Showing papers on "Parametric oscillator published in 2021"
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TL;DR: In this paper, a nanoresonator driven into parametric-direct internal resonance provided supporting evidence for the microscopic theory of nonlinear dissipation, and the parametric resonance of a graphene nanodrum was tuned to reach successive two-to-one internal resonances, leading to a nearly two-fold increase in nonlinear damping.
Abstract: Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.
38 citations
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TL;DR: In this article, a nonlinear parameter-excited model of spinning pipes conveying fluid is proposed by considering the spinning speed and flow velocity are perturbed periodically, and the stability and nonlinear parametric vibrations of such system are studied analytically and numerically.
35 citations
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TL;DR: In this article, the authors analyzed the low frequency end of the spectrum with an emphasis on a physical understanding, such as the suppressed production of gravitational waves due to the excitation of an over-damped harmonic oscillator and their enhancement due to being frozen out while outside the horizon.
Abstract: The low frequency part of the gravitational wave spectrum generated by local physics, such as a phase transition or parametric resonance, is largely fixed by causality, offering a clean window into the early Universe. In this work, this low frequency end of the spectrum is analyzed with an emphasis on a physical understanding, such as the suppressed production of gravitational waves due to the excitation of an over-damped harmonic oscillator and their enhancement due to being frozen out while outside the horizon. Due to the difference between sub-horizon and super-horizon physics, it is inevitable that there will be a distinct spectral feature that could allow for the direct measurement of the conformal Hubble rate at which the phase transition occurred. As an example, free-streaming particles (such as the gravity waves themselves) present during the phase transition affect the production of super-horizon modes. This leads to a steeper decrease in the spectrum at low frequencies as compared to the well-known causal k3 super-horizon scaling of stochastic gravity waves. If a sizable fraction of the energy density is in free-streaming particles, they even lead to the appearance of oscillatory features in the spectrum. If the universe was not radiation dominated when the waves were generated, a similar feature also occurs at the transition between sub-horizon to super-horizon causality. These features are used to show surprising consequences, such as the fact that a period of matter domination following the production of gravity waves actually increases their power spectrum at low frequencies.
31 citations
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TL;DR: In this article, a two-element piezoelectric energy harvester with both bistability and parametric resonance characteristics is presented to tackle the issue of reducing the potential barrier and triggering the parametric threshold amplitude.
29 citations
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TL;DR: In this paper, a low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding.
Abstract: A low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding. The governing partial differential equations describing the fluid–structure interactions are formulated and multi-mode approximations are obtained using the Galerkin projection method. The one mode approximation is applied in this study and two different resonances are investigated by employing the method of multiple scales. They are the 1:1 internal resonance between the structure and wake oscillator (also known as ‘lock-in’ phenomenon) and the combined 1:1 internal and 1:2 parametric resonances. Bifurcations under the varying nondimensional shedding frequency for different mass–damping parameters are investigated and the results of multiple-scale analysis are compared with direct numerical simulations. Analytical responses are calculated using the continuation method and their stability is determined by examining the eigenvalues of the corresponding characteristic equations. Effects of the system parameters including the amplitude of the tension variation, vortex shedding frequency and mass–damping parameter on the system bifurcations have been investigated. The analytical approach has allowed to probe bifurcations occurring in the system and to identify stable and unstable responses. It is shown that the combined resonances can induce large-amplitude vibration of the structure. Counter-intuitively, the amplitude of such responses increases rapidly as the amplitude of the tension variation grows. Comparisons between the analytical and numerical results confirm that the span of the system vibration can be accurately predicted analytically with respect to the obtained response amplitudes of responses. The proposed multi-mode approximation and presented findings of this study can be used to enhance design process of top tension risers.
25 citations
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TL;DR: A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed in this paper.
Abstract: A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed. On the basis of the theory, the Schrodinger equation and the energy spectrum for the quantum LC circuit were derived. By introducing special forms of position-dependent LC-electric components, the associated creation and annihilation operators were obtained and analyzed. The quantization of the DC-driven Josephson circuit and its parametric amplifier were studied in details. The main outcome of this study concerns the finite form of the energy expectation value at very high temperature in contrast to the results obtained in literature which is time-dependent. Further details were analyzed and discussed.
22 citations
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TL;DR: In this paper, a simple design for a Josephson parametric amplifier, using a lumped element resonator comprising a superconducting quantum interference device whose useful bandwidth is enhanced with an on-chip impedance-matching circuit, is presented.
