Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging

TL;DR

This paper demonstrates how imaging spontaneous photons can generate complex quantum states, nonlinear measurements, and anomalous diffusion in single atoms or molecules, introducing Levy-driven continuous measurements with unique properties.

Contribution

It introduces a novel method to achieve quantum superpositions, nonlinear observables, and anomalous diffusion through photon imaging, and analyzes Levy processes in continuous quantum measurements.

Findings

Imaging spontaneous photons enables complex quantum states and measurements.

Levy processes can drive anomalous diffusion in quantum systems.

Gaussian Levy density is uniquely stable for continuous measurements.

Abstract

We show that well-separated quantum superposition states, measurements of strongly nonlinear observables, and quantum dynamics driven by anomalous diffusion can all be achieved for single atoms or molecules by imaging spontaneous photons that they emit via resonance florescence. To generate anomalous diffusion we introduce continuous measurements driven by L\'evy processes, and prove a number of results regarding their properties. In particular we present strong evidence that the only stable L\'evy density that can realize a strictly continuous measurement is the Gaussian.