Threshold Of Parametric Instability Research Articles

Spin-transfer-assisted parametric pumping of magnons in yttrium iron garnet

The combination of parametric pumping and spin-transfer torque is a powerful approach that enables high-level control over magnetic excitations in thin-film ferromagnets. The excitation parameters, such as pumping power and external field strength, affect the instabilities of individual magnon modes. We theoretically explore how the simultaneous effects of parametric pumping and spin transfer torque influence these magnetic instabilities in a thin-film ferromagnet. Within the Landau-Lifshitz-Gilbert framework, we perform micromagnetic simulations of magnon excitations in yttrium iron garnet by pumping, spin transfer torque, and a combination of the two. We find that consistent with experimental results, the magnitude and direction of the spin-transfer torque tune the parametric instability thresholds.

Effect of probing signal on the output signals spectrum of nonlinear spin waves in a cross based on waveguides of iron-yttrium garnet film

Subject. A change in the spectrum of spin waves (SW) in a magnetic cross is investigated when two signals pass through it: a pump signal and a probe signal. Objective. Detection of specific features in formation of the spectra of the output signals of SW in the multiport structure based on a yttrium iron garnet (YIG) film in the case of excitation of two magnetostatic surface waves (MSSW) simultaneously by the input antenna, where the first, with power higher than the first-order parametric instability threshold is the pump, and the second one is a probe. Methods. The experiments were performed for a cross structure from YIG film in the form of two orthogonal waveguides with the SW wire antennas placed at the ends of the waveguides, where one of the antennas on the transversely magnetized waveguide was considered as the input. Result. It was found that by choosing the probing signal frequency, one can significantly (by 10 dB) change the relative signal levels for the satellite waves at the output antennas, which are secondary MSSWs with some new frequencies and appear in the output signals spectrum as a result of the thresholdless processes of merging of parametric spin waves generated by MSSW pumping. In this case the secondary MSSWs frequencies can differ at the output antennas located on orthogonal waveguides. Discussion. The discovered effect is associated with the nonreciprocal nature of propagation of both the pumping wave and the waves generated at parametric instability condition in the structure.

Parametric Generation of Propagating Spin Waves in Ultrathin Yttrium Iron Garnet Waveguides

Herein, experimental demonstration of the parallel parametric generation of spin waves in a microscaled yttrium iron garnet waveguide with nanoscale thickness is presented. Using Brillouin light scattering microscopy, the parametric excitation of the first and second waveguide modes by a stripline microwave pumping source is observed. Micromagnetic simulations reveal the wave vector of the parametrically generated spin waves. Based on analytical calculations, which are in excellent agreement with experiments and simulations, it is proved that the spin‐wave radiation losses are the determinative term of the parametric instability threshold in this miniaturized system. The used method enables the direct excitation and amplification of nanometer spin waves dominated by exchange interactions. The presented results pave the way for integrated magnonics based on insulating nanomagnets.

Purcell enhancement of the parametric down-conversion in two-dimensional nonlinear materials

Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads to a strong Purcell enhancement of the nonlinear processes and compensates for a small interaction volume. The generic feature of such devices which makes them especially challenging for analysis is strong dissipation of both the nonlinear polarization and highly confined modes of a subwavelength cavity. Here we solve a quantum-electrodynamic problem of the spontaneous and stimulated parametric down-conversion in a nonlinear quasi-2D waveguide or cavity. We develop a rigorous Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. Within a relatively simple model, we take into account the nonlinear coupling of the quantized cavity modes, their interaction with a dissipative reservoir and the outside world, amplification of thermal noise and zero-point fluctuations of the electromagnetic field, and other relevant effects. We derive closed-form analytic results for relevant quantities such as the spontaneous parametric signal power and the threshold for parametric instability. We find a strong reduction in the parametric instability threshold for 2D nonlinear materials in a subwavelength cavity and provide a comparison with conventional nonlinear photonic devices.

Threshold of parametric instability in the ionospheric heating experiments

Many observations in the ionospheric heating experiment, by a powerful high frequency electromagnetic wave with ordinary polarization launched from a ground-based facility, is attributed to parametric instability (PI). In this paper, the general dispersion relation and the threshold of the PI excitation in the heating experiment are derived by considering the inhomogeneous spatial distribution of pump wave field. It is shown that the threshold of PI is influenced by the effective electron and ion collision frequencies and the pump wave frequency. Both collision and Landau damping should be considered in the PI calculation. The derived threshold expression has been used to calculate the required threshold for excitation of PI for several ionospheric conditions during heating experiments conducted employing EISCAT high frequency transmitter in Tromsø, Norway, on 2nd October 1998, 8th November 2001, 19th October 2012 and 7th July 2014. The results indicate that the calculated threshold is in good agreement with the experimental observations.

