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Applied Physics Letters

Squeezing-enhanced rotating-angle measurement beyond the quantum limit

Kui Liu, Chunxiao Cai, Juan Li, Long Ma, Hengxin Sun, Jiangrui Gao

Published Dec 24, 2018• 45 citations
Publisher

Abstract

Aided by quantum sources, quantum metrology helps to enhance measurement precision. Here, we introduce a method to enhance the measurement of a rotation angle. As a proof of principle, assisted by a quantum state called the squeezed orbital-angular-position (OAP) state and balance homodyne detection, we demonstrate in experiments 3 dB-enhanced measurements of a rotation-angle beyond the shot noise limit. A precision of up to 17.7 nrad/Hz is obtained. Furthermore, we discuss means to further improve the measurement with a high-order precision OAP squeezed state. The method holds promise for future practical applications, such as in high-sensitive Sagnac interferometry.

DOI
10.1063/1.5066028

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Aided by quantum sources, quantum metrology helps to enhance measurement precision. Here, we introduce a method to enhance the measurement of a rotation angle. As a proof of principle, assisted by a quantum state called the squeezed orbital-angular-position (OAP) state and balance homodyne detection, we demonstrate in experiments 3 dB-enhanced measurements of a rotation-angle beyond the shot noise limit. A precision of up to 17.7 nrad/Hz is obtained. Furthermore, we discuss means to further improve the measurement with a high-order precision OAP squeezed state. The method holds promise for future practical applications, such as in high-sensitive Sagnac interferometry.
An experimental scheme is proposed for squeezing-enhanced simultaneous measurement of the polarization angle and ellipticity of laser beam beyond the shot noise limit. In the scheme, a two-mode squeezed light is exploited to enhance the sensitivity of the measurement of polarization rotation angle, and a single-mode squeezed light is used to improve the sensitivity of ellipticity measurement. Noise analysis is performed to show that the signal-to-noise ratios in both the measurements of polarization angle and ellipticity can exceed the shot noise limit. This work is expected to be of considerable interest for experiments such as the observation of vacuum magnetic birefringence, gravitational wave detection, spin–orbital interaction, material characterization, polarization microscopy, atomic magnetometer, or biomedical optics.
We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the "standard quantum limit" for nonentangled states. All methods use a form of quantum mechanical "squeezing." In a system of two entangled trapped (9)Be(+) ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.
Precision enhancement is demonstrated in an optical spatial measurement based on a weak-value amplification (WVA) system and splitlike detection, by injecting a TEM10{\mathrm{TEM}}_{10}TEM10​ squeezed vacuum beam. We have experimentally realized high-precision optical spatial measurement beyond the shot-noise limit by using squeezing-assisted WVA. Based on the WVA technique, which can amplify the signal by increasing the number of photons that are injected into the interferometer, squeezed-beam injection can reduce the noise level and can further improve the signal-to-noise ratio (SNR). As a result, an SNR improvement of 2 dB, i.e., 1.3 times precision enhancement, can be achieved, and the obtained displacement and tilt sensitivity are 4.96fm/Hz4.96\phantom{\rule{0.2em}{0ex}}\mathrm{fm}/\sqrt{\text{Hz}}4.96fm/Hz​ and 0.39prad/Hz0.39\phantom{\rule{0.2em}{0ex}}\mathrm{prad}/\sqrt{\text{Hz}}0.39prad/Hz​, respectively, by using a 2-dB squeezed-beam injection and 2.6% postselection probability in the WVA process. Our work provides an effective method to accomplish higher precision in quantum spatial measurement, which has potential applications in gravitational wave interferometer calibration, super-resolution quantum imaging, etc.
Improvements in precision beyond the limit set by the vacuum state or zero-point fluctuations of the field are reported for two optical experiments. Both experiments employ the squeezed light from an optical parametric oscillator to reduce the level of fluctuations in one of two quadrature phase amplitudes below the shot-noise level (SNL). The first experiment follows the work of Caves1 on precision interferometry with squeezed states. An increase in signal-to-noise of 2.5 dB relative to the SNL is demonstrated for the detection of phase modulation in a Mach-Zehnder interferometer. In the second experiment amplitude modulation is encoded on a weak signal beam with an acoustooptic modulator. For the case of a squeezed signal beam compared with a beam in a coherent state, an improvement in sensitivity of 2.5 dB is achieved for the detection of amplitude changes of the field. The observed increases in sensitivity in both experiments are currently limited by simple linear losses in propagation and detection and not by the degree of available squeezing.
Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe's dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum SWITCH involving gates generated by both discrete and continuous variables. The unknown rotation angle θθθ is measured with precision scaling as 1/4ml1/4ml1/4ml when a photon undergoes a rotation of 2mθ2mθ2mθ and an angular momentum shift of 2lℏ2l \hbar2lℏ. With a practical enhancement factor as high as 2317, the ultimate precision in our experiment is 0.0105′′0.0105^{\prime \prime}0.0105′′ when using 7.16×1077.16\times10^77.16×107 photons, corresponding to a normalized precision of ≈10−4\approx 10^{-4}≈10−4rad per photon. No photon interaction occurs in our experiment, and the precision enhancement consumes only a linearly increasing amount of physical resources while achieving a nonlinear scaling of the precision. We further indicate that this nonlinear enhancement roots in an in-depth exploration of the Heisenberg uncertainty principle (HUP), and our findings not only deepen the understanding of the HUP but also pave a pathway for advancements in quantum metrology.