Fano-like Anti-resonances in Nanomechanical and Optomechanical Systems

TL;DR

This paper analyzes the noise spectra of coupled nanomechanical and optomechanical systems, revealing Fano-like anti-resonances in the detector noise spectrum due to system interactions.

Contribution

It derives a general linear Langevin framework to describe noise spectra and uncovers Fano-like anti-resonances in detector noise in coupled resonator systems.

Findings

Detector noise exhibits Fano-like resonance and anti-resonance features.

The resonator spectrum follows a thermal form with effective damping and frequency shift.

Examples include a single electron transistor and a cavity resonator coupling.

Abstract

We study a resonator coupled to a generic detector and calculate the noise spectra of the two sub-systems. We describe the coupled system by a closed, linear, set of Langevin equations and derive a general form for the finite frequency noise of both the resonator and the detector. The resonator spectrum is the well-known thermal form with an effective damping, frequency shift and diffusion term. In contrast, the detector noise shows a rather striking Fano-like resonance, i.e. there is a resonance at the renormalized frequency, and an anti-resonance at the bare resonator frequency. As examples of this effect, we calculate the spectrum of a normal state single electron transistor coupled capacitively to a resonator and of a cavity coupled parametrically to a resonator.