Complete characterization of beam deflection based on double weak value amplification system

TL;DR

This work addresses the challenge of simultaneously measuring two spatial attitude parameters, yaw $\theta$ and pitch $\varphi$, by introducing a double weak value amplification scheme with Hermite-Gaussian post-selection. The experimental setup couples two independent high-order-mode BHD detectors through a Sagnac and an unbalanced Mach–Zehnder interferometer, enabling complete two-dimensional beam deflection characterization. The authors derive the theory of the double WVA process and demonstrate experimentally that minimum detectable yaw and pitch reach $\theta_{\min} = 83\ \mathrm{prad}$ and $\varphi_{\min} = 89\ \mathrm{prad}$, with corresponding beam displacements $d_\theta \approx 0.79\ \mathrm{pm}$ and $d_\varphi \approx 0.85\ \mathrm{pm}$. This work extends weak-value metrology to multi-parameter spatial sensing and suggests pathways to further enhancement, such as using higher-order or squeezed injected beams to push precision beyond current limits.

Abstract

The precise measurement of spatial attitude parameters is critical for applications in inertial navigation, industrial monitoring, instrument calibration, quantum metrology, etc. In this work, we theoretically investigate and experimentally realize the simultaneous measurement of the yaw and pitch angles using a Hermite-Gaussian-postselected double weak value system integrated with two sets of high-order-mode balanced homodyne detections, thereby achieving a complete characterization of the beam deflection. Signals of the yaw and pitch angles that are involved in TEM$_{10}$ and TEM$_{01}$ modes output from two dark ports of the system can be measured independently. As a result, the obtained minimum measurable yaw and pitch angles of beam deflection are 83 prad and 89 prad, respectively. Meanwhile, the corresponding displacements are 0.79 pm and 0.85 pm, respectively. This work expands the beam deflection measurement to two dimensions, which provides a new insight for future high-precision multi-parameter spatial precise detection.

Figures (5)

• Figure 1: The experimental configuration for simultaneously measuring yaw and pitch angles using a double weak value amplification system incorporating two high-order-mode BHD systems.
• Figure 2: Schematic diagram of the double weak value amplification system based on the HG post-selection. S and U denote the Sagnac and UMZ interferometers, respectively.
• Figure 3: Experimental results for an input power of 50 µW. The noise power spectra obtained from dark ports I and II under different PZT driving voltages are shown in (a) and (b). The linear relationships between the yaw and pitch angles and the PZT driving voltage are depicted in (c) and (d). The local beam power is 1 mW, and the resolution bandwidth (RBW) is 10 Hz.
• Figure 4: Experimental results for different post-selection probabilities. The noise power spectra obtained from dark port I and II under different post-selection probabilities are shown in (a) and (b), respectively. The corresponding of signal peak SNRs and theoretical predictions are shown in (c) and (d). The output powers from dark port I and II are set as (0.25 µW (0.5%), 4.12 µW (8.2%), 7.63 µW (15.2%), 9.65 µW (19.3%), 12.3 µW (24.6%)) and (0.91 µW (2.0%), 3.78 µW (8.4%), 7.76 µW (17.2%), 11.22 µW (24.7%), 13.25 µW (29.4%)), respectively.
• Figure 5: Experimental results and theoretical predictions for measuring yaw ((a), (c), (e)) and pitch ((b), (d), (f)) angles. The noise power spectra under different input powers are shown in (a) and (b). The noise power spectra at 3 dB SNR for an input power of 800 µW are presented in (c) and (d). The integrated experimental and theoretical results are summarized in (e) and (f).