Showing papers on "Parametric oscillator published in 2018"
TL;DR: In this article, a quantum-limited parametric amplifier based on an array of superconducting nonlinear asymmetric inductive elements is proposed to handle large input signals without sacrificing other desirable characteristics.
Abstract: Quantum-limited Josephson parametric amplifiers are a key component in many precision microwave measurement setups, such as for the readout of superconducting qubits in a quantum computer. As qubit setups scale up, these amplifiers must be optimized to handle input signals of ever-larger power. The authors design a quantum-limited parametric amplifier based on an array of superconducting nonlinear asymmetric inductive elements. This ``SNAIL'' is optimized to handle large input signals without sacrificing other desirable characteristics. The method can be extended to improve all forms of parametrically induced mixing in quantum information applications.
85 citations
TL;DR: It is demonstrated that the implementation of a two-phonon Jaynes-Cummings Hamiltonian under coherent driving of the qubit yields a dissipative phase transition with similarities to the one predicted in the model of the degenerate parametric oscillator.
Abstract: We present a method to implement two-phonon interactions between mechanical resonators and spin qubits in hybrid setups, and show that these systems can be applied for the generation of nonclassical mechanical states even in the presence of dissipation. In particular, we demonstrate that the implementation of a two-phonon Jaynes-Cummings Hamiltonian under coherent driving of the qubit yields a dissipative phase transition with similarities to the one predicted in the model of the degenerate parametric oscillator: beyond a certain threshold in the driving amplitude, the driven-dissipative system sustains a mixed steady state consisting of a ``jumping cat,'' i.e., a cat state undergoing random jumps between two phases. We consider realistic setups and show that, in samples within reach of current technology, the system features nonclassical transient states, characterized by a negative Wigner function, that persist during timescales of fractions of a second.
65 citations
TL;DR: In this article, the authors analyzed the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness.
54 citations
TL;DR: It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.
Abstract: In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: the pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.
45 citations
TL;DR: In this article, the Hamilton's principle was used to discretize the partial differential governing equation to a two-degree-of-freedom nonlinear system under combined parametric and external excitations.
45 citations
TL;DR: In this article, the authors show how to choose pump-tone parameters to reduce this distortion, so that anyone with such a JPA can squeeze harder for better measurements, without needing extra hardware or a more complicated scheme.
Abstract: ``Squeezed'' states of the microwave field, which allow one to beat the Heisenberg uncertainty limit for some phase values, find diverse applications in improving quantum measurements. These states can be created using a Josephson parametric amplifier (JPA) operated with a single current pump, but nonlinearities limit the available squeezing. The authors show how to choose pump-tone parameters to reduce this distortion, so that anyone with such a JPA can squeeze harder for better measurements, without needing extra hardware or a more complicated scheme.
41 citations
TL;DR: In this paper, the Galerkin method was applied, the shape function being that governing the beam's natural vibrations, evidencing the possibility of in-plane and out-of-plane vibrations as well as fully non-planar vibrations in the combination resonance range.
37 citations
TL;DR: In this paper, a three-wave mixing pathway in a system of two-and three-coupled phonon modes has been demonstrated, which points to the possibility of multimode frequency combs.
Abstract: This paper is motivated by the recent demonstration of a phononic frequency comb. While previous experiments have shown the existence of a three-wave mixing pathway in a system of two-coupled phonon modes, this work demonstrates a similar pathway in a system of three-coupled phonon modes. This paper also presents a number of interesting experimental facts concomitant to the three-mode parametric resonance based frequency comb observed in a specific micromechanical device. The experimental validation of frequency combs via three-mode parametric resonance along with the previous demonstration of two-mode frequency combs points to the ultimate possibility of multimode frequency combs.
36 citations
TL;DR: In this paper, a damped parametric pendulum with friction was identified twice by means of its precise and imprecise mathematical model using a laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon.
34 citations
10 Oct 2018
TL;DR: In this article, a computationally efficient multi-DoF nonlinear model is proposed, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.
