Linear Coupling Research Articles

Ultrasensitive displacement measurement with nonlinear optomechanical coupling and squeezed light injection

We propose an ultrasensitive displacement measurement scheme to overcome the standard quantum limit (SQL) in the unresolved sideband cavity optomechanical system with nonlinear optomechanical coupling and squeezed light injection. By introducing the optimized quantum correlation, which is enabled by suitable choices of the squeezing angle, squeezing level, power of the probe light, and measurement angle of homodyne detection, the off-resonant displacement sensitivity reaches 6 dB below the SQL in linear optomechanical coupling. In contrast, displacement sensitivities with a coherent probe plus variational readout and squeezed probe plus fixed measurement angle (phase quadrature) are 2.6 dB and 4.6 dB below the SQL, respectively. By combining linear and quadratic optomechanical coupling, we show that the displacement sensitivity can be further improved to 9.6 dB below the SQL. Our results have potential applications in gravitational-wave detectors, quantum metrology, and the search for dark matter.

Theoretical Study of Excited-State Dynamics of Hypercoordinated Carbon Molecule

Structural and dynamical aspects of vibronically coupled S1 (dipole-allowed, “bright”) and S2 (dipole-forbidden, “dark”) states of hypercoordinated carbon molecule, 1,8-dimethoxy-9-dimethoxymethylanthracene monocation, are investigated. Potential energy surfaces are modeled within the linear vibronic coupling scheme. Quantum dynamics simulation show that the nuclear wavepacket initiated on the “bright” S1 state would move to “dark” S2 within a few femtoseconds via an accessible conical intersection. A dynamical equilibrium of wavepacket exchange between S1 and S2 is observed after 50 fs of propagation time. The activity of vibrational motions associated with the hypercoordinated carbon and C−H vibrations is analyzed using the reduced nuclear densities. Our findings illustrate that the excited-state nonadiabatic behavior has to be taken into account while analyzing the optical properties of this hypercoordinated carbon molecule.

Photodynamics of the Molecular Ruby [Cr(ddpd)2]3.

The introduction of strong-field ligands can enable luminescence in first-row transition-metal complexes. In this way, earth-abundant near-infrared emitters can be obtained using early 3d metals. A prime example is the molecular ruby [Cr(ddpd)2]3+ (ddpd = N,N'-dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine) that can achieve high phosphorescence quantum yields at room temperature in aqueous solution. To understand these remarkable properties, here, we simulate its photodynamics in water using trajectory surface hopping on linear vibronic coupling potentials parametrized from multiconfigurational CASSCF/CASPT2 calculations. We find that after excitation to the second absorption band, a relaxation cascade through metal-centered states occurs. After an initial back-and-forth intersystem crossing with higher-lying doublet states, the complex relaxes through a manifold of quartet metal-centered states to the low-lying doublet metal-centered states which are responsible for the experimentally observed emission. These electronic processes are driven by an elongation of the Cr-ligand bond lengths as well as the twisting motion of the trans-coordinated pyridine units in the ddpd ligands. The low-lying doublet states are reached within 1-2 ps and are close in geometry to the doublet minima, thus explaining the high phosphorescence quantum yield of the molecular ruby [Cr(ddpd)2]3+.

CAGMon: A Novel Tool for Identifying and Diagnosing Coherent Associations and Causalities between Multi-channels of the Gravitational Wave Detector

The ground-based gravitational-wave telescopes such as LIGO, Virgo, and KAGRA are very complicated and sensitive compositions of advanced devices. Therefore, they are influenced not only by the mutual interaction among mechanical and electronics systems but also by the surrounding environment. To categorize and reduce noises from many channels interconnected by such instruments and environment for achieving the detection of gravitational waves, it needs to increase a signal-to-noise ratio and reduce false alarm rate from coincident spurious events. Therefore, it is of great importance to identify associations between inter-correlated channels. In this work, we present a novel tool called CAGMon for identifying (non-) linear couplings between inter-correlated channels, which can be applied to the practical cases of the gravitational-wave detector.