On mathematical models for describing parametric and modulation instabilities

The development of modulation instability of a finite amplitude wave is considered. A modified S-theory, previously developed in the works of V. Ye. Zakharov, was used to describe unstable modes. It is noted that near the instability threshold a self-similar spatial wave structure can form at different scales. The dynamics of the instability is analyzed in a model of a high intensity practically undamped oceanic wave, the mechanism of the formation of anomalous amplitude waves is shown. The modes of excitation of parametric instabilities are discussed. It is noted, that there is a similarity in the development of modulation and parametric instabilities, however there are also differences related to the nature of the dynamics of the wave packets of unstable perturbations. The nature of parametric instabilities is associated with the presence of a high-frequency, spatially homogeneous component of one or more parameters of the medium. Since the wave number of such HF oscillations is zero, or extremely small, in comparison with the characteristic lengths of the system, the spectrum of unstable disturbances is also located symmetrically, resembling the unstable spectrum of modulation instability. However, the growing perturbations practically do not move in space. Far from the threshold of parametric instability, a strong small-scale modulation of environmental parameters can form, which often takes on the character of a process with aggravation. The formation of self-similar spatial structures in the developed convection of a thin liquid or gas layer due to the development of modulation instability. The toroidal convection vortices generate poloidal vortices of large scale - the effect of a hydrodynamic dynamo and the experimental results of the investigation self-similar structures on the graphite are presented. The nature of self-consistent parametric instabilities is similar to the processes of modulation instability.

Nondegenerate Parametric Resonance in a Tunable Superconducting Cavity

We develop a theory for non-degenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a strong nonlinear regime at the parametric instability threshold, and calculate maximum gain values. Above the threshold, in the parametric oscillator regime the linear cavity response diverges at the oscillator frequency at all pump strengths. We show that this divergence is related to the continuous degeneracy of the free oscillator state with respect to the phase. Applying on-resonance input lifts the degeneracy and removes the divergence. We also investigate the quantum noise squeezing. It is shown that in the strong amplification regime the noise undergoes four-mode squeezing, and that in this regime the output signal to noise ratio can significantly exceed the input value. We also analyze the intermode frequency conversion and identify parameters at which full conversion is achieved.

A maser based on dynamical backaction on microwave light

The work of Braginsky introduced radiation pressure dynamical backaction, in which a mechanical oscillator that is parametrically coupled to an electromagnetic mode can experience a change in its rigidity and it's damping rate. The finite cavity electromagnetic decay rate can lead to either amplification or cooling of the mechanical oscillator, and lead in particular to a parametric oscillatory instability, associated with regenerative oscillations of the mechanical oscillator, an effect limiting the circulating power in laser gravitational wave interferometers. These effects implicitly rely on an electromagnetic cavity whose dissipation rate vastly exceeds that of the mechanical oscillator, a condition naturally satisfied in most optomechanical systems. Here we consider the opposite limit, where the mechanical dissipation is engineered to dominate over the electromagnetic one, essentially reversing role of electromagnetic and mechanical degree of freedom. As a result, the electromagnetic field is now subject to dynamical backaction: the mechanical oscillator provides a feedback mechanism which modifies the damping rate of the electromagnetic cavity. We describe this phenomenon in the spirit of Braginsky's original description, invoking finite cavity delay and highlighting the role of dissipation. Building on previous experimental work, we demonstrate this dynamical backaction on light in a superconducting microwave optomechanical circuit. In particular, we drive the system above the parametric instability threshold of the microwave mode, leading to maser action and demonstrate injection locking of the maser, which stabilizes its frequency and reduces its noise.

