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Experimentally Quantifying the Advantages of Weak-Values-Based Metrology

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

Published Jan 1, 2015• 4 citations
Publisher

Abstract

We measure optical beam deflections both using a weak-values technique and by focusing. By introducing controlled modulations, the WVT outperforms focusing. Post-selecting on 1% of the photons, we obtain 99% of the available Fisher information.
DOI
10.1364/cleo_qels.2015.fm1a.2

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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 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.
Weak measurement technology can be used to achieve ultra-precision modulation of variables. Based on this, to achieve precise modulation of beam deflection, we establish a model of beam propagation using weak measurement, theoretically deduce the general formula of the deflection angle, and illustrate the general process of precise modulation of the angular shift of the beam. By controlling the post-selection state of the weak measurement, the angular shift of the beam can be precisely regulated. The deflection angle is proportional to the imaginary part of the weak value. We describe a simulation and discuss how precise angle tuning can be achieved by controlling experimental parameters.
A weak value is an effective description of the influence of a pre and post-selected ‘principal’ system on another ‘meter’ system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and deflections in otherwise unperturbed variables: this motivates investigation of the potential benefits of the protocol in precision metrology. We present a visual interpretation of weak value experiments in phase space, enabling an evaluation of the effects of three types of detector noise as ‘Fisher information efficiency’ functions. These functions depend on the marginal distribution of the Wigner function of the ‘meter’, and give a unified view of the weak value protocol as a way of protecting Fisher information from detector imperfections. This approach explains why weak value techniques are more effective for avoiding detector saturation than for mitigating detector jitter or pixelation.