# Experimental measurement of quantum-first-passage-time distributions

## TL;DR

This paper reports the first experimental measurement of quantum first-passage-time distributions using a trapped ion system, introducing a novel measurement protocol applicable to various quantum systems.

## Contribution

It develops a new composite-phase laser pulse sequence for tunable measurements of quantum first-passage times in a trapped ion.

## Key findings

- Measured QFPTDs of ion energy under electric-field noise
- Established connection between quantum and classical FPTDs
- Developed a broadly applicable measurement protocol

## Abstract

Classical First-Passage-Time Distributions (FPTDs) have been extensively studied both theoretically and experimentally. Their quantum counterparts, Quantum First-Passage-Time Distributions (QFPTDs), remain largely unexplored and have deep implications for both fundamental physics and the development of emerging quantum technologies. We measure the first QFPTDs using a motional mode of a single trapped ion. We develop a novel composite-phase laser pulse sequence to perform tunable stroboscopic projective measurements of the motional state of a trapped ion. We measure QFPTDs of the ion energy when coupled to electric-field noise and establish a clear connection with its classical counterpart. The measurement protocol developed here is broadly applicable to other quantum systems and provides a powerful method for exploring a broad range of QFPTD phenomena. With these results we open a new field of experimental investigations of QFPT processes with potential future relevance to quantum search algorithms, unraveling connections between classical and quantum dynamics, and study of the quantum measurement problem.