2005/02/23 by Ugo Boscain, Paolo Mason, Boscain, Ugo +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0502151
arxiv created 2005/02/23 · openalex publication_date 2005/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |Ω(t)|≤ M the bound on the field amplitude. For each values of E and M, we provide the explicit expression of the time optimal trajectory steering the state one to the state two in terms of a parameter that should be computed numerically. For M<E the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M→∞ the time needed to reach the state two tends to zero. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained in the Rotating Wave Approximation.