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Frontiers in Optics

Technical Advantages for Weak-Value Amplification

Julián Martínez-Rincón, Gerardo I. Viza, G. B. Alves, Andrew N. Jordan, John C. Howell

Published Jan 1, 2015• 1 citation
Publisher

Abstract

We consider different types of technical noise in an optical context and show that weak-value amplification techniques (using a small fraction of photons) compare favourably with standard techniques (using all of them). We measure small beam deflections of an optical beam by monitoring the dark port in a Sagnac interferometer (weak-value technique) or by focusing the entire beam onto a split detector (standard technique). In all cases, the weak-value technique performs favourable in precision respect to the standard technique.

DOI
10.1364/fio.2015.jw2a.37

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We consider different types of technical noise in an optical context and show that weak-value amplification techniques (using a small fraction of photons) compare favourably with standard techniques (using all of them). We measure small beam deflections of an optical beam by monitoring the dark port in a Sagnac interferometer (weak-value technique) or by focusing the entire beam onto a split detector (standard technique). In all cases, the weak-value technique performs favourable in precision respect to the standard technique.
We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-value technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-value-based technique. By postselecting on 11%1 of the photons, we obtain 9999%99 of the available Fisher information of the beam deflection parameter.
We report on the use of an interferometric weak value technique to amplify small transverse deflections of an optical beam. Our techniques consists of coupling the beam’s transverse degrees of freedom to the which-path states of a Sagnac interferometer. The theory for the amplification, including signal to noise ratio considerations, is presented along with the experimental results which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and showed the signal to noise ratio to be amplified by a factor of 150.
The amplification obtained using weak values is quantified through a detailed investigation of the signal-to-noise ratio for an optical beam-deflection measurement. We show that for a given deflection, input power and beam radius, the use of interferometric weak values allows one to obtain the optimum signal-to-noise ratio using a coherent beam. This method has the advantage of reduced technical noise and allows for the use of detectors with a low saturation intensity. We report on an experiment which improves the signal-to-noise ratio for a beam-deflection measurement by a factor of 54 when compared to a measurement using the same beam size and a quantum-limited detector.