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Applied Physics Letters

Small-tilt measurement based on weak-value-amplification with balanced homodyne detection

ChaoXia Zhang, YongLang Lai, Rongguo Yang, Kui Liu, Jing Zhang, Hengxin Sun, Jiangrui Gao

Published Jan 16, 2023• 9 citations
Publisher

Abstract

We experimentally realize a great precision enhancement in the small-tilt measurement by using a Sagnac interferometer and balanced homodyne detection (BHD) of high-order optical modes, together with the weak-value amplification (WVA) technique. Smaller minimum measurable tilt and higher signal-to-noise ratio can be obtained by using BHD, compared with the split detection. The precision of 3.8 nrad can be obtained under our present experimental condition. It is shown that combining WVA technique and BHD can strengthen each other's advantages and can behave better for some special application scenarios, such as extremely weak output, wider measurement bandwidth, etc. Moreover, the precision can be further enhanced by experimental parameter optimization.

DOI
10.1063/5.0132992

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We experimentally realize a great precision enhancement in the small-tilt measurement by using a Sagnac interferometer and balanced homodyne detection (BHD) of high-order optical modes, together with the weak-value amplification (WVA) technique. Smaller minimum measurable tilt and higher signal-to-noise ratio can be obtained by using BHD, compared with the split detection. The precision of 3.8 nrad can be obtained under our present experimental condition. It is shown that combining WVA technique and BHD can strengthen each other's advantages and can behave better for some special application scenarios, such as extremely weak output, wider measurement bandwidth, etc. Moreover, the precision can be further enhanced by experimental parameter optimization.
We propose precision measurements of ultra-small angular velocities of a mirror within a modified Sagnac interferometer, where the counter-propagating beams are spatially separated, using the recently proposed technique of almost-balanced weak values amplification (ABWV) [Phys. Rev. Lett.116, 100803 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.100803]. The separation between the two beams provides additional amplification with respect to using collinear beams in a Sagnac interferometer. Within the same setup, the weak-value amplification technique is also performed for comparison. Much higher amplification factors can be obtained using the almost-balanced weak values technique, with the best one achieved in our experiments being as high as 1.2×107. In addition, the amplification factor monotonically increases with decreasing of the post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification (WVA) at small post-selection phases. Both techniques consist of measuring the angular velocity. The sensitivity of the ABWV technique is ∼38 nrad/s per averaged pulse for a repetition rate of 1 Hz and ∼33 nrad/s per averaged pulse for the WVA technique.
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.
In this paper, we propose a scheme for angular rotation Ω measurement in an optic-fiber-based Sagnac interferometer based on cascaded weak-value amplification (CWVA). CWVA is a modified standard weak-value amplification (SWVA) technique for further enhancing temporal shifts based on the principle of the Vernier effect. By choosing the appropriate CWVA parameters and the repetition time intervals of the Vernier scale, the temporal shifts in SWVA can be further amplified by measuring the envelope shifts in CWVA. Our comprehensive simulations demonstrate that CWVA enables the detection of minuscule rotations in the range of 1.0×10 −9 rad/s≤Ω≤10×10 −9 rad/s, with significantly improved sensitivity and superior signal-to-noise ratios compared to SWVA. The enhancement with a larger detection band may have great influence on physics and related sciences, such as rotational seismology and gravitational sensing.
In this letter, we propose a precision method for phase estimation based on the weak-value amplification (WVA) technique using a monochromatic light source. The anomalous WVA significantly suppresses the technical noise with respect to the intensity difference signal induced by the phase delay when the post-selection procedure comes into play. The phase measured precision of this method is proportional to the weak-value of a polarization operator in the experimental range. Our results compete well with the wide spectrum light phase weak measurements and outperform the standard homodyne phase detection technique.
The precision enhancement is demonstrated in an optical spatial measurement based on weak value amplification (WVA) system and split-like detection, by injecting a TEM10_{10}10​ squeezed vacuum beam. It is the first time to experimentally realize 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 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, a SNR improvement of 2dB, i.e., 1.3 time precision enhancement, can be achieved, by using a 2dB squeezed beam injection and 2.6\% postselection probability in 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.