ENSO coupling to the equatorial Atlantic: Analysis with an extended improved recharge oscillator model

IntroductionObservational and modeling studies have examined the interactions between El Niño-Southern Oscillation (ENSO) and the equatorial Atlantic variability as incorporated into the classical charge-recharge oscillator model of ENSO. These studies included the role of the Atlantic in the predictability of ENSO but assumed stationarity in the relationships, i.e., that models’ coefficients do not change over time. A recent work by the authors has challenged the stationarity assumption in the ENSO framework but without considering the equatorial Atlantic influence on ENSO.MethodsThe present paper addresses the changing relationship between ENSO and the Atlantic El Niño using an extended version of the recharge oscillator model. The classical two-variable model of ENSO is extended by adding a linear coupling on the SST anomalies in the equatorial Atlantic. The model’s coefficients are computed for different periods. This calculation is done using two methods to fit the model to the data: (1) the traditional method (ReOsc), and (2) a novel method (ReOsc+) based on fitting the Fisher’s Z transform of the auto and cross-correlation functions.ResultsWe show that, during the 20th century, the characteristic damping rate of the SST and thermocline depth anomalies in the Pacific have decreased in time by a factor of 2 and 3, respectively. Moreover, the damping time of the ENSO fluctuations has doubled from 10 to 20 months, and the oscillation period of ENSO has decreased from 60-70 months before the 1960s to 50 months afterward. These two changes have contributed to enhancing ENSO amplitude. The results also show that correlations between ENSO and the Atlantic SST strengthened after the 70s and the way in which the impact of the equatorial Atlantic is added to the internal ENSO variability.ConclusionsThe remote effects of the equatorial Atlantic on ENSO must be considered in studies of ENSO dynamics and predictability during specific time-periods. Our results provide further insight into the evolution of the ENSO dynamics and its coupling to the equatorial Atlantic, as well as an improved tool to study the coupling of climatic and ecological variables.

Piezoelectric energy harvesting from extremely low-frequency vibrations via gravity induced self-excited resonance

In this paper, we originally present a gravity induced self-excited vibration generator based on a cantilever piezoelectric resonator. The configuration is composed of a sliding rod, a sleeve, a transduction unit. To estimate output voltage and investigate dynamic responses of the generator, an equivalent model based on mechanical structure was established and numerically solved. The effects of the cantilever length, tip mass and linear coupling factor on the open circuit voltage were discussed. In addition, we also conducted series of experiments to validate the theoretical responses. In a 10s cycle (namely 0.1Hz excitation frequency) scenario, the transduction unit responds with structural resonant frequency of 8.621Hz. The results of the experiments show that the open circuit voltage of the generator increases with increment of the cantilever beam length and the tip mass, which agrees well with simulation estimations. We also conducted impedance matching experiments to examine power response in the load spectrum, of which the results indicate that the prototype peak power reaches maximum 1.897 mW. We also discussed the change of gravity potential energy of the prototype and compared it with electric energy. This work provides a novel approach for piezoelectric energy harvesting from extremely low frequency excitations.

Decay for strain gradient porous elastic waves

We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t^{-1/2}. Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more “efficient” than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark-beta scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity cases.

Symmetry results of solutions for elliptic systems with linear couplings

This paper is devoted to study the symmetry and monotonicity of positive solutions for linear coupling elliptic systems in a ball in R N . Using the Alexandrov–Serrin method of moving planes combined with the strong maximum principle, we prove that the solutions of elliptic systems with linear couplings in a ball are symmetric w.r.t. 0 and radially decreasing. For our problems, the tangential gradient of solutions and the coupling conditions play important roles in using the moving plane method. Our results on the symmetry of solutions are further research based on the existence of solutions in [1].

Mind the GAP: quantifying the breakdown of the linear vibronic coupling Hamiltonian.

