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Physical Review A

Sub- μm axial precision depth imaging with entangled two-color Hong-Ou-Mandel microscopy

Cyril Torre, Alex R. McMillan, Jorge Monroy-Ruz, Jonathan C. F. Matthews

Published Aug 24, 2023• 8 citations
Publisher

Abstract

Using two entangled photons of different colors in a Hong-Ou-Mandel interference scheme, the authors show that they can precisely measure the thickness of a semitransparent sample. The depth sensitivity is adjustable and the method is resilient against fluctuations commonly encountered in biological samples.
DOI
10.1103/physreva.108.023726

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The quantum interference of two wavelength-entangled photons overlapping at a beamsplitter results in an oscillating interference pattern. The frequency of the beat note is dependent on the wavelength separation of the entangled photons but is robust to wavelength scale perturbations that can limit the practicality of standard interferometry. Here we use two-colour entanglement interferometry to evaluate the variation in thickness of a semi-transparent sample in combination with two-dimensional raster scanning. The axial precision and the dynamic range of the microscope are actively controlled by adjusting the wavelength separation of the entangled photon pairs. Sub-μmμmμm precision is reported using up to 12.3 nm12.3~nm12.3 nm of detuning and ∼104\sim10^4∼104 detected photon pairs.
Sub-μm\mu\mathrm{m}μm Axial Precision Depth Imaging with Entangled Two-Colour Hong-Ou-Mandel Microscopy
Hong-Ou-Mandel (HOM) interference results in a modified probability of bunching events when indistinguishable photons with a relative timing offset interact at a beamsplitter. Lyons et al. recently achieved attosecond precision in time delay measurement by applying a classical Fisher information analysis to HOM interference [1]. More recently an increase in the measurement precision has been shown by detuning the central wavelengths of the signal and idler from an entangled two-colour photon pair source and applied in temperature drift detection for optical fibres [2]. Here we exploit the timing resolution of the HOM interference to implement a robust 3D imaging microscope with tuneable sensitivity from millimetre to sub-micrometre.
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.