Abstract: Wave energy devices are designed, and controlled, to be extremely responsive to incoming wave excitation, hence, maximising power absorption. Due to the consequent large motion excursions, highly nonlinear behaviour is likely to occur, especially in relation to variations in wetted surface. Moreover, nonlinearities may induce parametric instability, or activate internal mechanisms for exchanging energy between different degrees of freedom (DoFs), usually affecting the overall efficiency of the device. Consequently, single-DoF linear models may produce overly optimistic power production predictions, and neglect important dynamics of the system. One highly nonlinear phenomenon, potentially detrimental to power absorption for several wave energy converters, is parametric roll/pitch; due to parametric excitation, part of the energy flow is internally diverted, from the axis where the power take-off is installed, to a secondary axis, generating parasitic motion. This paper proposes a computationally efficient multi-DoF nonlinear model, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.
32 citations
TL;DR: In this paper, a stoichiometric silicon nitride (SiN) membrane-based electromechanical system was developed, in which the spring constant of the mechanical resonator can be dynamically controlled via piezoelectric actuation.
Abstract: We develop a stoichiometric silicon nitride (SiN) membrane-based electromechanical system, in which the spring constant of the mechanical resonator can be dynamically controlled via piezoelectric actuation. The degenerate parametric amplifier is studied in this configuration. We observe the splitting of mechanical mode in the response spectra of a phase-sensitive parametric amplifier. In addition, we demonstrate that the quality factor Q of the membrane oscillator can be significantly enhanced by more than two orders of magnitude due to the coherent amplification, reaching an effective Q factor of ∼3 × 108 at room temperature. The nonlinear effect on the parametric amplification is also investigated, as well as the thermomechanical noise squeezing. This system offers the possibility to integrate electrical, optical and mechanical degrees of freedom without compromising the exceptional material properties of SiN membranes, and can be a useful platform for studying cavity optoelectromechanics.
TL;DR: In this article, the authors numerically obtain the full time evolution of a parametrically driven-dissipative Bose-Einstein condensate in an optical cavity and investigate the implications of driving for the phase diagram.
Abstract: We numerically obtain the full time-evolution of a parametrically driven-dissipative Bose-Einstein condensate in an optical cavity and investigate the implications of driving for the phase diagram. Beyond the normal and su-perradiant phases, a third nonequilibrium phase emerges as a many-body parametric resonance. This dynamical phase switches between two symmetry-broken superradiant configurations. The switching is accompanied by a substantial occupation of other momentum states not retained in the mapping to the Dicke model. The emergent phase shows features of nonintegrability and thermalization.
TL;DR: In this article, a parametric excitation of a repulsive force electrostatic resonator is studied, and a correspondence of the model to Mathieu's Equation is made to prove the existence and location of parametric resonance.
Abstract: In this paper, parametric excitation of a repulsive force electrostatic resonator is studied. A theoretical model is developed and validated by experimental data. A correspondence of the model to Mathieu's Equation is made to prove the existence and location of parametric resonance. The repulsive force creates a combined response that shows parametric and subharmonic resonance when driven at twice its natural frequency. The resonator can achieve large amplitudes of almost 24 μm and can remain dynamically stable while tapping on the electrode. Because the pull-in instability is eliminated, the beam bounces off after impact instead of sticking to the electrode. This creates larger, stable trajectories that would not be possible with traditional electrostatic actuation. A large dynamic range is attractive for MEMS resonators that require a large signal-to-noise ratio.
TL;DR: In this article, the interaction of localized parametric pumping with spin waves of different amplitudes, propagating in a ferromagnetic nanowire, is studied analytically and by micromagnetic simulations.
Abstract: The interaction of a localized parametric pumping with spin waves of different amplitudes, propagating in a ferromagnetic nanowire, is studied analytically and by micromagnetic simulations. It is shown that parametric amplification of spin waves by localized pumping becomes less efficient with an increase in the spin wave amplitude due to the influence of nonlinear 4-magnon processes. In a certain range of spin wave amplitudes, the parametric amplifier acts as a stabilizer of the spin wave amplitude, as its action significantly reduces the spread of the spin wave amplitude in the vicinity of a certain mean value. The stabilization effect becomes more pronounced for higher pumping strength and larger relative lengths of the pumping localization region, compared to the spin wave mean free path. In contrast, the use of relatively short pumping localization regions allows one to efficiently amplify large-amplitude nonlinear spin waves.