Excited state dynamics play a critical role across a broad range of scientific fields. Importantly, the highly non-equilibrium nature of the states generated by photoexcitation means that excited state simulations should usually include an accurate description of the coupled electronic-nuclear motion, which often requires solving the time-dependent Schrödinger equation (TDSE). One of the biggest challenges for these simulations is the requirement to calculate the PES over which the nuclei evolve. An effective approach for addressing this challenge is to use the approximate linear vibronic coupling (LVC) Hamiltonian, which enables a model potential to be parameterised using relatively few quantum chemistry calculations. However, this approach is only valid provided there are no large amplitude motions in the excited state dynamics. In this paper we introduce and deploy a metric, the global anharmonicity parameter (GAP), which can be used to assess the accuracy of an LVC potential. Following its derivation, we illustrate its utility by applying it to three molecules exhibiting different rigidity in their excited states.

Fine-structure of electromagnetic radiation reflected from the O–X mode conversion zone in magnetized plasma

The linear coupling between the ordinary and extraordinary waves in the vicinity of the plasma cutoff is used for the heating of overdense plasma in toroidal magnetic devices. If the mode coupling is not perfect, there is reflected ordinary wave radiation. In this paper, we analyze the structure of this radiation in a realistic case of an incident beam with a finite aperture. It is shown that reflection from the evanescent layer in inhomogeneous gyrotropic plasma results in wave distributions with a non-zero-angular momentum. A helicity of the reflected beam results in unusual effects, at least in the plasma electrodynamics, which are identified and discussed.

Stability of the chemostat system including a linear coupling between species

<p style='text-indent:20px;'>In this paper, we consider a resource-consumer model taking into account a linear coupling between species (with constant rate). The corresponding operator is proportional to a discretization of the Laplacian in such a way that the resulting dynamical system can be viewed as a regular perturbation of the classical chemostat system. We prove the existence of a unique locally asymptotically stable steady-state for every value of the transfer-rate and every value of the dilution rate not exceeding a critical value. In addition, we give an expansion of the steady-state in terms of the transfer-rate and we prove a uniform persistence property of the dynamics related to each species. Finally, we show that this equilibrium is globally asymptotically stable for every value of the transfer-rate provided that the dilution rate is with small enough values.</p>

Nonlinear degradation of O-X-B mode conversion in MAST Upgrade

Spherical tokamaks like the MAST Upgrade device are often operated in an overdense regime. As a consequence, conventional electron cyclotron resonance heating (ECRH) and current drive (ECCD) are typically not possible. MAST Upgrade is planned to investigate a mode coupling scheme known as O-X-B at high power, which may allow gyrotrons to heat and drive current in overdense plasmas by coupling electromagnetic waves to electrostatic electron Bernstein waves (EBWs) at the upper hybrid (UH) layer. However at the gyrotron beam intensities planned for MAST Upgrade, several nonlinear effects may degrade the linear mode coupling into EBWs. Using particle-in-cell simulations, parametric decay instabilities (PDIs) and stochastic electron heating (SEH) are investigated in the region near the UH layer. It is found that nonlinear effect could have a substantial impact on the O-X-B scheme in MAST Upgrade at high gyrotron intensities.

Manganese substitution induced magnetic transformation and magnetoelectricity in SrFe12O19.

