Dissipative Coupling Research Articles

A variational phase-field model For ductile fracture with coalescence dissipation

A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. The model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.

Ultralow threshold bistability and generation of long-lived mode in a dissipatively coupled nonlinear system: Application to magnonics

The prospect of a system possessing two or more stable states for a given excitation condition is of topical interest with applications in information processing networks. In this work, we establish the remote transfer of bistability from a nonlinear resource in a dissipatively coupled two-mode system. As a clear advantage over coherently coupled settings, the dissipative nature of interaction is found to support a lower pumping threshold for bistable signals. For comparable parameters, the bistability threshold for dissipatively coupled systems is lower by a factor of about 5. The resulting hysteresis can be studied spectroscopically by applying a probe field through the waveguide and examining the polariton character of the transmitted field. Our model is generic, apropos of an extensive set of quantum systems, and we demonstrate our results in the context of magnonics where experimental interest has flourished of late. As a consequence of dissipative coupling and the nonlinearity, a long-lived mode emerges, which is responsible for heightened transmission levels and pronounced sensitivity in signal propagation through the fiber.

Dissipative optomechanical coupling with a membrane outside of an optical cavity

We theoretically study an optomechanical system, which consists of a two-sided cavity and a mechanical membrane that is placed outside of it. The membrane is positioned close to one of its mirrors, and the cavity is coupled to the external light field through the other mirror. Our study is focused on the regime where the dispersive optomechanical coupling in the system vanishes. Such a regime is found to be possible if the membrane is less reflecting than the adjacent mirror, yielding a potentially very strong dissipative optomechanical coupling. Specifically, if the absolute values of amplitude transmission coefficients of the membrane and the mirror, $t$ and $t_m$ respectively, obey the condition $ t_m^2< t\ll t_m\ll 1$, the dissipative coupling constant of the setup exceeds the dispersive coupling constant for an optomechanical cavity of the same length. The dissipative coupling constant and the corresponding optomechanical cooperativity of the proposed system are also compared with those of the Michelson-Sagnac interferometer and the so-called "membrane-at-the-edge" system, which are known for a strong optomechanical dissipative interaction. It is shown that under the above condition, the system proposed here is advantageous in both aspects. It also enables an efficient realization of the two-port configuration, which was recently proposed as a promising optomechanical system, providing, among other benefits, a possibility of quantum limited optomechanical measurements in a system, which does not suffer from any optomechanical instability.

Coherent and dissipative cavity magnonics

Strong interactions between magnetic materials and electrodynamic cavities mix together spin and photon properties, producing unique hybridized behavior. The study of such coupled spin-photon systems, known as cavity magnonics, is motivated by the flexibility and controllability of these hybridized states for spintronic and quantum information technologies. In this Tutorial, we examine and compare both coherent and dissipative interactions in cavity magnonics. We begin with a familiar case study, the coupled harmonic oscillator, which provides insight into the unique characteristics of coherent and dissipative coupling. We then examine several canonical cavity-magnonic systems, highlighting the requirements for different coupling mechanisms, and conclude with recent applications of spin-photon hybridization, for example, the development of quantum transducers, memory architectures, isolators, and enhanced sensing.

Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators.

We analytically and numerically show that the Hillery-Zubairy’s entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.

Emulating the local Kuramoto model with an injection-locked photonic crystal laser array

The Kuramoto model is a mathematical model for describing the collective synchronization phenomena of coupled oscillators. We theoretically demonstrate that an array of coupled photonic crystal lasers emulates the Kuramoto model with non-delayed nearest-neighbor coupling (the local Kuramoto model). Our novel strategy employs indirect coupling between lasers via additional cold cavities. By installing cold cavities between laser cavities, we avoid the strong coupling of lasers and realize ideal mutual injection-locking with effective non-delayed dissipative coupling. First, after discussing the limit cycle interpretation of laser oscillation, we demonstrate the synchronization of two indirectly coupled lasers by numerically simulating coupled-mode equations. Second, by performing a phase reduction analysis, we show that laser dynamics in the proposed device can be mapped to the local Kuramoto model. Finally, we briefly demonstrate that a chain of indirectly coupled photonic crystal lasers actually emulates the one-dimensional local Kuramoto chain. We also argue that our proposed structure, which consists of periodically aligned cold cavities and laser cavities, will best be realized by using state-of-the-art buried multiple quantum well photonic crystals.