Abstract: Broadband quantum-limited amplifiers play a critical role in the single-shot readout of superconducting qubits, but a popular implementation, the traveling wave parametric amplifier, involves a complex design and fabrication process. Here, we present a simple design for a Josephson parametric amplifier, using a lumped element resonator comprising a superconducting quantum interference device whose useful bandwidth is enhanced with an on-chip impedance-matching circuit. We demonstrate a flux-coupling geometry that maximizes the coupling to the Josephson loop and minimizes spurious excitation of the amplifier resonant circuit. The amplifier, which operates in a flux-pumped mode, is demonstrated with a power gain of more than 20 dB over a bandwidth of about 300 MHz, where approximate noise measurements indicate quantum-limited performance. A procedure is given for optimizing the bandwidth for this kind of amplifier, using a linearized circuit simulation while minimizing non-linearities.
21 citations
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TL;DR: In this paper, the stability and Shilnikov-type multi-pulse jumping chaotic vibrations are investigated for a nonlinear rotor-active magnetic bearing (AMB) system with the time varying stiffness and 16-pole legs under the mechanical-electric-electromagnetic excitations.
Abstract: The stability and Shilnikov-type multi-pulse jumping chaotic vibrations are investigated for a nonlinear rotor-active magnetic bearing (AMB) system with the time varying stiffness and 16-pole legs under the mechanical-electric-electromagnetic excitations. The ordinary differential governing equation of motion for the rotor-AMB system is given by a two-degree-of-freedom nonlinear dynamical system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equations of the rotor-AMB system are obtained by using the method of multiple scales under the cases of 1:1 internal resonance, primary parametric resonance and 1/2 subharmonic resonance. Some coordinate transformations are employed to find the type and number of the equilibrium points for the averaged equations. Using the global perturbation method developed by Kavacic and Wiggins, the explicit sufficient conditions near the resonance are obtained for the existence of the Shilnikov-type multi-pulse jumping homoclinic orbits and chaotic vibrations. This implies that the Shilnikov-type multi-pulse jumping chaotic vibrations may occur for the rotor-AMB system in the sense of Smale horseshoes. Numerical simulations are presented to verify the analytical predictions by using the fourth-order Runge-Kutta method. The Shilnikov-type multi-pulse jumping chaotic vibrations can exist in the rotor-AMB system with the time varying stiffness and 16-pole legs under the mechanical-electric-magnetic excitations.
21 citations
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TL;DR: In this paper, the authors investigated the dynamic behaviour of curved pipes in the shape of circular arcs conveying fluid and the effects of flow velocity and tube curvature on vibration modes and natural frequencies.
19 citations
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TL;DR: In this article, a model of describing parametric vibrations of a simply supported pipe conveying pulsating fluid is presented, where the three-dimensional motion equation of the system is a set of two nonlinear partial differential equations developed on the basis of Euler-Bernoulli beam theory, geometric nonlinearity and Kelvin-Voigt damping model.
18 citations
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TL;DR: In this article, the authors show how the Jaynes-cummings-Rabi model of cavity quantum electrodynamics can be realized via an isomorphism to the Hamiltonian of a qubit inside a parametric amplifier cavity.
Abstract: We show how the Jaynes-Cummings-Rabi model of cavity quantum electrodynamics can be realized via an isomorphism to the Hamiltonian of a qubit inside a parametric amplifier cavity. This realization clears the way to observe the full spectrum of the Rabi model via a probe applied to a parametric amplifier cavity containing a qubit and a parametric oscillator operating below threshold. An important outcome of the isomorphism is that the actual frequencies are replaced by detunings which make it feasible to reach the ultrastrong coupling regime. We find that inside this regime the probed spectrum displays a narrow resonance peak that is traced back to the transition between ground and first excited states. The exact form of these states is given at an energy crossing and then extended numerically. At the crossing, the eigenstates are entangled states of field and atom where the field is found inside squeezed cat states.
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TL;DR: In this article, the authors demonstrate the measurement of a superconducting qubit using a non-reciprocal parametric amplifier to directly monitor the microwave field of a readout cavity.