TL;DR: Channel-resolved measurements of the anharmonic coupling of the coherent A_{1g} phonon in photoexcited bismuth to pairs of high wave vector acoustic phonons are reported.
Abstract: We report channel-resolved measurements of the anharmonic coupling of the coherent ${A}_{1g}$ phonon in photoexcited bismuth to pairs of high wave vector acoustic phonons. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This coupling drives temporal oscillations in the phonon mean-square displacements at the ${A}_{1g}$ frequency that are observed across the Brillouin zone by femtosecond x-ray diffuse scattering. We extract anharmonic coupling constants between the ${A}_{1g}$ and several representative decay channels that are within an order of magnitude of density functional perturbation theory calculations.
TL;DR: It is found that different two-dimensional semiconductors yield degenerate and non-degenerate emission at various spectral regions due to doubly resonant mode excitation, which can be tuned by varying the incidence angle of the external pump laser.
Abstract: Optical parametric oscillators are widely used as pulsed and continuous-wave tunable sources for innumerable applications, such as quantum technologies, imaging, and biophysics. A key drawback is material dispersion, which imposes a phase-matching condition that generally entails a complex design and setup, thus hindering tunability and miniaturization. Here we show that the burden of phase-matching is surprisingly absent in parametric micro-resonators utilizing mono-layer transition-metal dichalcogenides as quadratic nonlinear materials. By the exact solution of nonlinear Maxwell equations and first-principle calculations of the semiconductor nonlinear response, we devise a novel kind of phase-matching-free miniaturized parametric oscillator operating at conventional pump intensities. We find that different two-dimensional semiconductors yield degenerate and non-degenerate emission at various spectral regions due to doubly resonant mode excitation, which can be tuned by varying the incidence angle of the external pump laser. In addition, we show that high-frequency electrical modulation can be achieved by doping via electrical gating, which can be used to efficiently shift the threshold for parametric oscillation. Our results pave the way for the realization of novel ultra-fast tunable micron-sized sources of entangled photons—a key device underpinning any quantum protocol. Highly miniaturized optical parametric oscillators may also be employed in lab-on-chip technologies for biophysics, detection of environmental pollution and security.
TL;DR: In this article, the effect of time delay on the energy harvesting performance of a delayed nonlinear MEMS device was investigated and it was shown that there exists an optimum range of excitation frequency beyond the principal parametric resonance where quasi-periodic vibration-based energy harvesting is maximum.
Abstract: This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.
07 Feb 2018
TL;DR: In this paper, the concept of Plasmonic Parametric Resonance (PPR) was introduced, which is a novel way to amplify high-order PLASmonic modes with a uniform optical pump.
Abstract: Here we review the concept of Plasmonic Parametric Resonance (PPR): a novel way to amplify high-order plasmonic modes with a uniform optical pump PPR originates from a temporal permittivity modulation The threshold conditions for PPR and schemes of experimental realization and detection are also discussed
TL;DR: In this article, a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs), forming a non-linear quarter-wave resonator, is presented.
Abstract: We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs), forming a non-linear quarter-wave resonator This device was fabricated using a very simple single step fabrication process It shows a large bandwidth (45 MHz), an operating frequency tunable between 59 GHz and 68 GHz and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective non-linear LC series resonator that quantitatively describes these figures of merit without fitting parameters Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower
TL;DR: In this article, the induced instability due to parametric resonance of rectangular plates traversed by inertial loads and lying on elastic foundations was investigated by applying the incremental harmonic balance (IHB) method.
TL;DR: It is shown that, for specific geometrical features of the mirror, parametric resonance simultaneously activates a spurious yaw mode, and a numerical model is developed capable of capturing the key phenomena and of providing guidelines for a robust design.
