2014/10/31 by Yusuf Turek, Hirokazu Kobayashi, H. Kobayashi +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Gaussian #Mathematics #Observable #Orbital Angular Momentum in Optics #Physics #Pure mathematics #Quantum Information and Cryptography #Quantum mechanics #Statistical physics #Von Neumann architecture #math-ph #math.MP #msc:78A10 #msc:81P15 #physics.optics #quant-ph
paper · pdf · doi:10.1088/1367-2630/17/8/083029
published as New J. Phys. 17, 083029 (2015) · 22 pages, 9 figures
openalex publication_date 2015/08/18 · arxiv created 2015/08/19 · arxiv updated 2015/08/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable with and for an arbitrary interaction strength, where represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak- and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex.