The first passage time in quantum dynamics

Rong-Tao Qiu, Wu-Sheng Dai, Mi Xie

Joseph M. Ryan, Simon Gorbaty, Thomas J. Kessler +3 more

Classical first-passage time distributions 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 composite-phase laser pulse sequence to perform tunable stroboscopic single-shot projective measurements of the motional state of a trapped ion. We measure QFPTDs of the ion energy when coupled to electric-field noise. 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 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.

Joseph M. Ryan, Simon Gorbaty, Stephen W. Teitsworth +1 more

The quantum first-passage problem involves stochastic trajectories conditioned on measurement outcomes. The timing statistics of such trajectories remain largely unexplored in open quantum systems. Here, we investigate the first-passage time to an energy threshold for a ubiquitous model: a harmonic oscillator driven by classical additive noise. We find that projective measurements and energy quantization lead to substantial differences between the quantum and classical first-passage-time distributions at low thresholds, while these differences gradually diminish as the threshold energy increases. We treat the problem using both ensemble-averaged conditioned density-matrix dynamics and trajectory-resolved stochastic pure-state dynamics. The two descriptions yield indistinguishable timing statistics. Quantization effects appear in the ensemble-level phase-space distributions of the surviving states and vanish at larger threshold energies. Individual trajectories reveal emergent quantum signatures from the repeated measurements, such as persistent Wigner negativity. Our results provide a framework for using first-passage processes to create measurement-induced nonclassical resource states and to study the quantum-classical crossover of monitored systems.

SC Althorpe, Pavel Soldán, Gabriel G. Balint‐Kurti