In this study, manganese substituted strontium hexaferrite (SrFe12-xMnxO19; x = 0, 3, 5, and 7) prepared by the sol-gel auto-combustion method are studied. We observed that the substituted Mn preferentially goes to the 2a and 12k sites of Fe. Raman modes related to the 12k site suggest the stiffening of the lattice. The transformation of the grain's shape from hexagonal (x = 0 and 3) to rhombohedral (x = 7) was observed, as shown in the micrographs obtained from FESEM. The thermomagnetic curves show the shift of TC to lower temperatures with the increase in the Mn content. From x = 5 onwards, the growth of another magnetic phase (FiM2) of lower coercivity apart from the parent phase (FiM1) of higher coercivity is seen. The FiM2 phase was found to increase with the Mn content in the sample (16.4(3)% for x = 5 but 66.2(5)% for x = 7). Although the magnetization for both FiM1 and FiM2 decreases with the increase in temperature, both magnetic phases behave in contrast to each other for x = 5 and x = 7. The study suggests a transformation of the compound from high magnetic anisotropy (x = 0) to low magnetic anisotropy (x = 7). The x = 5 composition sample displays the highest value of the first-order ME coefficient (0.83(2) mV × cm-1 × Oe-1). The observed value for x = 5 composition is ∼2.5 times higher than that of the parent x = 0 composition sample (0.33(2) mV × cm-1 × Oe-1). The studies thus suggest that the x = 5 composition is one of the viable candidates for magnetoelectric applications.

Stability properties for a problem of light scattering in a dispersive metallic domain

<p style='text-indent:20px;'>In this work, we study the well-posedness and some stability properties of a PDE system that models the propagation of light in a metallic domain with a hole. This model takes into account the dispersive properties of the metal. It consists of a linear coupling between Maxwell's equations and a wave type system. We prove that the problem is well posed for several types of boundary conditions. Furthermore, we show that it is polynomially stable and that the exponential stability is conditional on the exponential stability of the Maxwell system.</p>

A Soft Sensor Model for Predicting Cement-Specific Surface Area Based on Convolution Fast Recurrent Unit Network

Due to the time lag, nonlinearity, and variable coupling in the process sector, production variables are hard to measure directly and require accurate soft sensor models. In light of this, this research proposes a soft sensor convolution neural network fast recurrent unit (CNN-FRU) network model. Convolution is used to get spatial features and get rid of redundancy data in variables. FRU changes the linear coupling constraint within a gated recurrent unit (GRU) and solves the problem of blocked information flow in GRU. It can be used to extract time-varying delay characteristics from complex processes industry data. FRU is compared with GRU and long short-term memory (LSTM) on a standard dataset to demonstrate the advantages of FRU in terms of training speed and accuracy. As a specific application in the process industry, the proposed soft sensor model is trained and validated on the cement-specific surface area dataset. The experimental results demonstrate that the soft sensor model can be generalized better.

Multi-scroll Systems Synchronization on Strongly Connected Digraphs

In this paper, we study the synchronization problem in complex dynamic networks of Piece Wise Linear (PWL) systems. PWL systems exhibit multi-scrolls and belong to a special class of Unstable Dissipative Systems (UDS). We consider strongly connected digraphs and linear diffusive couplings. The synchronization regions are computed using the concept of disagreement vectors, generalized algebraic connectivity of the network topology, and Lyapunov functions, which provide lower bounds on the coupling gain of the network. Then, different combinations of linear diffusive coupling are explored by changing the observed and measured variables to illustrate the contribution of our results. The theoretical results are validated by numerical simulations.

Frequency characteristic of a uniformly rotating laser gyro in exact and polynomial forms

In some inertial navigation systems of a carousel type, laser gyros operate in regime of uniform rotation. For development of such systems and computer simulation of their work, one needs to have the “exact” (in wide range of angular velocities ) analytical expression for counterpropagating waves beat frequency of uniformly rotating device. This expression may be obtained by solving the well-known system of laser gyro dynamic equations with accuracy to second order in parameters of counterpropagating waves linear coupling. But before use of such non-dithered laser gyros in the named inertial system, their metrological parameters (scale factors and null shifts) must be preliminary calibrated. For synthesis and qualitative analysis of methodical errors of the procedure of such calibration on a quickly rotating platform of a single-axis stand, one needs also to have the approximate analytical expression for counterpropagating waves beat frequency in the form of polynomial
 with coefficients , ..., which involve parameters of the exact expression for . As analysis of the literature shows, the known expression for and the known relations for some of coefficients of polynomial are not complete and, therefore, must be modified. In the paper, the result of such modification is presented.

