Topic
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.
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TL;DR: The quantum-mechanical problem of the simple harmonic oscillator confined into a box has been solved in this paper, where the probability amplitudes are parabolic cylinder functions and the energy levels are established by a numerical procedure as the roots of a polynomial.
Abstract: The quantum-mechanical problem of the simple harmonic oscillator confined into a box has been solved. The probability amplitudes are parabolic cylinder functions. The energy levels are established by a numerical procedure as the roots of a polynomial. These are given in tabular form. Interestingly, once the box size shrinks below a critical level, the energy levels radically increase from their unboxed values. This critical length is the effective oscillation length for an unboxed oscillator of lowest energy.
35 citations
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TL;DR: In this article, the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson-junction circuit were studied and the correlations of the radiation were quantified.
Abstract: Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson-junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts, each encompassing 2N photons; this accounts for the bunching of the photon pairs produced in the course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.
35 citations
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TL;DR: In this paper, a pulsed marginal oscillator was developed for use in pulsed ion cyclotron resonance experiments, where a gated amplifier was incorporated in the feedback loop for pulsing the oscillator on and off.
Abstract: A pulsed marginal oscillator has been developed for use in pulsed ion cyclotron resonance experiments. The circuit performs quite well as a means of detecting gaseous ions in a magnetic field when the cyclotron frequency of the ions is equal to the resonant frequency of the oscillator. A pulsed marginal oscillator is different from previous marginal oscillator designs in that a gated amplifier is incorporated in the feedback loop for pulsing the oscillator on and off. This feature is important for delayed detection of ions which are formed as a result of chemical reactions in the gas phase. Oscillation levels from 2 to 500 mV (p‐p) are obtained over a frequency range fram 50 kHz to 2 MHz.
35 citations
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TL;DR: In this article, the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity were computed and their dependence on the size of the cavity and the space dimension was analyzed.
Abstract: We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.
35 citations
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TL;DR: In this paper, the authors derived the properties of a pump-resonant singly resonant optical parametric oscillator for which the pump and one of the parametrically generated waves share a common cavity.
Abstract: We derive the properties of a pump-resonant singly resonant optical parametric oscillator for which the pump and one of the parametrically generated waves share a common cavity. Wave-vector mismatch and focusing effects are taken into account. We calculate the oscillation threshold and its dependence on emission wavelengths as the result of mode shape changes. The conversion efficiencies for signal and idler waves are calculated. It is shown that one can maximize the conversion efficiencies by optimizing mirror transmissivities. The interference effects that occur in a standing-wave geometry and the mode content of the nonresonant wave are also analyzed.
35 citations