation frequencies are chosen to excite both the center of mass of the chain and at least one of the internally resonant frequencies, which are significantly higher than the linearized angular eigenfrequency of the center of mass within the well. The relative motion of the particles quickly reaches a steady state because of the non-small internal damping, allowing for the derivation of an efficient force field for the center of mass. Eliminating fast dynamics reduces the system’s degrees of freedom to one, employing a probabilistic approach based on the relative motion’s probability density function. The reduced 1 DoF model is appropriate for further investigation using various methods established in the literature.

Resolving Photoinduced Femtosecond Three-Dimensional Solute-Solvent Dynamics through Surface Hopping Simulations.

Photoinduced dynamics in solution is governed by mutual solute-solvent interactions, which give rise to phenomena like solvatochromism, the Stokes shift, dual fluorescence, or charge transfer. Understanding these phenomena requires simulating the solute's photoinduced dynamics and simultaneously resolving the three-dimensional solvent distribution dynamics. If using trajectory surface hopping (TSH) to this aim, thousands of trajectories are required to adequately sample the time-dependent three-dimensional solvent distribution functions, and thus resolve the solvent dynamics with sub-Ångstrom and femtosecond accuracy and sufficiently low noise levels. Unfortunately, simulating thousands of trajectories with TSH in the framework of hybrid quantum mechanical/molecular mechanical (QM/MM) can be prohibitively expensive when employing ab initio electronic structure methods. To tackle this challenge, we recently introduced a computationally efficient approach that combines efficient linear vibronic coupling models with molecular mechanics (LVC/MM) via electrostatic embedding [Polonius et al., JCTC 2023, 19, 7171-7186]. This method provides solvent-embedded, nonadiabatically coupled potential energy surfaces while scaling similarly to MM force fields. Here, we employ TSH with LVC/MM to unravel the photoinduced dynamics of two small thiocarbonyl compounds solvated in water. We describe how to estimate the number of trajectories required to produce nearly noise-free three-dimensional solvent distribution functions and present an analysis based on approximately 10,000 trajectories propagated for 3 ps. In the electronic ground state, both molecules exhibit in-plane hydrogen bonds to the sulfur atom. Shortly after excitation, these bonds are broken and reform perpendicular to the molecular plane on timescales that differ by an order of magnitude due to steric effects. We also show that the solvent relaxation dynamics is coupled to the electronic dynamics, including intersystem crossing. These findings are relevant to advance the understanding of the coupled solute-solvent dynamics of solvated photoexcited molecules, e.g., biologically relevant thio-nucleobases.

Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

On the backreaction of Dirac matter in JT gravity and SYK model

We model backreaction in AdS2 JT gravity via a proposed boundary dual Sachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it from the perspective of quantum entanglement and chaos. The boundary effective action accounts for the backreaction through a linear coupling of the Dirac fermions to the Gaussian-random two-body Majorana interaction term in the low-energy limit. We calculate the time evolution of the entanglement entropy between graviton and Dirac fermion fields for a separable initial state and find that it initially increases and then saturates to a finite value. Moreover, in the limit of a large number of fermions, we find a maximally entangled state between the Majorana and Dirac fields in the saturation region, implying a transition of the von Neumann algebra of observables from type I to type II. This transition in turn indicates a loss of information in the holographically dual emergent spacetime. We corroborate these observations with a detailed numerical computation of the averaged nearest-neighbor gap ratio of the boundary spectrum and provide a useful complement to quantum entanglement studies of holography.