Abstract: The main torsional mode of electrostatically actuated micromirrors is known to be dominated by parametric resonance when the actuation is performed via in-plane comb fingers. Here, we show that, for specific geometrical features of the mirror, parametric resonance simultaneously activates a spurious yaw mode. Due to the large torsional rotations, the two modes are nonlinearly coupled, inducing mutual stiffness variations and an unexpected temperature dependence of the main mode. After presenting an experimental evidence of the coupling, we develop and discuss a numerical model capable of capturing the key phenomena and of providing guidelines for a robust design.
TL;DR: In this article, an octave-spanning parametric amplifier with a dual-pump scheme was proposed, enabled by advanced dispersion flattening and strong Kerr nonlinearity in a silicon-rich nitride waveguide.
Abstract: Optical amplification is one of the main applications of nonlinear optics, and broadband optical parametric amplifiers are useful not only for multiple data channels in a communication system but for ultrashort optical pulses in ultrafast optics as well. We propose an octave-spanning parametric amplifier in a dual-pump scheme, enabled by advanced dispersion flattening and strong Kerr nonlinearity in a silicon-rich nitride waveguide. A comprehensive nonlinear model is used to study cascaded (non)degenerate parametric processes, by taking wavelength-dependent nonlinearity and all-order dispersion into account. The obtained gain spectrum has a 3-dB bandwidth of one octave from 126 to 244 THz (i.e., 1151 nm), and the gain reaches 11 dB. We show that the proposed amplifier is in principle tolerant to variations of physical parameters, such as pump power, propagation loss, and dispersion. We also examine the amplification of an ultrafast 13-fs soliton pulse with a sech2 waveform. The gain can reach 8 dB, with the pulse shape well maintained.
20 Jun 2018
TL;DR: In this article, a nanosecond mirrorless optical parametric oscillator (OPO) pump at 1 mu m was presented. The gain medium of the OPO was periodically poled Rubidium-doped KTP with a grating per...
Abstract: We report on the development of a nanosecond mirrorless optical parametric oscillator (OPO) pumped at 1 mu m. The gain medium of the OPO was periodically poled Rubidium-doped KTP with a grating per ...
TL;DR: In this article, the authors study theoretically the Landau-Zener transition in a two-level system strongly coupled to a single resonator mode (harmonic oscillator) and propose an analytical solution for the transition probability when the oscillator is highly excited.
Abstract: Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the transition probability is possible when the oscillator is highly excited, i.e., at high temperatures. Then the relative change of the excitation level of the oscillator in the course of the transition is small. The physical picture of the transition in the presence of coupling to the oscillator becomes transparent in the limiting cases of slow and fast oscillator. A slow oscillator effectively renormalizes the drive velocity. As a result, the transition probability either increases or decreases depending on the oscillator phase. The net effect is, however, the suppression of the transition probability. On the contrary, a fast oscillator renormalizes the matrix element of the transition rather than the drive velocity. This renormalization makes the transition probability a nonmonotonic function of the coupling amplitude.
TL;DR: In this paper, the authors demonstrate the emergence of two different frequency comb regimes using a single tone external drive signal, each associated with two different modes and mutually exclusive well-bounded regimes for each component frequency comb exist.
Abstract: This paper builds on the recent demonstration of three-wave mixing based phononic frequency comb. Here, in this process, an intrinsic coupling between the drive and resonant frequency leads to a frequency comb of spacing corresponding to the separation between drive and resonant frequency. In this paper, through the coupling with other identical devices, we demonstrate the emergence of two different frequency comb regimes using a single tone external drive signal. Several interesting features for coupled frequency combs are identified, including the following: (1) the spacing of the component frequency combs are controlled by two different resonant frequencies, each associated with two different modes; (2) the nonlinear drive level dependence is different for the component frequency combs; (3) mutually exclusive well-bounded regimes for each component frequency comb exist, and such regimes are not merely described by well-known parametric resonance thresholds.
01 Aug 2018
TL;DR: In this article, a review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin-systems with discrete variables, and new entropy-information inequalities are obtained for Franck-Condon factors.