Cross-sublattice spin pumping and magnon level attraction in van der Waals antiferromagnets

We theoretically study spin pumping from a layered van der Waals antiferromagnet in its canted ground state into an adjacent normal metal. We find that the resulting dc spin pumping current bears contributions along all spin directions. Our analysis allows for detecting intra- and cross-sublattice spin-mixing conductances via measuring the two in-plane spin current components. We further show that sublattice symmetry-breaking Gilbert damping can be realized via interface engineering and induces a dissipative coupling between the optical and acoustic magnon modes. This realizes magnon level attraction and exceptional points in the system. Furthermore, the dissipative coupling and cross-sublattice spin pumping contrive to produce an unconventional spin current in the out-of-plane direction. Our findings provide a route to extract the spin mixing conductance matrix and uncovers the unique opportunities, such as level attraction, offered by van der Waals antiferromagnet-normal metal hybrids.

Chaotic behavior of a stack of intrinsic Josephson junctions at the transition to branching for overcritical currents

Phase dynamics of a stack of coupled intrinsic Josephson junctions was investigated in the framework of capacitively coupled Josephson junctions with diffusion current model. We study the transition from the current-voltage characteristic specific to Josephson junctions arrays with small dissipation and weak coupling between the junctions to the arrays with strong coupling between the junctions and high dissipation. Low dissipative arrays of Josephson junctions are characterized by the absence of branching for overcritical currents which appears for highly dissipative arrays. Described branching appears due to charging on the superconducting layers and charge traveling waves generation. Arrays of Josephson junctions with intermediate values of coupling and dissipation parameters are characterized by the chaotic behavior, confirmed by positive Lyapunov exponent, and branching on the current voltage characteristic for both sub- and overcritical currents.

Dynamics of Coupled Thermoacoustic Oscillators Under Asymmetric Forcing

Quenching of limit cycle oscillations (LCO), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in quenching of LCO has rarely been studied despite its practical applicability. We study the dynamics of two thermoacoustic oscillators simultaneously subjected to mutual coupling and asymmetric external forcing through experiments and theoretical modeling. We investigate the forced response of both identical and non-identical thermoacoustic oscillators for two different amplitudes of LCO. Under mutual coupling alone, identical thermoacoustic oscillators display the occurrence of partial amplitude death and amplitude death, whereas under forcing alone, asynchronous quenching of LCO is observed at non-resonant conditions. When the oscillators are simultaneously subjected to mutual coupling and asymmetric forcing, we observe a larger parametric region of oscillation quenching than when the two mechanisms are utilized individually. This enhancement in the region of oscillation quenching is due to the complementary effect of amplitude death and asynchronous quenching. However, a forced response of coupled non-identical oscillators shows that the effect of forcing is insignificant on synchronization and quenching of oscillations in the oscillator which is not directly forced. Finally, we qualitatively capture the experimental results using a reduced-order theoretical model of two coupled Rijke tubes which are coupled through dissipative and time-delay coupling and asymmetrically forced. We believe that these findings offer fresh insights into the combined effects of mutual and forced synchronization in a system of coupled nonlinear oscillators.

Optically controlled polariton condensate molecules

A condensed matter platform for analogue simulation of complex two-dimensional molecular bonding configurations, based on optically trapped exciton-polariton condensates is proposed. The stable occupation of polariton condensates in the excited states of their optically configurable potential traps permits emulation of excited atomic orbitals. A classical mean field model describing the dissipative coupling mechanism between p-orbital condensates is derived, identifying lowest threshold condensation solutions as a function of trap parameters corresponding to bound and antibound $\pi$ and $\sigma$ bonding configurations, similar to those in quantum chemistry.

