One-electron parametric oscillator

Christopher M. Wilson, T. Duty, Per Delsing

A parametric oscillator is an oscillating system in which one of the parameters, typically either the resonance frequency or damping, can be modulated by an external pump. Parametric oscillations can be found in a wide variety of systems including radiofrequency circuits, optical and mechanical systems, and even single electrons in a Penning trap. In recent years, interest in parametric oscillators has revived in many areas of physics, ranging from basic physics to applications. For instance, they are being used as quantum-limited amplifiers in an increasingly large number of experiments in quantum information and computing. At the same time, interest in their basic physics in the quantum regime, in which they are a model system for driven, nonlinear systems, has grown commensurately. This chapter gives a largely self-contained introduction to the theoretical description of the dynamics of parametric oscillators, both classical and quantum, and reviews some of the recent experimental work in superconducting circuits.

Matthew T. Rakher, Kartik A. Srinivasan

Ching-Hsiang Tseng, Daphna G. Enzer, G. Gabrielse +1 more

The parametric oscillation of a single trapped electron is studied and used to measure enhanced spontaneous emission. Hysteresis in this motion provides a 1-bit memory to store information about excitations made with the electron ``in the dark.'' The time dependence and stability criteria for the parametric excitation are examined. The cyclotron motions for one and two electrons are also studied.

HERBERT WALTHER

Tsuyoshi Yamamoto

Superconducting parametric amplifier, originally developed more than half a century ago, gained renewed interests in some experiments of superconducting quantum electronics about a decade ago, and now has become an indispensable tool in the field of superconducting quantum information processing. More recently, there are several proposals, where a parametric oscillator, which is a parametric amplifier pumped above the threshold, is used as a quantum bit and the network of the parametric oscillators solve some computational tasks. Here, we briefly introduce the research activity on the development of the superconducting parametric devices, including our results, with some historical backgrounds.

В. С. Попов, A. M. Perelomov