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Applied Optics

Analysis of an inverse weak-value tiltmeter in the kilohertz regime

Benjamin A. Baldwin, Garrett K. Josemans, John Edward Gray

Published May 6, 2022• 1 citation
Publisher

Abstract

We present a follow-on experiment to the recent study from The University of Rochester [ Opt. Lett. 42 , 2479 ( 2017 ) OPLEDP 0146-9592 10.1364/OL.42.002479 ], which reported a new architecture for an inverse weak-value tiltmeter. We recreate the Rochester tiltmeter and specifically investigate mirror oscillations in the low-kilohertz frequency regime, which is relevant to certain potential applications, such as Coriolis vibratory gyroscopes. We find that the inverse weak-value amplification effect persists in this regime, although our measured noise floors are higher than those obtained in the Rochester experiment—approximately 2 p r a d / H z for mirror oscillation frequencies between 1 and 25 kHz.

DOI
10.1364/ao.455631

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We present a follow-on experiment to the recent study from The University of Rochester [ Opt. Lett. 42 , 2479 ( 2017 ) OPLEDP 0146-9592 10.1364/OL.42.002479 ], which reported a new architecture for an inverse weak-value tiltmeter. We recreate the Rochester tiltmeter and specifically investigate mirror oscillations in the low-kilohertz frequency regime, which is relevant to certain potential applications, such as Coriolis vibratory gyroscopes. We find that the inverse weak-value amplification effect persists in this regime, although our measured noise floors are higher than those obtained in the Rochester experiment—approximately 2 p r a d / H z for mirror oscillation frequencies between 1 and 25 kHz.
We present an expanded mathematical model of the optical weak value amplification device introduced by Duck, Stevenson, and Sudarshan in 1989 [ Phys. Rev. D 40 , 2112 ( 1989 ) PRVDAQ 0556-2821 10.1103/PhysRevD.40.2112 ]. We model the pointer behavior in and around the weak value and inverse weak value amplification regions with respect to the incidence angle of the birefringent crystal. We present laboratory measurements that support the validity of this model. We measure a tilt sensitivity of ∼.58m/rad, which represents an amplification of 390 times over nonamplified refraction. This corresponds to an increase in SNR of ∼110 times with respect to shot noise. This paper demonstrates the novel utility of a birefringence-based WVA device as a sensitive tiltmeter, to our knowledge.
We present an investigation into the tilt sensitivity of the canonical, optical, weak-value amplification device (COWVAD), introduced by Duck, Stevenson, and Sudarshan in 1989, for potential application in a Coriolis vibratory gyroscope (CVG). We model the breakdown of the weak-value amplification effect in this device with respect to angle of incidence between the laser beam and the surface of the birefringent crystal. Additionally, we model the effect of beam divergence due to misalignment of the crystals optic axis. We found that the presence of beam divergence allows the architecture to be placed in an inverse weak-value amplification configuration. We found that weak-value amplification occurs at angles other than those reported in Duck 1989. We also present laboratory measurements that support the validity of the mathematical model. The maximum tilt sensitivity measured was ~.58 m/rad, which, while 390 times greater than it would be without weak-value amplification, does not represent the maximum possible sensitivity of the device through weak-value amplification.
Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.
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.
A modified weak-value-amplification (MWVA) technique to measure a mirror's velocity based on the Vernier effect is proposed. To demonstrate its enhanced sensitivity and higher signal-to-noise ratio (SNR), we use two cascaded Michelson interferometers with similar optical structures. One has a fixed mirror and acts as a fixed part of the Vernier scale, while the other, with a moving mirror, acts as a sliding part of the Vernier scale for velocity sensing. The envelope of the cascaded interferometers shifts much more than a single one with a certain enhancement factor, which is related to the free space range difference between them. In addition, we calculate the SNR based on the Fisher information with both the MWVA and traditional weak-value-amplification (TWVA) techniques. The results show that both the SNR and the sensitivity with our MWVA technique is greater than that of the TWVA technique within the range of our time measurement window. In particular, MWVA can present a viable and effective alternative to the TWVA technique out of the limit of resolution. Furthermore, by using the principles of the Vernier effect, it is applicable and convenient to improve the sensitivity and SNR in measuring other quantities with the TWVA technique.