Suppressing Dissipation in a Floquet-Hubbard System

The concept of `Floquet engineering' relies on an external periodic drive to realise novel, effectively static Hamiltonians. This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions. The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense. The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking. Here, we show how two-path quantum interference, applied to strongly-correlated fermions in a driven optical lattice, suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin-correlations by two to three orders of magnitude. Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase. This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of a driven Hubbard system, opening an avenue to realising low-temperature phases of matter in interacting Floquet systems.

Using Strictly Dissipative Impedance Coupling in the Waveform Relaxation Method for the Analysis of Interconnect Circuits

Dissipative impedance coupling is introduced in the waveform relaxation algorithm with longitudinal partitioning to address the slow convergence of standard resistive coupling in the analysis of low-loss highly reactive circuits. The pertinence, feasibility, and consistency of the proposed WR algorithm are demonstrated. Its convergence is examined for any passive linear time-invariant (LTI) system. Rational-with-delay impedances are presented to decouple general transmission line circuits. The proposed coupling strategy uses coarse macromodeling of the transmission lines to construct the coupling impedances directly as passive distributed auxiliary circuits. Numerical examples show a superior speed of convergence and further runtime savings.

Magnetic dynamics with Weyl fermions

Transport of charge and valley degrees of freedom coupled to order-parameter dynamics in magnetic Weyl semimetals is studied in the framework of nonequilibrium thermodynamics. In addition to the established valley-related transport anomalies that are rooted in band-structure topology, we construct dissipative couplings between the three dynamic constituents of the system driven out of equilibrium by electromagnetic perturbations. We show how the valley degree of freedom mediates an effective coupling between the charge and magnetic sectors of the system, through a combination of the chiral anomaly, on the electric side, and the Onsager-paired valley torque and pumping, on the magnetic side. This work compliments previous studies of magnetic Weyl semimetals by a more systematic analysis of collective dissipation. We discuss several concrete examples of the valley-mediated current-driven magnetic instabilities and charge pumping, and extend the theory to the antiferromagnetic case.

Strain-Mediated Giant Magnetoelectric Coupling in a Crystalline Multiferroic Heterostructure.

Multiferroic heterostructures based on the strain-mediated mechanism present ultralow heat dissipation and large magnetoelectric coupling coefficient, two conditions that require endless improvement for the design of fast nonvolatile random access memories with reduced power consumption. This work shows that a structure consisting of a [Pb(Mg1/3Nb2/3)O3]0.7-[PbTiO3]0.3 (001) substrate on which a crystalline FeGa(001)/MgO(001) bilayer is deposited exhibits a giant magnetoelectric coupling coefficient of order 15 × 10–6 s m–1 at room temperature. That result is a 2-fold increment over the previous highest value. The spatial orientation of the magnetization vector in the epitaxial FeGa film is switched 90° with the application of electric field. The symmetry of the magnetic anisotropy is studied by the angular dependence of the remanent magnetization, demonstrating that poling the sample generates a switchable uniaxial magnetoelastic anisotropy in the film that overcomes the native low 4-fold magnetocrystalline anisotropy energy. Magnetic force microscopy shows that the switch of the easy axis activates the displacement of domain walls and the domain structures remain stable after that point. This result highlights the interest in single-crystalline structures including materials with large magnetoelastic coupling and small magnetocrystalline anisotropy for low-energy-consuming spintronic applications.

Heat evacuation from active Raman media using frequency-selective dissipative coupling

We propose to use frequency-selective quasi parity-time symmetry to reduce the heat generated by coherent anti-Stokes Raman scattering (CARS) reversed cycles in active Raman media with phase mismatch. This is accomplished using a coupled-waveguide structure, which includes the active Raman waveguide (RW), where the Stokes signal undergoes amplification via stimulated Stokes Raman scattering (SSRS), and a dissipative waveguide (DW), which is tuned to the anti-Stokes wavelength so as to evacuate the corresponding anti-Stokes photons from the RW by coupling. The DW introduces optical loss that partially offsets the growth of the anti-Stokes signal in the RW and hence suppress the reversed CARS cycles that would otherwise result into heat generation in the RW. It is shown that the frequency-selective quasi parity-time symmetry provided by the DW can reduce the heat in active Raman media by a very factor of up to five when the CARS phase mismatch is compensated for by the optimum level of coupling between the RW and the DW.

