Heating and thermal squeezing in parametrically-driven oscillators with added noise

TL;DR

This paper presents a comprehensive theoretical model for understanding heating and thermal squeezing in parametrically-driven oscillators with added thermal noise, highlighting the effects of pump amplitude and stability on these phenomena.

Contribution

The paper introduces a detailed analytical framework combining Green functions, Floquet theory, and averaging techniques to describe thermal effects in driven oscillators, including quantitative estimates and explanations.

Findings

Heating and thermal squeezing occur near the first parametric instability zone.

Floquet multipliers change from complex conjugates to real as pump amplitude increases.

Analytical predictions closely match numerical simulations.

Abstract

In this paper we report a theoretical model based on Green functions, Floquet theory and averaging techniques up to second order that describes the dynamics of parametrically-driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincare map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects cause most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.