Abstract: The act of observing a quantum object fundamentally perturbs its state, resulting in a random walk toward an eigenstate of the measurement operator. Ideally, the measurement is responsible for all dephasing of the quantum state. In practice, imperfections in the measurement apparatus limit or corrupt the flow of information required for quantum feedback protocols, an effect quantified by the measurement efficiency. Here, we demonstrate the efficient measurement of a superconducting qubit using a nonreciprocal parametric amplifier to directly monitor the microwave field of a readout cavity. By mitigating the losses between the cavity and the amplifier, we achieve a measurement efficiency of $(72\ifmmode\pm\else\textpm\fi{}4)%$. The directionality of the amplifier protects the readout cavity and qubit from excess backaction caused by amplified vacuum fluctuations. In addition to providing tools for further improving the fidelity of strong projective measurement, this work creates a test bed for the experimental study of ideal weak measurements, and it opens the way toward quantum feedback protocols based on weak measurement such as state stabilization or error correction.
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TL;DR: In this paper, a reservoir-engineered entanglement for a cascaded bosonic system consisting of three modes was studied, where the adjacent pairs couple to each other via both the beam-splitter interaction and the coherent parametric interaction with the interaction strengths being tunable.
Abstract: We study reservoir-engineered entanglement for a cascaded bosonic system consisting of three modes, where the adjacent pairs couple to each other via both the beam-splitter interaction and the coherent parametric interaction with the interaction strengths being tunable. We focus on an optomechanical realization of the model by combining a nondegenerate parametric amplifier and an auxiliary cavity. A great steady-state cavity-mechanical entanglement can be achieved by optimizing the ratio of the interaction strengths, where the optomechanical cavity enacts the cold reservoir, simultaneously laser cooling the pair of hybrid modes delocalized over the auxiliary cavity and the mechanical oscillator. In comparison with the case of cooling a single delocalized mode, the dual-mode cooling approach allows one to obtain a greater amount of entanglement with higher cooling efficiencies and to explore strong entanglement in much broader parameter regions, where the rotating-wave approximation fails for the single-mode cooling case. Moreover, we show that the steady-state cavity-mechanical entanglement is robust to the mechanical thermal noise of the high temperature. The improved reservoir engineering approach can potentially be generalized to other bosonic systems with asymmetric beam-splitter and parametric interactions.
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TL;DR: In this article, a finite-sized spatiotemporal crystal is proposed and analyzed to enable simultaneous engineering of energy and momentum band gaps and provide a guideline for implementation of advanced dispersion-engineered parametric oscillators.
Abstract: Photonic crystals have revolutionized the field of optics with their unique dispersion and energy band gap engineering capabilities, such as the demonstration of extreme group and phase velocities, topologically protected photonic edge states, and control of spontaneous emission of photons. Time-variant media have also shown distinct functionalities, including nonreciprocal propagation, frequency conversion, and amplification of light. However, spatiotemporal modulation has mostly been studied as a simple harmonic wave function. Here, we analyze time-variant and spatially discrete photonic crystal structures, referred to as spatiotemporal crystals. The design of spatiotemporal crystals allows engineering of the momentum band gap within which parametric amplification can occur. As a potential platform for the construction of a parametric oscillator, a finite-sized spatiotemporal crystal is proposed and analyzed. Parametric oscillation is initiated by the energy and momentum conversion of an incident wave and the subsequent amplification by parametric gain within the momentum band gap. The oscillation process dominates over frequency mixing interactions above a transition threshold determined by the balance between gain and loss. Furthermore, the asymmetric formation of momentum band gaps can be realized by spatial phase control of the temporal modulation, which leads to directional radiation of oscillations at distinct frequencies. The proposed structure would enable simultaneous engineering of energy and momentum band gaps and provide a guideline for implementation of advanced dispersion-engineered parametric oscillators.
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TL;DR: In this article, the authors proposed a method for a high-fidelity $R_x$ gate by exciting the KPO outside the qubit space parity-selectively, which can be implemented by only adding a driving field.
Abstract: A Kerr-nonlinear parametric oscillator (KPO) can stabilize a quantum superposition of two coherent states with opposite phases, which can be used as a qubit. In a universal gate set for quantum computation with KPOs, an $R_x$ gate, which interchanges the two coherent states, is relatively hard to perform owing to the stability of the two states. We propose a method for a high-fidelity $R_x$ gate by exciting the KPO outside the qubit space parity-selectively, which can be implemented by only adding a driving field. In this method, utilizing higher effective excited states leads to a faster $R_x$ gate, rather than states near the qubit space. The proposed method can realize a continuous $R_x$ gate, and thus is expected to be useful for, e.g., recently proposed variational quantum algorithms.