Hybrid Dissipative and Dispersive Optomechanically Induced Transparency

Traditionally, the optical interference and energy conversion could be modulated by dissipation and dispersion in nonlinear optomechanical systems. Here, in this article, we study the enhancement of dissipative coupling on transparency under generalized optomechanical coupling and theoretically illustrate the generation of optomechanically induced transparency with gain and interference tuning. It enables the enhancement of the controlling of fast (slow) light by an order of magnitude. This unifies the dispersive and dissipative coupling into generalized coupling in the study of optomechanically induced transparency and extends its applications from optical switching to optically controlled amplification under the red-sideband optical pumping.

Entanglement and quantum discord in optically coupled coherent Ising machines

We present analytical and numerical simulation results for squeezing, entanglement, and quantum discord in a dissipatively coupled coherent Ising machine (CIM). Both analytical solutions and numerical simulation results, which are obtained with positive-$P$, truncated-Wigner, and truncated-Husimi representations for the density operator, predict the presence of entanglement and quantum discord, below and above the threshold of CIM. The entanglement criteria and quantum discord are evaluated as a function of the dissipative coupling strength relative to the background loss. For coupled two DOPOs, while entanglement disappears as the background loss exceeds the Ising coupling strength, the quantum discord remains finite even with a large linear loss. For one-dimensional lattice of DOPOs, while entanglement disappears for DOPO pair with large distance, quantum discord remains finite.

Quasinormal-Mode Perturbation Theory for Dissipative and Dispersive Optomechanics.

Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in the engineering of optomechanical systems. In this Letter, we show that quasinormal-mode-based perturbation theory is capable of correctly predicting both dispersive and dissipative optomechanical couplings. We validate our model through simulations and also by comparison with experimental results reported in the literature. Finally, we apply this formalism to plasmonic systems, used for molecular optomechanics, where strong dissipative coupling signatures in the amplification of vibrational modes could be observed.

Synchronization of surface acoustic wave (SAW)-based delay-coupled self-oscillating MEMS

Coupled limit cycle oscillators have potential usage in neurocomputing, pattern recognition, signal processing units such as multilayer perceptrons and stable timekeeping devices. Here, we study the synchronization dynamics of parametrically excited coupled dome-shaped MEMS (microelectromechanical system), exhibiting limit cycle oscillations and hysteresis, which have previously been shown to synchronize with an external reference signal [1, 2]. The coupling considered here is through surface acoustic wave (SAW), emanating in the substrate near each oscillator, due to periodic forcing of the same, which acts as a base vibration term for the forced oscillator. Dynamics of the individual MEMS can be adequately modeled as Mathieu–van der Pol–Duffing (MVDPD) oscillator [3], while the effect of SAW can be added as a delay coupling term, because of finite time involved in travel of this signal, resulting in a set of delay differential equations (DDEs). Various solutions for different parameter values are identified and the synchronization regions mapped under the case of a general dissipative type coupling. Numerical integration of the DDE for the system as well as the ODE obtained by applying the Krylov–Bogoliubov averaging method to the same is used for detailed analysis. The averaged equations are further reduced to get a phase equation which can be used to map the regions of synchronization at a much smaller computational budget. It is found that in general the delay terms lead to an increase in the synchronization region, while a cubic coupling term would be more effective. Effect of different parameters of individual oscillator on synchronization is also studied, which provide guidance for fabrication and testing of the optimized system.

Complete synchronization of chaos in systems with nonlinear inertial coupling

Abstract The effect of complete synchronization of chaotic oscillations and complex spatial structures in systems with nonlinear inertial coupling of the memristive type is studied. Three models of interacting systems with complex dynamics are considered: a system of two radio engineering chaotic self-oscillators, a system of two logistic maps, and a two-layer multiplex network of logistic maps with a dissipative nonlocal intra-layer coupling and a nonlinear inertial local coupling between the layers. For all three models, the influence of memristive coupling is shown. It consists in the dependence of the synchronization boundary on the initial state of the coupling elements. It has been established that this property is retained with inertial nonlinear coupling close to memristive (with strong inertiality).