Interferometer with a driven trapped ion

TL;DR

This paper introduces a novel interferometric method using a single trapped ion to measure weak forces, leveraging spin-dependent forces and geometrical phases for enhanced stability and sensitivity.

Contribution

It presents a new interferometric scheme employing time-dependent spin-dependent forces on a trapped ion, with explicit relations between forces and populations, and strategies to minimize errors.

Findings

Explicit formulas relating force to measurement outcomes

Design of trap trajectories to reduce anharmonicity errors

Method's robustness to motional state variations in harmonic regime

Abstract

We propose an interferometric measurement of weak forces using a single ion subjected to designed time-dependent spin-dependent forces. Explicit expressions of the relation between the unknown force and the final populations are found considering different scenarios, such as the weak force acting on two branches, on one branch, or having errors in the driving force. The flexibility to design the trap trajectories is used to minimize errors due to anharmonicities in the trap. The advantages of the approach are the use of geometrical phases, which provides stability, the possibility to design faster-than-adiabatic processes with sensitivity control, and the independence of the results on the motional states for the small-oscillations regime in which the effective potentials are purely harmonic.