Frequency measurements beyond the Heisenberg time-energy limit with a single atom

TL;DR

This paper demonstrates a frequency estimation method using a single atom that surpasses the Heisenberg time-energy limit, and discusses the fundamental limits and advantages of quantum algorithms and entanglement in frequency sensing.

Contribution

It introduces a technique that exceeds the Heisenberg limit with a single atom and analyzes the fundamental uncertainty bounds with multiple atoms, independent of entanglement.

Findings

Achieved frequency uncertainty below the Heisenberg limit with a single atom.

Proposed a $\

for multiple atoms, improving as $\

Abstract

The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information on the field frequency can be used to infer the atomic transition [4, 5]. Here we demonstrate a frequency estimation technique that provides an uncertainty orders of magnitude below the Heisenberg limit with a single atom. With access to $N$ atoms, we propose a fundamental uncertainty limit improving as $\sqrt{N}$, regardless of whether entanglement is employed. We describe implementation of the quantum fourier transform to estimate an unknown frequency without using entanglement. A comparison to classical algorithms severely limits the benefit that quantum algorithms provide for frequency estimation and that entanglement provides to quantum sensing in general.