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TL;DR: This system investigated high energy, near and mid-infrared optical vortex lasers formed by a 1 μm optical vortex-pumped KTiOAsO4 (KTA) optical parametric oscillator, which can be selectively transferred to the signal or idler output by changing the reflectivity of the output coupler.
Abstract: We investigated high energy, near and mid-infrared optical vortex lasers formed by a 1 μm optical vortex-pumped KTiOAsO4 (KTA) optical parametric oscillator. The orbital angular momentum (OAM) of the pump beam can be selectively transferred to the signal or idler output by changing the reflectivity of the output coupler. With this system, 1.535 µm vortex signal output with an energy of 2.04 mJ and 3.468 µm vortex idler output with an energy of 1.75 mJ were obtained with a maximum pump energy of 21 mJ, corresponding to slope efficiencies of 14% and 10%, respectively. The spectral bandwidth (full width at half maximum, FWHM) of the signal and idler vortex outputs were measured to be Δλs ~ 1.3 nm (~ 5.5 cm-1) and Δλi ~ 1.7 nm (~ 1.4 cm-1), respectively.
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TL;DR: In this paper, a broadband flux-pumped Josephson parametric amplifier integrated with an on-chip coplanar waveguide impedance transformer is presented, achieving an operational bandwidth over 600 MHz with a gain above 15 dB, and a high saturation power with quantum-limited noise performance.
Abstract: The rapid progress towards scalable quantum processors demands amplifiers with large bandwidths and high saturation powers. For this purpose, we present a broadband flux-pumped Josephson parametric amplifier integrated with an on-chip coplanar waveguide impedance transformer. Our device can be fabricated with simple and straightforward photo-lithography. This device experimentally achieves an operational bandwidth over 600 MHz with a gain above 15 dB, and a high saturation power with quantum-limited noise performance. In addition, the center frequency of this device can be tuned over several hundred megahertz, which in turn broadens the effective operational bandwidth to around 1 GHz.
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TL;DR: Park et al. as discussed by the authors proposed a measurement method for out-of-plane motion detection in an encapsulated electrostatic MEMS gyroscope based on a variant of the harmonic detection of resonance (HDR) of the motion-induced current.
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TL;DR: In this paper, a low-loss Josephson metamaterial comprising superconducting non-linear asymmetric inductive elements was used to generate frequency (colour) entangled photons from vacuum fluctuations at a rate of 11 mega entangled bits per second with a potential rate above gigabit per second.
Abstract: Entangled microwave photons form a fundamental resource for quantum information processing and sensing with continuous variables. We use a low-loss Josephson metamaterial comprising superconducting non-linear asymmetric inductive elements to generate frequency (colour) entangled photons from vacuum fluctuations at a rate of 11 mega entangled bits per second with a potential rate above gigabit per second. The device is operated as a traveling wave parametric amplifier under Kerr-relieving biasing conditions. Furthermore, we realize the first successfully demonstration of single-mode squeezing in such devices - $2.4\pm0.7$ dB below the zero-point level at half of modulation frequency.
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TL;DR: In this paper, a gate-defined quantum dot is embedded into a mechanical resonator under strong actuation conditions, and the Coulomb peak positions synchronously oscillate with the mechanical vibrations, enabling a single-electron "chopper" mode.
Abstract: Numerous reports have elucidated the importance of mechanical resonators comprising quantum-dot-embedded carbon nanotubes (CNTs) for studying the effects of single-electron transport. However, there is a need to investigate the single-electron transport that drives a large amplitude into a nonlinear regime. Herein, a CNT hybrid device has been investigated, which comprises a gate-defined quantum dot that is embedded into a mechanical resonator under strong actuation conditions. The Coulomb peak positions synchronously oscillate with the mechanical vibrations, enabling a single-electron “chopper” mode. Conversely, the vibration amplitude of the CNT versus its frequency can be directly visualized via detecting the time-averaged single-electron tunneling current. To understand this phenomenon, a general formula is derived for this time-averaged single-electron tunneling current, which agrees well with the experimental results. By using this visualization method, a variety of nonlinear motions of a CNT mechanical oscillator have been directly recorded, such as Duffing nonlinearity, parametric resonance, and double-, fractional-, mixed- frequency excitations. This approach opens up burgeoning opportunities for investigating and understanding the nonlinear motion of a nanomechanical system and its interactions with electron transport in quantum regimes.