Effect of the Thermal Fluctuations of the Photophysics of GC and CG DNA Steps: A Computational Dynamical Study

Here we refine and assess two computational procedures aimed to include the effect of thermal fluctuations on the electronic spectra and the ultrafast excited state dynamics of multichromophore systems, focusing on DNA duplexes. Our approach is based on a fragment diabatization procedure that, from a given Quantum Mechanical (QM) reference method, can provide the parameters (energy and coupling) of the reference diabatic states on the basis of the isolated fragments, either for a purely electronic excitonic Hamiltonian (FrDEx) or a linear vibronic coupling Hamiltonian (FrD-LVC). After having defined the most cost-effective procedure for DNA duplexes on two smaller fragments, FrDEx is used to simulate the absorption and Electronic Circular Dichroism (ECD) spectra of (GC)5 sequences, including the coupling with the Charge Transfer (CT) states, on a number of structures extracted from classical Molecular Dynamics (MD) simulations. The computed spectra are close to the reference TD-DFT calculations and fully consistent with the experimental ones. We then couple MD simulations and FrD-LVC to simulate the interplay between local excitations and CT transitions, both intrastrand and interstrand, in GC and CG steps when included in a oligoGC or in oligoAT DNA sequence. We predict that for both sequences a substantial part of the photoexcited population on G and C decays, within 50-100 fs, to the corresponding intrastrand CT states. This transfer is more effective for GC steps that, on average, are more closely stacked than CG ones.

Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware

Quantum computers may provide good solutions to combinatorial optimization problems by leveraging the Quantum Approximate Optimization Algorithm (QAOA). The QAOA is often presented as an algorithm for noisy hardware. However, hardware constraints limit its applicability to problem instances that closely match the connectivity of the qubits. Furthermore, the QAOA must outpace classical solvers. Here, we investigate swap strategies to map dense problems into linear, grid and heavy-hex coupling maps. A line-based swap strategy works best for linear and two-dimensional grid coupling maps. Heavy-hex coupling maps require an adaptation of the line swap strategy. By contrast, three-dimensional grid coupling maps benefit from a different swap strategy. Using known entropic arguments we find that the required gate fidelity for dense problems lies deep below the fault-tolerant threshold. We also provide a methodology to reason about the execution-time of QAOA. Finally, we present a QAOA Qiskit Runtime program and execute the closed-loop optimization on cloud-based quantum computers with transpiler settings optimized for QAOA. This work highlights some obstacles to improve to make QAOA competitive, such as gate fidelity, gate speed, and the large number of shots needed. The Qiskit Runtime program gives us a tool to investigate such issues at scale on noisy superconducting qubit hardware.

Semiclassical spin transport in LaO/STO system in the presence of multiple Rashba spin-orbit couplings

The interaction between linear and cubic spin–orbit couplings with magnetic moments and mobile spin-polarized carriers in the LaAlO3/SrTiO3 (LaO/STO) system provides new avenues for spin transport applications. We study the interplay between linear and cubic Rashba spin orbit coupling (RSOC) on in-plane magnetic moments in the LaO/STO system using the Boltzmann transport theory based on the relaxation time approximation (RTA) and the more refined Schliemann-Loss (SL) delta-potential scattering model. In general, both methods yield a linear (quadratic) relationship in the spin accumulation (spin current) when one of the three RSOC strengths is varied and the other two fixed. The simultaneous presence of multiple types of RSOC with distinct angular dependencies facilitates the breaking of the k-space symmetry of the Fermi surface, thus ensuring a finite spin accumulation upon integration over the entire Fermi surface. While the oft-used RTA method is sufficiently accurate for spin accumulation calculations, the more refined SL model is required for spin current calculations because the RTA method neglects the anisotropy of the Fermi contour arising from the cubic RSOC terms. Based on the refined SL model and under optimal tuning of the RSOC parameters, the spin charge conversion in LaO/STO is predicted to reach a remarkable efficiency of 30%.