2003/09/11 by Shohini Ghose, Paul M. Alsing, Paul Alsing +4 · 5 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.1103/physreva.69.052116
published as Phys. Rev. A69 (2004) 052116 · 8 pages, 5 figures
arxiv created 2003/09/11 · openalex publication_date 2004/05/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via a continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling, we find that classical dynamics emerges only when the position and spin actions are both large compared to \ensuremathℏ. These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result, it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin-(1)/(2) particle. When the conditions for classicality are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence, we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.