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arXiv:1305.4520 · Physical Review A

Strengthening weak-value amplification with recycled photons

Justin Dressel, Kevin Lyons, Andrew N. Jordan, Trent Graham, Paul G. Kwiat

Published Aug 13, 2013• 72 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.023821

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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.
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.
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.
Weak measurement has been proven to amplify the detection of changes in meters while discarding most photons due to the low probability of postselection. Previous power-recycling schemes enable the failed postselection photons to be repeatedly selected, thus overcoming the inefficient postselection and increasing the precision of detection. In this study, we focus on the polarization-based weak value angular-velocity measurement and introduce three cyclic methods to enhance the accuracy of detecting time shifts in a Gaussian beam: power-recycling, signal-recycling, and dual-recycling schemes. By incorporating one or two partially transmitting mirrors into the system, both the power and the signal-to-noise ratio of the detected light are substantially enhanced. Compared to nonpolarization schemes, polarization-based approaches offer several advantages, including lower optical loss, unique cyclic directions, and a wider optimal region. These features effectively reduce crosstalk among different light paths and theoretically eliminate the walk-off effect, thus yielding improvements in both theoretical performance and application.
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 measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power-recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, driven by the combined effects of power cycling and entanglement. Furthermore, we analyze three types of errors: cavity power loss, walk-off errors, and readout errors. The conclusions suggest that entanglement is beneficial in mitigating the effects of cavity losses. Moreover, entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. Additionally, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy of the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.