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arXiv:1504.08210 · Physical Review Letters

Power-Recycled Weak-Value-Based Metrology

Kevin Lyons, Justin Dressel, Andrew N. Jordan, John C. Howell, Paul G. Kwiat

Published Apr 29, 2015• 70 citations
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Abstract

We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in all the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.

DOI
10.1103/physrevlett.114.170801

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We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in all the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.
Weak value amplification permits small effects to be measured as observable changes at the sacrifice of power due to postselection. The power-recycling scheme has been proven to eliminate this inefficiency of the rare postselection, thus surpassing the limit of the shot noise and improving the precision of the measurement. However, the improvement is strictly limited by the system setup, especially the system loss. Here we introduce a dual-recycling model based on the interferometric weak-value-based deflection measurement. Two mirrors, the power-recycling mirror and signal-recycling mirror, are placed at the bright and dark port of the interferometer, respectively, creating a composite resonator. The results show that both the power and the signal-to-noise ratio (SNR) are greatly enhanced in a wider range of experimental parameters compared to the power-recycling scheme. This work considerably loosens the constraint of the system setup and further explores the real advantage of weak measurement over traditional schemes.
The weak-value-based metrology is very promising and has attracted a lot of attention in recent years because of its remarkable ability in signal amplification. However, it is suggested that the upper limit of the precision of this metrology cannot exceed that of classical metrology because of the low sample size caused by the probe loss during postselection. Nevertheless, a recent proposal shows that this probe loss can be reduced by the power-recycling technique, and thus enhance the precision of weak-value-based metrology. Here we experimentally realize the power-recycled interferometric weak-value-based beam-deflection measurement and obtain the amplitude of the detected signal and white noise by discrete Fourier transform. Our results show that the detected signal can be strengthened by power recycling, and the power-recycled weak-value-based signal-to-noise ratio can surpass the upper limit of the classical scheme, corresponding to the shot-noise limit. This work sheds light on higher precision metrology and explores the real advantage of the weak-value-based metrology over classical metrology.
Weak-value-amplification has been proven to be advantageous in the detection of small physical effects. However, most of the data are discarded due to the rare post-selection, resulting in a limitation of precision. Here we introduce a dual-recycling cavity based on the interferometric weak-value-based velocity measurement. By properly inserting two partially transmitting mirrors, both the power and signal-to-noise ratio (SNR) are improved, and the peak of the improvement corresponds to two identical matched mirrors. The dual recycling approach also provides a wider optimal range compared to that of the power-recycling scheme. In addition, the practical consideration is discussed to stabilize the lengths of dual-recycling cavity.
We consider the use of cyclic weak measurements to improve the sensitivity of weak-value amplification precision measurement schemes. Previous weak-value experiments have used only a small fraction of events, while discarding the rest through the process of ``postselection.'' We extend this idea by considering recycling of events which are typically unused in a weak measurement. Here we treat a sequence of polarized laser pulses effectively trapped inside an interferometer using a Pockels cell and polarization optics. In principle, all photons can be postselected, which will improve the measurement sensitivity. We first provide a qualitative argument for the expected improvements from recycling photons, followed by the exact result for the recycling of collimated beam pulses, and numerical calculations for diverging beams. We show that beam degradation effects can be mitigated via profile flipping or Zeno reshaping. The main advantage of such a recycling scheme is an effective power increase, while maintaining an amplified deflection.
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.
In a quantum-noise limited system, weak-value amplification using postselection normally does not produce more sensitive measurements than standard methods for ideal detectors: the increased weak value is compensated by the reduced power due to the small postselection probability. Here, we experimentally demonstrate recycled weak-value measurements using a pulsed light source and optical switch to enable nearly deterministic weak-value amplification of a mirror tilt. Using photon counting detectors, we demonstrate a signal improvement by a factor of 4.4±0.2 and a signal-to-noise ratio improvement of 2.10±0.06, compared to a single-pass weak-value experiment, and also compared to a conventional direct measurement of the tilt. The signal-to-noise ratio improvement could reach around six for the parameters of this experiment, assuming lower loss elements.