Parametric oscillator

About: Parametric oscillator is a research topic. Over the lifetime, 5836 publications have been published within this topic receiving 95631 citations. The topic is also known as: Parametric excitation.

Flux‐flow‐type Josephson oscillator for millimeter and submillimeter wave region. IV. Thin‐film coupling

Abstract: Power emission from a flux‐flow‐type Josephson oscillator with a thin‐film coupling method is studied experimentally. The thickness of one electrode of the oscillator is made thin enough to allow electromagnetic fields generated by the oscillator to be emitted through the thin‐film electrode. Radiation power from the oscillator is detected with superconductor‐insulator‐superconductor detectors, which are fabricated on top of the oscillator. Experimental results show that sufficient power can be obtained from the oscillator by using the thin‐film coupling method when the thickness of the electrode is comparable to the London penetration depth. The results obtained are in reasonable agreement with theoretical predictions. The thin‐film coupling method will be useful when the oscillator is connected to external circuits, such as an impedance matching circuit.

Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems.

Abstract: We consider the effect on a generic period-doubling bifurcation of a periodic perturbation, whose frequency ${\ensuremath{\omega}}_{1}$ is near the period-doubled frequency ${\ensuremath{\omega}}_{0}$/2. The perturbation is shown to always suppress the bifurcation, shifting the bifurcation point and stabilizing the behavior at the original bifurcation point. We derive an equation characterizing the response of the system to the perturbation, analysis of which reveals many interesting features of the perturbed bifurcation, including (1) the scaling law relating the shift of the bifurcation point and the amplitude of the perturbation, (2) the characteristics of the system's response as a function of bifurcation parameter, (3) parametric amplification of the perturbation signal including nonlinear effects such as gain saturation and a discontinuity in the response at a critical perturbation amplitude, (4) the effect of the detuning (${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{0}$/2) on the bifurcation, and (5) the emergence of a closely spaced set of peaks in the response spectrum. An important application is the use of period-doubling systems as small-signal amplifiers, e.g., the superconducting Josephson parametric amplifier.

The harmonic oscillator propagator

Abstract: The Feynman propagator for the harmonic oscillator is evaluated by a variety of path-integral-based means.

Study of the parametric oscillator driven by narrow‐band noise to model the response of a fluid surface to time‐dependent accelerations

Abstract: A stochastic formulation is introduced to study the large amplitude and high‐frequency components of residual accelerations found in a typical microgravity environment (or g‐jitter). The linear response of a fluid surface to such residual accelerations is discussed in detail. The analysis of the stability of a free fluid surface can be reduced in the underdamped limit to studying the equation of the parametric harmonic oscillator for each of the Fourier components of the surface displacement. A narrow‐band noise is introduced to describe a realistic spectrum of accelerations, that interpolates between white noise and monochromatic noise. Analytic results for the stability of the second moments of the stochastic parametric oscillator are presented in the limits of low‐frequency oscillations, and near the region of subharmonic parametric resonance. Based upon simple physical considerations, an explicit form of the stability boundary valid for arbitrary frequencies is proposed, which interpolates smoothly between the low frequency and the near resonance limits with no adjustable parameter, and extrapolates to higher frequencies. A second‐order numerical algorithm has also been implemented to simulate the parametric stochastic oscillator driven with narrow‐band noise. The simulations are in excellent agreement with our theoretical predictions for a very wide range of noise parameters. The validity of previous approximate theories for the particular case of Ornstein–Uhlenbeck noise is also checked numerically. Finally, the results obtained are applied to typical microgravity conditions to determine the characteristic wavelength for instability of a fluid surface as a function of the intensity of residual acceleration and its spectral width.

Squeezing a Thermal Mechanical Oscillator by Stabilized Parametric Effect on the Optical Spring

Abstract: We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the ?3??dB limit in the noise reduction, associated with parametric resonance, with a best experimental result of ?7.4??dB . While the present experiment is in the classical regime, in a moderately cooled system our technique may allow squeezing of a macroscopic mechanical oscillator below the zero-point motion.