Large Quantum Delocalization of a Levitated Nanoparticle using Optimal Control: Applications for Force Sensing and Entangling via Weak Forces

TL;DR

This paper introduces an optimal control protocol to significantly delocalize a levitated nanoparticle's quantum state, enhancing force sensing and entanglement capabilities while considering realistic noise effects.

Contribution

It presents a bang-bang control method to rapidly expand and contract the nanoparticle's quantum state, enabling exploration of macroscopic quantum regimes with noise analysis.

Findings

Protocol achieves large-scale quantum delocalization

Enhances force sensing sensitivity

Increases entangling rate of nanoparticles

Abstract

We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility to invert it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticle's center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments.