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Springer eBooks

First-Passage-Time Distributions in a Bistable Two-Mode Laser

Daan Lenstra, Surendra Singh

Published Jan 1, 1984• 0 citations
Publisher
DOI
10.1007/978-1-4757-0605-5_24

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arXiv:2508.21790•Physical Review Research•Apr 1, 2026•1 citation
As a result of quantum fluctuations, a bistable system will undergo spontaneous transitions from one state to the other. For a bistable two-mode laser we present a theoretical analysis of the switching statistics by treating it as a one-dimensional first-passage---time (FPT) problem for the intensity of one of the modes. The methodology is also applicable to other bistable systems, such as in optical bistability. Several new asymptotic results for the small- and large-time behavior of various FPT distributions are given. The switching-time distribution is introduced as a weighted integral over FPT distributions and asymptotic expressions for this distribution are given. Several results of Monte Carlo computer simulations of the FPT problem are presented.
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.