Optimal Phonon-to-Spin Mapping in a system of a trapped ion

TL;DR

This paper introduces an optimized protocol for accurately mapping phonon number states to a spin state in a trapped ion system, enabling precise quantum measurements and applications like work distribution analysis.

Contribution

It develops a novel, optimized method for phonon-to-spin mapping using amplitude-modulated fields and numerical algorithms, advancing quantum measurement techniques in trapped ions.

Findings

Achieves high fidelity in phonon-to-spin mapping.

Provides analysis of fidelity scaling with Hilbert space size.

Demonstrates application in quantum work distribution measurement.

Abstract

We propose a protocol for measurement of the phonon number distribution of a harmonic oscillator based on selective mapping to a discrete spin-1/2 degree of freedom. We consider a system of a harmonically trapped ion, where a transition between two long lived states can be driven with resolved motional sidebands. The required unitary transforms are generated by amplitude-modulated polychromatic radiation fields, where the time-domain ramps are obtained from numerical optimization by application of the Chopped RAndom Basis (CRAB) algorithm. We provide a detailed analysis of the scaling behavior of the attainable fidelities and required times for the mapping transform with respect to the size of the Hilbert space. As one application we show how the mapping can be employed as a building block for experiments which require measurement of the work distribution of a quantum process.