Experimental measurement of quantum-first-passage-time distributions

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. Here, we report the first measurements of QFPTDs using a quantized bosonic motional mode of a single trapped ion. In order to do these measurements, we develop a novel quantum signal-processing technique to perform tunable stroboscopic projective measurements of the bosonic state. We measure QFPTDs of the ion energy when coupled to noisy electric fields and establish a clear connection with their 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. We also describe future applications of experimental QFPTD measurements, which range from quantum search algorithms to unraveling connections between classical and quantum dynamics, to precision measurement.