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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.


Papers
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Journal ArticleDOI
TL;DR: An approximating method is developed for determining the time evolution of harmonic oscillators with arbitrary derivable functions of the frequency or the mass and the approximate solution is shown to tend to the analytical one in the limiting case.
Abstract: The time evolution of a quantum harmonic oscillator with a series of sudden jumps of the mass or the frequency is determined in the form of a recursion relation. An approximating method is developed for determining the time evolution of harmonic oscillators with arbitrary derivable functions of the frequency or the mass. The approximate solution is shown to tend to the analytical one in the limiting case. As a demonstration of the approximating method, the solution of the problem of damped oscillation in the square of the oscillator frequency is presented.

43 citations

Journal ArticleDOI
TL;DR: In this article, a Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator is characterized and compared with degenerate and non-degenerate parametric amplification using a pair of modes.
Abstract: We characterize a Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator. The fundamental resonance frequency is ∼1 GHz, but we use higher modes of the resonator for our measurements. An on-chip tuning line allows for magnetic flux pumping of the amplifier. We investigate and compare degenerate parametric amplification, involving a single mode, and nondegenerate parametric amplification, using a pair of modes. We show that we reach quantum-limited noise performance in both cases.

42 citations

Proceedings ArticleDOI
02 Apr 2003
TL;DR: In this paper, the authors present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever and show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation.
Abstract: In this paper we present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular illustrate that parametric resonance phenomena occur in capacitively actuated micro-cantilevers. The combined parametric/harmonic mode of operation is investigated as well and experimental data are provided.

42 citations

Journal ArticleDOI
TL;DR: In this paper, a traveling-wave Josephson parametric amplifiers (TWJPAs) based on superconducting circuits are proposed for quantum information processing, where the interacting pump and signal/idler microwaves propagate with similar phase velocities through two different transmission lines, enabling parametric gain.
Abstract: With potentially quantum limited performance and wide frequency bandwidth, traveling-wave Josephson parametric amplifiers (TWJPAs) based on superconducting circuits are in urgent demand for quantum information processing. This study designs a TWJPA in which the interacting pump and signal/idler microwaves propagate with similar phase velocities through two different transmission lines, thereby enabling parametric gain. Such operation is possible due to a chain of SQUIDs that form the signal transmission line, which is magnetically coupled to a separate pump $L\phantom{\rule{0}{0ex}}C$ line. The proposed circuit may greatly simplify the measurement setup and solve the problem of pump depletion.

42 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two level system, more specifically by a quasi-instantaneous phase change.
Abstract: We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system---more specifically, by a quasi-instantaneous phase change. This enables us to isolate the dissipative evolution to which the oscillator may be exposed in addition. With this method we study the decoherence time of a photon mode in cavity QED, and that of the quantized harmonic motion of trapped ions. We comment on the relation to spin echoes and multipath interferometry.

42 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202366
2022133
2021123
2020139
2019145
2018135