Turbulence in the system of capillary waves on the surface of water

The experimental results of studying wave turbulence in a system of capillary waves on the surface of water in a cylindrical vessel are presented. Waves on the surface are excited by vertical vibrations of the water-filled vessel with accelerations below the parametric-instability threshold at a fixed frequency fp or in the frequency band from 30 to 50 Hz. The deviation of the surface from equilibrium is recorded by a laser beam reflecting from water. It is shown experimentally that the position of the high-frequency boundary of the inertial range fb of the turbulent cascade is shifted towards high frequencies with an increase in the pump amplitude А and described by the power function fb ~ Aβ with index β equal to 1.2 ± 0.1 for monochromatic pumping and 1.10 ± 0.15 for broadband pumping. The value of the index β for monochromatic pumping is close to the theoretical estimate; for broadband pumping, it is less by a factor of 2.5. In the dissipation region f > fb, the turbulent distribution is damped exponentially with the characteristic frequency fd depending on the amplitude and spectral characteristic of the excitation force. It follows from the amplitude dependences that the frequency fd is proportional to the frequency of the boundary of the inertial range fb.

Single-shot read-out of a superconducting qubit using a Josephson parametric oscillator.

We propose and demonstrate a read-out technique for a superconducting qubit by dispersively coupling it with a Josephson parametric oscillator. We employ a tunable quarter wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with 185±15 photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot read-out performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing.

A theoretical investigation on the parametric instability excited by X‐mode polarized electromagnetic wave at Tromsø

AbstractRecent ionospheric modification experiments performed at Tromsø, Norway, have indicated that X‐mode pump wave is capable of stimulating high‐frequency enhanced plasma lines, which manifests the excitation of parametric instability. This paper investigates theoretically how the observation can be explained by the excitation of parametric instability driven by X‐mode pump wave. The threshold of the parametric instability has been calculated for several recent experimental observations at Tromsø, illustrating that our derived equations for the excitation of parametric instability for X‐mode heating can explain the experimental observations. According to our theoretical calculation, a minimum fraction of pump wave electric field needs to be directed along the geomagnetic field direction in order for the parametric instability threshold to be met. A full‐wave finite difference time domain simulation has been performed to demonstrate that a small parallel component of pump wave electric field can be achieved during X‐mode heating in the presence of inhomogeneous plasma.

Generation of a vortex flow by waves on the surface of a liquid

The formation of a vortex flow in a vessel with a liquid undergoing harmonic oscillations in a vertical direction has been studied experimentally. It has been found that the vortex flow does not occur in a cylindrical vessel until the amplitude of the oscillations exceeds a threshold value, at which the Faraday parametric instability develops and azimuthal modes emerge on the surface. The vortices appear in a square vessel and in a cylindrical vessel with broken symmetry at amplitudes below the parametric instability threshold. The formation of a vortex flow is presumably caused by the interaction of surface waves propagating at an angle with respect to each other.

Multimode phononic correlations in a nondegenerate parametric amplifier

We describe the realization of multimode phononic correlations that arise from nonlinear interactions in a mechanical nondegenerate parametric amplifier. The nature of these correlations differs qualitatively depending on the strength of the driving field in relation to the threshold for parametric instability. Below this threshold, the correlations are manifest in a combined quadrature of the coupled mechanical modes. In this regime, the system is amenable to back-action evading measurement schemes for the detection of weak forces. Above threshold, the correlations are manifest in the amplitude difference between the two mechanical modes, akin to intensity difference squeezing observed in optical parametric oscillators. We discuss the crossover of correlations between these two regimes and applications of this quantum-compatible mechanical system to nonlinear metrology and out-of-equilibrium dynamics.

Stabilization of three-wave vortex beams in the waveguide

We consider two-dimensional (2D) localized vortical modes in the three-wave system with the quadratic () nonlinearity, alias nondegenerate second-harmonic (SH)-generating system, guided by the isotropic harmonic-oscillator (alias parabolic) confining potential. In addition to the straightforward realization in optics, the system models mixed atomic-molecular Bose–Einstein condensates. The main issue is stability of the vortex modes, which is investigated through computation of instability growth rates for eigenmodes of small perturbations, and by means of direct simulations. The threshold of parametric instability for single-color beams, represented solely by the SH with zero vorticity, is found in an analytical form with the help of the variational approximation. Trapped states with vorticities in the two fundamental-frequency components and the SH one (the so-called hidden-vorticity modes) are completely unstable. Also unstable are semi-vortices, with component vorticities . However, full vortices, with charges , have a well-defined stability region. Unstable full vortices feature regions of robust dynamical behavior, where they periodically split and recombine, keeping their vortical content.

