Powerful approaches to squeeze the motional state of a harmonic oscillator rely on the stepwise modulation of its resonance frequency. Such protocols can be limited by forces that vary slowly between experimental runs but are constant during a single experimental shot. Such shot-to-shot noise gives rise to a spread in experimental outcomes that masks the uncertainty intrinsic to quantum theory. Taking inspiration from spin-echo protocols, we propose a decoupling technique that, under ideal conditions, perfectly cancels shot-to-shot force noise in squeezing experiments based on parametric modulation. We implement the protocol using an optically levitated nanoparticle, where shot-to-shot force noise arises from slowly varying stray fields acting on the charge carried by the particle. Using our oscillator-echo protocol, we demonstrate shot-to-shot noise suppression to the measurement-backaction limit.
@article{arxiv.2604.02175,
title = {Shot-to-shot noise cancellation for parametric oscillators},
author = {Martynas Skrabulis and Martin Colombano Sosa and Nicola Carlon Zambon and Andrei Militaru and Massimiliano Rossi and Lukas Novotny and Martin Frimmer},
journal= {arXiv preprint arXiv:2604.02175},
year = {2026}
}