Quantum Imaging of Birefringent Samples using Hong-Ou-Mandel Interference

TL;DR

The paper tackles quantifying birefringence in samples using a Hong–Ou–Mandel interferometer, addressing the limitation that thickness variations distort conventional HOM dips. By employing a narrowband, long-coherence photon pair, the HOM dip becomes broad and thickness-insensitive, allowing changes in coincidence rates to reveal polarization effects. The authors develop a complete statistical framework, including a Fisher-information analysis and a maximum-likelihood estimator, and validate it through raster-scanned experimental imaging of polymer birefringent shards. The results align with classical polarization imaging while offering robustness to thickness, low-light operation, and enhanced edge contrast, highlighting potential advantages for photosensitive or low-signal samples. This work enables quantum-based, quantitative birefringence imaging with reduced sensitivity to sample thickness and noise.

Abstract

Two-photon interference in a Hong-Ou-Mandel (HOM) interferometer can be used as a quantum sensing mechanism due to the sensitivity of the interference dip to perturbations of the photon indistinguishability. In particular, recent works have generalized this concept to microscopy setups, but the sensitivity to optical path differences constrains its application to samples with thickness variation typically below a few micrometers if tracking changes in the coincidences at a fixed delay. Extending the concept to polarization microscopy and circumventing this limitation, this manuscript explores the use of a narrowband photon pair source with coherence length >1 mm to broaden the HOM dip. Thus, realistic sample-thickness variations introduce negligible temporal distinguishability, and changes in coincidence rate at the dip centre are then dominated by sample-induced polarization effects. To compute the polarization rotation, we develop a statistical model for the interferometer, derive the Fisher information, and establish a maximum-likelihood estimator for the local fast-axis angle. Recording dip and baseline frames at each sample position via raster scanning, the experimental results validate the framework, agreeing with classical polarized-intensity images while demonstrating operation at a maximum-precision regime and insensitiveness to layer thickness. Overall, the approach enclosed provides a quantum-based quantitative imaging of birefringent structures, which can motivate further advantageous applications, including enhanced signal-to-noise ratio and lower damage imaging of photosensitive samples.

Figures (4)

• Figure 1: Schematic of the experimental setup. Photon pairs from a commercial narrowband SPDC source are separated into reference and sample arms. Polarizing beam splitters (not shown) and half-wave plates prepare and control the polarization in each arm. In the sample arm, two $f=50\,\mathrm{mm}$ lenses focus the photons onto the sample, which is mounted on motorized $x$--$y$ translation stages for raster scanning. The reference arm includes a motorized translation stage that controls the relative delay $\Delta z$, thereby setting the HOM-dip position. The photons are then recombined at a $50:50$ beam splitter and detected with single-photon avalanche diodes. The coincidence events are recorded with a time-tagger. Bandpass filters centered at $810\,\mathrm{nm}$ (not shown) suppress stray light.
• Figure 2: Normalized coincidences as a function of the sample photon polarization angle measured at $\Delta z\approx0$, left axis. On the right axis we have the inverse variance $1/(NVar(\theta_{exp}))$ obtained from $N\sim3\times10^7$ repeated acquisitions at each angle (right axis), compared with $F_{\theta}$ from equation \ref{['eq:fisher_expression']}. The inset shows the corresponding angle estimates obtained using Eq. \ref{['eq:angle_equation']}. Because the input angles are known, we can readily resolve the angle degeneracy.
• Figure 3: HOM dip as a function of delay for different points on the sample. Top: false-color image of the sample acquired with a CMOS camera and a polarizer. Bottom: corresponding HOM dips as a function of delay, with markers indicating the sample positions at which each dip was measured. We measured each curve $10$ times with each data point acquired for $T=5.25$ s.
• Figure 4: Result of the spatial variation of the polarization rotation angle $\theta$ obtained through a 2D raster scan of a selected region of the sample. The first column shows the classical measurement acquired with a CMOS camera and a polarizer using the Malus' law $I=I_0\cos^22\theta$. The second column shows the quantum measurement obtained from Eq. \ref{['eq:angle_equation']}. The top row presents a wide-area scan of the sample, and the bottom row shows a close-up of the region highlighted by the red square. We measured each point only once during $T=5.25$ s.