NONLINEAR DEVELOPMENT OF THER-MODE INSTABILITY AND THE MAXIMUM ROTATION RATE OF NEUTRON STARS

We describe how the nonlinear development of the R mode instability of neutron stars influences spin up to millisecond periods via accretion. Our arguments are based on nearly-resonant interactions of the R mode with pairs of "daughter modes". The amplitude of the R mode saturates at the lowest value for which parametric instability leads to significant excitation of a particular pair of daughters. The lower bound on this limiting amplitude is proportional to the damping rate of the daughter modes that are excited parametrically. Based on this picture, we show that if modes damp because of dissipation in a very thin boundary layer at the crust-core boundary then spin up to frequencies larger than about 300 Hz does not occur. Within this conventional scenario the R mode saturates at an amplitude that is too large for angular momentum gain from accretion to overcome gravitational loss to gravitational radiation. We conclude that lower dissipation is required for spin up to frequencies much higher than 300 Hz. We conjecture that if the transition from the fluid core to the crystalline crust occurs over a distance much longer than 1 cm then a sharp viscous boundary layer fails to form. In this case, damping is due to shear viscosity dissipation integrated over the entire star; the rate is slower than if a viscous boundary layer forms. We use statistical arguments and scaling relations to estimate the lowest parametric instability threshold from first principles. The resulting saturation amplitudes are low enough to permit spin up to higher frequencies. Further, we show that the requirement that the lowest parametric instability amplitude be small enough to allow continued spin up imposes an upper bound to the frequencies that may be attained via accretion that may plausibly be about 750 Hz. Within this framework, the R mode is unstable for all millisecond pulsars, whether accreting or not.

Parametric excitation of magnetization oscillations controlled by pure spin current

We report an experimental investigation of parametric excitation of magnetization oscillations in a permalloy microdisk in the presence of a pure spin current. The latter is generated by an adjacent Pt layer due to the spin Hall effect. We demonstrate that the spin torque induced by the pure spin current can significantly reduce the threshold for parametric instability, and modify the frequency range of the parametrically excited oscillation at a given pumping power. Our results show that pure spin currents can be utilized for stimulation and control of nonlinear dynamic magnetic phenomena in microscopic structures.

Dynamics of polaritons in semiconductor microcavities near instability thresholds

A theoretical study is presented on the dynamics of polaritons in semiconductor microcavities near parametric instability thresholds. With upward or downward ramp of optical pump, different instability modes emerge in parameter space defined by damping and detuning. According to these modes, stationary short-wave, stationary periodic, oscillatory periodic, and oscillatory uniform parametric instabilities are distinguished. By multiple scale expansion, the dynamics near threshold can be described by a critical mode with a slowly varying amplitude for the last three instabilities. Furthermore, it is found that the evolutions of their amplitudes are governed by real or complex Ginzburg–Landau equations.

Effect of Horizontal Vibration on the Interfacial Instability in a Horizontal Hele-Shaw Cell

The e ect of periodic oscillations on the interfacial instability of two immiscible fluids, confined in a horizontal Hele-Shaw cell, is investigated. A linear stability analysis of the basic state leads to a periodic Mathieu oscillator corresponding to the amplitude of the interface. Then, the threshold of parametric instability of the interface is characterized by harmonic or subharmonic periodic solutions. We show that the relevant parameters that control the interface are the Bond number, density ratio, Weber number and amplitude and frequency of oscillations.

Transformation of electromagnetic waves in turbulent magnetized plasmas

In the present paper, on the basis of kinetic theory fluctuations the transformation of transverse electromagnetic waves into longitudinal Langmuir oscillations in turbulent magnetized plasma subjected to the influence of a lower hybrid pump wave is investigated. We consider the case when the decay of the pump into daughter and ion-acoustic waves occurs. The transformation cross section of electromagnetic waves by turbulent density fluctuations in the region above the parametric instability threshold is calculated. The comparative preference of transformation and scattering processes is discussed.

Wave-vortex interaction

We present an experimental study of the effect of an electromagnetically generated vortex flow on parametrically amplified waves at the surface of a vertically vibrated fluid layer. The underlying vortex flow, generated by a periodic Lorentz force, creates spatiotemporal fluctuations that nonlinearly interact with the standing surface waves. We measure the power spectral density of the surface wave amplitude and we characterize the bifurcation diagram by recording the subharmonic response of the surface to the external vibration. We show that the parametric instability is delayed in the presence of spatiotemporal fluctuations due to the vortex flow. In addition, the dependence of the amplitude of the subharmonic response on the distance to the instability threshold is modified. This shows that the nonlinear saturation mechanism of the waves is modified by the vortex flow.