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TL;DR: In this paper, the authors studied the squeezing effect arising in the interacting qubit-oscillator system with the presence of a parametric oscillator in the Rabi model and employed the generalized rotating wave approximation which works well in a wide range of coupling strength as well as detuning.
Abstract: The squeezing effect arising in the interacting qubit-oscillator system is studied with the presence of a parametric oscillator in the Rabi model. To solve the system, we employ the generalized rotating wave approximation which works well in the wide range of coupling strength as well as detuning. The analytically derived approximate energy spectrum portrays good agreement with the numerically determined spectrum of the Hamiltonian. For the initial state of the bipartite system, the dynamical evolution of the reduced density matrix corresponding to the oscillator is obtained by partial tracing over the qubit degree of freedom. The oscillator’s reduced density matrix yields the nonnegative phase space quasi-probability distribution known as Husimi Q-function which is utilized to compute the quadrature variance. It is noticed that the squeezing produced in the oscillator sector gets reduced with increasing coupling strength. We demonstrate the role of the parametric term to obtain adequate squeezing in the strong coupling regime. We also study the revival–collapse phenomenon and the generation of squeezed coherent state.
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TL;DR: In this article, the authors investigated the out-of-plane dynamic stability of an arch under a vertical periodical base excitation by using both analytical and experimental methods and proposed a method of time domain analytical solution to determine the critical excitation frequencies.
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TL;DR: In this article, the authors present a cryogenic microwave noise source with a characteristic impedance of 50 Ω, which can be installed in a coaxial line of a cryostat.
Abstract: We present a cryogenic microwave noise source with a characteristic impedance of 50 Ω, which can be installed in a coaxial line of a cryostat. The bath temperature of the noise source is continuously variable between 0.1 K and 5 K without causing significant back-action heating on the sample space. As a proof-of-concept experiment, we perform Y-factor measurements of an amplifier cascade that includes a traveling wave parametric amplifier and a commercial high electron mobility transistor amplifier. We observe system noise temperatures as low as 680−200+20 mK at 5.7 GHz corresponding to 1.5−0.7+0.1 excess photons. The system we present has immediate applications in the validation of solid-state qubit readout lines.
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TL;DR: In this article, the effects of high-frequency parametric excitation on the principal parametric resonance of a nonlinear beam are studied both theoretically and experimentally, and it is found that the principal Parametric resonance can be effectively controlled and suppressed by high frequency excitation.
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TL;DR: In this paper, the authors studied the 3D collective long-term response of beams exposed to resonances and showed that slow synchrotron oscillation plays a significant role in the early time evolution of emittance growth.
Abstract: Understanding the 3D collective long-term response of beams exposed to resonances is of theoretical interest and essential for advancing high intensity synchrotrons. This study of a hitherto unexplored beam dynamical regime is based on 2D and 3D self-consistent particle-in-cell simulations and on careful analysis using tune spectra and phase space. It shows that in Gaussian-like beams Landau damping suppresses all coherent parametric resonances, which are of higher than second order (the ``envelope instability''). Our 3D results are obtained in an exemplary stopband, which includes the second order coherent parametric resonance and a fourth order structural resonance. They show that slow synchrotron oscillation plays a significant role. Moreover, for the early time evolution of emittance growth the interplay of incoherent and coherent resonance response matters, and differentiation between halo and different core regions is essential. In the long-term behavior we identify a progressive, self-consistent drift of particles toward and across the resonance, which results in effective compression of the initial tune spectrum. However, no visible imprint of the coherent features is left over, which only control the picture during the first one or two synchrotron periods. An intensity limit criterion and an asymptotic formula for long-term rms emittance growth are suggested. Comparison with the commonly used non-self-consistent ``frozen space charge'' model shows that in 3D this approximation yields a fast and useful orientation, but it is a conservative estimate of the tolerable intensity.
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TL;DR: In this paper, the authors studied the nonequilibrium evolution of a quantum Brownian oscillator, coupled to a nonstationary quantum field bath and inquired whether a fluctuation-dissipation relation can exist after/if it approaches equilibration.
