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.
