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arXiv:2505.15956 · Science Advances

Fast quantum interferometry at the nanometer and attosecond scales with energy-entangled photons

Colin P. Lualdi, Spencer J. Johnson, Michael Vayninger, Kristina A. Meier, Swetapadma Sahoo, Simeon Bogdanov, Paul G. Kwiat

Published May 21, 2025• 13 citations
arXivHTMLPDF

Abstract

In classical optical interferometry, loss and background complicate achieving fast nanometer-resolution measurements with illumination at low light levels. Conversely, quantum two-photon interference is unaffected by loss and background, but nanometer-scale resolution is physically difficult to realize. As a solution, we enhance two-photon interference with highly nondegenerate energy entanglement featuring photon frequencies separated by 177 THz. We observe measurement resolution at the nanometer (attosecond) scale with only O (10 4 ) photon pairs, despite the presence of background and loss. Our nondestructive thickness measurement of a metallic thin film agrees with atomic force microscopy, which often achieves better resolution via destructive means. With contactless, nondestructive measurements in seconds or faster, our instrument enables metrological studies in optically challenging contexts where background, loss, or photosensitivity are factors.

DOI
10.1126/sciadv.adw4938

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In classical optical interferometry, loss and background complicate achieving fast nanometer-resolution measurements with illumination at low light levels. Conversely, quantum two-photon interference is unaffected by loss and background, but nanometer-scale resolution is physically difficult to realize. As a solution, we enhance two-photon interference with highly nondegenerate energy entanglement featuring photon frequencies separated by 177 THz. We observe measurement resolution at the nanometer (attosecond) scale with only O (10 4 ) photon pairs, despite the presence of background and loss. Our nondestructive thickness measurement of a metallic thin film agrees with atomic force microscopy, which often achieves better resolution via destructive means. With contactless, nondestructive measurements in seconds or faster, our instrument enables metrological studies in optically challenging contexts where background, loss, or photosensitivity are factors.
The study of dynamic systems at the nanometer scale can benefit from the loss and background resilience offered by quantum two-photon interference. However, fast measurements with the required resolution are difficult to realize. As a solution, we introduce extreme energy entanglement between the photons undergoing interference. Using a flux probing analysis technique, we recover vibrational signals with frequencies as high as 21 kHz. Along with validating nanometer-scale precision and accuracy, we observe a significant quantum advantage when measuring in the presence of loss and background.
We present progress toward measuring nanometer-scale vibrations via a frequency-entangled two-photon interferometer. Unlike classical interference, two-photon – or Hong-Ou-Mandel – interference allows for optical metrology with resilience against imbalanced loss, dispersion, and optical background. However, the resolution of traditional degenerate frequency two-photon interference is limited by the photons’ bandwidths, requiring large bandwidths or long integration times to achieve nanometer-scale resolution. We have implemented a twophoton interferometer utilizing highly non-degenerate frequency-entangled photon pairs at 810 nm and 1550 nm, drastically increasing measurement sensitivity while retaining the advantages of two-photon interference. This enhancement comes via a beat note with frequency proportional to the photon detuning of 177 THz. The resulting measurement saturates the quantum Cram´er-Rao bound, maximizing the information extracted per photon. We have demonstrated a measurement resolution of 2.3 nm with fewer than 18,000 detected photon pairs, orders of magnitude better than previous results. By reflecting one photon from the pair off a target surface, we may use our system to study small-scale vibrations.
Hong-Ou-Mandel (HOM) interferometry enables delay estimation at the quantum precision limit but is traditionally constrained to path differences within the coherence time of the interfering photons. Here, we demonstrate single-measurement path-delay sensing at the measurement Cramer-Rao bound using spectrally resolved HOM interference, thereby removing the conventional dynamic-range limitation imposed by the photon coherence window, with no scanning required for calibration. By extracting delay information from the spectral interference fringes of spectrally entangled photon pairs, we retain near-optimal sensitivity over an operational range exceeding the photon coherence time by over two orders of magnitude. Using one million detected photon pairs, we achieve a time-delay precision of 20 attosecond (6 nm), while real-time operation (at 1 Hz) yields 330 attosecond (100 nm) precision. Because the estimator relies on fringe periodicity rather than absolute coincidence rates, the method is intrinsically robust to photon losses and variations in interference visibility, eliminating the need for recalibration. As a practical demonstration, we measure the thickness of a 300 um transmissive target with nanometer-scale precision. These results mark a significant step towards deploying quantum-limited measurements in real-world sensing applications using HOM interferometry.
The resilience of quantum two-photon interference against optical loss and background sets it apart from classical single-photon interference for the purpose of sensing. However, achieving fast measurements at the nanometer scale with two-photon interference is challenging, as attaining high resolution typically requires either ultrabroadband photons or many probe photons. To realize nanometer-scale measurements in a matter of seconds or less, we greatly increase the per-photon information content via highly non-degenerate energy entanglement. Our fast measurements thereby enable us to probe time-varying signals at the nanometer scale. To further develop our capabilities, we have drawn on single-photon imaging techniques to implement a robust protocol for reconstructing periodic signals from our relatively sparse detection data, complete with amplitude and frequency information. With this analysis regimen, we have successfully extracted complex multi-frequency signals as well as kHz-range acoustic vibrations. We review our method and present the results of an example measurement to illustrate our capabilities.