Abstract: Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin–systems with discrete variables. New entropy–information inequalities are obtained for Franck–Condon factors. Density matrices of qudit states are expressed in terms of probabilities of artificial qubits as well as the quantum suprematism approach to geometry of these states using the triadas of Malevich squares is developed. Examples of qubits, qutrits and ququarts are considered.
TL;DR: In this paper, the authors studied the axion mass in a range from 10−13 to 10−3 in the presence of the Chern-Simons term and the velocity of light in the background of axion dark matter.
Abstract: It is widely believed that axions are ubiquitous in string theory and could be the dark matter. The peculiar features of the axion dark matter are coherent oscillations and a coupling to the electromagnetic field through the Chern-Simons term. In this paper, we study consequences of these two features of the axion with the mass in a range from $10^{-13}\,{\rm eV}$ to $10^{3}\,{\rm eV}$. First, we study the parametric resonance of electromagnetic waves induced by the coherent oscillation of the axion. As a result of the resonance, the amplitude of the electromagnetic waves is enhanced and the circularly polarized monochromatic waves will be generated. Second, we study the velocity of light in the background of the axion dark matter. In the presence of the Chern-Simons term, the dispersion relation is modified and the speed of light will oscillate in time. It turns out that the change of speed of light would be difficult to observe. We argue that the future radio wave observations of the resonance can give rise to a stronger constraint on the coupling constant and/or the density of the axion dark matter.
TL;DR: In this paper, the dynamic instability of thin laminated composite plates subjected to harmonic in-plane loading is studied based on nonlinear analysis, and the equations of motion of the plate are developed using von Karman-type of plate equation including geometric nonlinearity.
Abstract: In this paper, the dynamic instability of thin laminated composite plates subjected to harmonic in-plane loading is studied based on nonlinear analysis. The equations of motion of the plate are developed using von Karman-type of plate equation including geometric nonlinearity. The nonlinear large deflection plate equations of motion are solved by using Galerkin’s technique that leads to a system of nonlinear Mathieu-Hill equations. Dynamically unstable regions, and both stable- and unstable-solution amplitudes of the steady-state vibrations are obtained by applying the Bolotin’s method. The nonlinear dynamic stability characteristics of both antisymmetric and symmetric cross-ply laminates with different lamination schemes are examined. A detailed parametric study is conducted to examine and compare the effects of the orthotropy, magnitude of both tensile and compressive longitudinal loads, aspect ratios of the plate including length-to-width and length-to-thickness ratios, and in-plane transverse wave number on the parametric resonance particularly the steady-state vibrations amplitude. The present results show good agreement with that available in the literature.
TL;DR: In this article, a rotating shaft with geometrical nonlinearity under parametric and external excitations is investigated and the effect of various parameters on the response of the system is studied.
Abstract: In this paper, dynamic response of a rotating shaft with geometrical nonlinearity under parametric and external excitations is investigated. Resonances, bifurcations, and stability of the response are analyzed. External excitation is due to shaft unbalance and parametric excitation is due to periodic axial force. For this purpose, combination resonances of parametric excitation and primary resonance of external force are assumed. Indeed, simultaneous effect of nonlinearity, parametric, and external excitations are investigated using analytical method. By applying the method of multiple scales, four ordinary nonlinear differential equations are obtained, which govern the slow evolution of amplitude and phase of forward and backward modes. Eigenvalues of Jacobian matrix are checked to find the stability of solutions. Both periodic and quasi-periodic motion were observed in the range of study. The influence of various parameters on the response of the system is studied. A main contribution is that the parametric excitation in the presence of nonlinearity can be used to suppress the forward synchronous vibration. Indeed, in the presence of combination parametric excitation, the energy is transferred from forward whirling mode to backward one. This property can be applied in control of rotor unbalance vibrations.
TL;DR: In this article, a dynamic stability of axially moving viscoelastic Rayleigh beams is derived with the extended Hamilton's principle and simple support boundary condition with the Routh-Hurwitz criterion.
Abstract: The dynamic stability of axially moving viscoelastic Rayleigh beams is presented. The governing equation and simple support boundary condition are derived with the extended Hamilton’s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscosity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.