Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions

TL;DR

This paper demonstrates a new quantum measurement method using motional Fock states of trapped ions, surpassing the standard quantum limit in frequency and displacement measurements, with potential for enhanced quantum sensing.

Contribution

It introduces a phase insensitive Fock state approach for quantum metrology, avoiding the control issues of squeezed vacuum protocols in trapped ion systems.

Findings

Achieved measurement sensitivities beyond the SQL.

Successfully used Fock states for frequency and displacement detection.

Maintained quantum gain despite classical noise sources.

Abstract

Non-vanishing fluctuations of the vacuum state are a salient feature of quantum theory. These fluctuations fundamentally limit the precision of quantum sensors. Nowadays, several systems such as optical clocks, gravitational wave detectors, matter-wave interferometers, magnetometers, and optomechanical systems approach measurement sensitivities where the effect of quantum fluctuations sets a fundamental limit, the so-called standard quantum limit (SQL). It has been proposed that the SQL can be overcome by squeezing the vacuum fluctuations. Realizations of this scheme have been demonstrated in various systems. However, protocols based on squeezed vacuum crucially rely on precise control of the relative orientation of the squeezing with respect to the operation imprinting the measured quantity. Lack of control can lead to an amplification of noise and reduces the sensitivity of the device. Here, we experimentally demonstrate a novel quantum metrological paradigm based on phase insensitive Fock states of the motional state of a trapped ion, with applications in frequency metrology and displacement detection. The measurement apparatus is used in two different experimental settings probing non-commuting observables with sensitivities beyond the SQL. In both measurements, classical preparation and detection noise are sufficiently small to preserve the quantum gain in a full metrological protocol.