Nanoradian-Scale Precision in Light Rotation Measurement via Indefinite Quantum Dynamics

TL;DR

The paper tackles ultra-precise measurement of light-beam rotations by introducing indefinite-time-direction quantum parameter estimation (IQPE), which leverages an auxiliary meter to create a superposition of forward and backward dynamics and to maximize the use of orbital angular momentum (OAM) resources. By comparing IQPE to standard SQPE, it shows that the IQPE framework naturally enhances the quantum Fisher information (QFI) via the mean-squared generator, enabling Heisenberg-like scaling in optical metrology and removing precision dead zones for polarization and OAM-rotation measurements. The authors provide theoretical bounds and apply them to Kerr-phase, birefringence, and especially OAM-based rotation measurements using Laguerre-Gaussian beams, culminating in a nanoradian-scale rotation precision of about $12.9\,\text{nrad}$ with a $150$-order LG beam in experiments. This approach promises broad impact across optical sensing and quantum metrology, with potential extensions to NV centers and NMR sensors, by enabling maximal resource utilization through indefinite quantum dynamics.

Abstract

The manipulation and metrology of light beams are pivotal for optical science and applications. In particular, achieving ultra-high precision in the measurement of light beam rotations has been a long-standing challenge. Instead of utilizing quantum probes like entangled photons, we address this challenge by incorporating a quantum strategy called "indefinite time direction" into the parameterizing process of quantum parameter estimation. Leveraging this quantum property of the parameterizing dynamics allows us to maximize the utilization of OAM resources for measuring ultra-small angular rotations of beam profile. Notably, a nanoradian-scale precision of light rotation measurement is finally achieved in the experiment, which is the highest precision by far to our best knowledge. Furthermore, this scheme holds promise in various optical applications due to the diverse range of manipulable resources offered by photons.

Figures (7)

• Figure 1: Schematic of the quantum parameter estimation procedure. a Standard quantum parameter estimation procedure. b Quantum parameter estimation procedure with indefinite time direction.
• Figure 2: Quantum Fisher information of the SQPE and the IQPE schemes. a Classical PS for polarization states. The northern and southern poles represent the right- and left-handed circular polarization states respectively. The states on the equator are linear polarization. b QFI of the birefringent phase $\varphi$ in the SQPE procedure with respect to various polarization states. c QFI of the birefringent phase $\varphi$ in the IQPE procedure with respect to various polarization states. d Modal PS for HLG modes with $N=l=4$. The northern and southern poles represent the LG modes with opposite topological charges. The states on the equator are HG modes. e QFI of the rotation angle $\alpha$ in the SQPE procedure with respect to various HLG beams. f QFI of the rotation angle $\alpha$ in the IQPE procedure with respect to various HLG beams. The values of QFIs are represented by the color intensity in b, c, e, and f.
• Figure 3: Schematic of light rotation process with indefinite time direction.
• Figure 4: Schematic of experimental setup. The $N$-order LG beam with the maximum OAM value $l=N$ is generated using a SLM and a spatial filter system. The polarization state is adjusted to an orientation angle of $\ang{45}$ using a HWP. The indefinite-time-direction rotation process is implemented in a polarized Sagnac interferometer, incorporating a Dove prism to enable the rotation of beam profile. The projective measurements of polarization are performed using a QWP, a HWP, and a PBS. Photodetectors PD1 and PD2 capture the projective photons.
• Figure 5: Experimental results of measured optical powers and relative phases. The blue lines and the purple lines represent the measured optical powers of PD1 and PD2, respectively. The corresponding values are labeled at the left y-axis. The gray shadows stand for the differential optical powers between two PDs. The orange lines represent the demodulated relative phases. The corresponding values are labeled at the right y-axis. a Experimental results when inputting the Gaussian beam. The relative phase $\Phi$ is solely determined by the additional relative phase $\Delta\varphi$ induced by systemic imperfections. b-g Experimental results when inputting the $N$-order LG beams with OAM values of $l=N=1, 4, 7, 10, 20, 30$. The relative phase $\Phi$ is determined by both the additional relative phase $\Delta\varphi$ and the angular rotation $\alpha$.