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TL;DR: In this paper, an amplification chain consisting of a kinetic-inductance traveling-wave parametric amplifier (KI-TWPA) placed at 4 K, followed by a HEMT placed at 70 K, and demonstrate a chain-added noise $T_\Sigma = 6.3\pm0.5$ K between 3.5 and 5.5 GHz.
Abstract: Most microwave readout architectures in quantum computing or sensing rely on a semiconductor amplifier at 4 K, typically a high-electron mobility transistor (HEMT). Despite its remarkable noise performance, a conventional HEMT dissipates several milliwatts of power, posing a practical challenge to scale up the number of qubits or sensors addressed in these architectures. As an alternative, we present an amplification chain consisting of a kinetic-inductance traveling-wave parametric amplifier (KI-TWPA) placed at 4 K, followed by a HEMT placed at 70 K, and demonstrate a chain-added noise $T_\Sigma = 6.3\pm0.5$ K between 3.5 and 5.5 GHz. While, in principle, any parametric amplifier can be quantum limited even at 4 K, in practice we find the KI-TWPA's performance limited by the temperature of its inputs, and by an excess of noise $T_\mathrm{ex} = 1.9$ K. The dissipation of the KI-TWPA's rf pump constitutes the main power load at 4 K and is about one percent that of a HEMT. These combined noise and power dissipation values pave the way for the KI-TWPA's use as a replacement for semiconductor amplifiers.
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TL;DR: In this paper, a novel analytical technique for feedback-based parametric excitation was proposed, where solely transverse displacement is given to the clamped end, and a new analytical method, not requiring any small parameter in the equation of motion, was proposed to obtain stability boundary in the parametric space.
Abstract: The problem of parametric resonance of a base-excited cantilever beam has been studied both analytically and numerically. The support motion of the cantilever beam is generated by a feedback mechanism whereby the feedback signal is generated after modulating the cantilever tip motion with a harmonic time signal. This paper contributes a novel analytical technique for feedback-based parametric excitation. In the studied method, solely transverse displacement is given to the clamped end. It is different from the other methods, where axial displacement is also provided as parametric pumping. A new analytical method, not requiring any small parameter in the equation of motion, has been proposed to obtain stability boundary in the parametric space. Harmonic balance is carried out in the temporal domain for stability analysis. For numerical study, discrete element method is used. Numerical analysis is carried out to study unstable and stable behaviour for the applied parametric excitation. The numerical simulation results have been found out to be in excellent agreement with the outputs of analytical study.
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TL;DR: In this paper, the authors present a control strategy for a micro-electro-mechanical gyroscope with a drive mode excited through parametric resonance, which is implemented using phase-locked loop (PLL) and automatic gain control (AGC) loop.
Abstract:
In this paper, we present a control strategy for a micro-electro-mechanical gyroscope with a drive mode excited through parametric resonance. The reduced order two degrees-of-freedom model of the device is built, and the drive mode control is implemented using phase-locked loop (PLL) and automatic gain control (AGC) loop. A sense mode vibration control algorithm is developed as well for enhanced sensor performance. The analysis of the drive mode control loops is conducted using the multiple scales method. The robustness of the suggested control loops to parameters perturbation is demonstrated using the model. A simplified linear model of the control loops is shown to predict the device behavior with good accuracy.
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TL;DR: In this article, the authors developed the concept of quasi-phasematching by implementing it in the recently proposed Josephson traveling-wave parametric amplifier (JTWPA) with three-wave mixing (3WM).
Abstract: We develop the concept of quasi-phasematching (QPM) by implementing it in the recently proposed Josephson traveling-wave parametric amplifier (JTWPA) with three-wave mixing (3WM). The amplifier is based on a ladder transmission line consisting of flux-biased radio frequency superconducting quantum interference devices (SQUIDs) whose nonlinearity is of χ ( 2 )-type. QPM is achieved in the 3WM process, ω p = ω s + ω i (where ωp, ωs, and ωi are the pump, signal, and idler frequencies, respectively) due to designing the JTWPA to include periodically inverted groups of these SQUIDs that reverse the sign of the nonlinearity. Modeling shows that the JTWPA bandwidth is relatively large (∼ 0.4 ω p) and flat, while unwanted modes, including ω 2 p = 2 ω p , ω + = ω p + ω s, and ω − = 2 ω p − ω s, are strongly suppressed with the help of engineered dispersion.