Optical monitoring of object position and alignment with nanoscale precision is critical for ultra-precision measurement applications, such as micro/nano-fabrication, weak force sensing, and microscopic imaging. Traditional optical nanometry methods often rely on precision nanostructure fabrication, multi-beam interferometry , or complex post-processing algorithms, which can limit their practical use. In this study, we introduced a simplified and robust quantum measurement technique with an achievable resolution of 2.2 pm and an experimental demonstration of 1 nm resolution, distinguishing it from conventional interferometry , which depended on multiple reference beams. We designed a metasurface substrate with a mode-conversion function, in which an incident Gaussian beam is converted into higher-order transverse electromagnetic mode (TEM) modes. A theoretical analysis, including calculations of the Fisher information , demonstrated that the accuracy was maintained for nanoscale displacements. In conclusion, the study findings provide a new approach for precise alignment and metrology of nanofabrication and other advanced applications.
Optical monitoring of object position and alignment with nanoscale precision is critical for ultra-precision measurement applications, such as micro/nano-fabrication, weak force sensing, and microscopic imaging. Traditional optical nanometry methods often rely on precision nanostructure fabrication, multi-beam interferometry , or complex post-processing algorithms, which can limit their practical use. In this study, we introduced a simplified and robust quantum measurement technique with an achievable resolution of 2.2 pm and an experimental demonstration of 1 nm resolution, distinguishing it from conventional interferometry , which depended on multiple reference beams. We designed a metasurface substrate with a mode-conversion function, in which an incident Gaussian beam is converted into higher-order transverse electromagnetic mode (TEM) modes. A theoretical analysis, including calculations of the Fisher information , demonstrated that the accuracy was maintained for nanoscale displacements. In conclusion, the study findings provide a new approach for precise alignment and metrology of nanofabrication and other advanced applications.
Optical precision measurement is evolving from conventional intensity and phase readout toward a paradigm centered on mode selection, statistical estimation, and information extraction. Conventional intensity- and phase-based schemes can achieve high sensitivity, but their performance is often constrained by finite-aperture diffraction, reference stability, optical path control, and environmental perturbations in systems. Quantum estimation theory provides a physical framework for optical resolution and measurement precision by optimizing the measurement basis. Inspired by spatial mode demultiplexing, this paper extends quantum parameter estimation from incoherent point-source resolution to small-displacement measurement. Metasurface enabled mode control converts displacement induced optical-field variations into measurable changes in orthogonal modal coefficients, providing a route for extracting sub-diffraction-scale displacement information. This paper introduces Rayleigh’s curse, Fisher information, and spatial mode projection, discusses their applications in one-dimensional displacement measurement and two-dimensional super-resolution imaging, and outlines future directions in digital optics, Engineering Optics 2.0, mode-basis optimization, two-dimensional information reconstruction, and intelligent optical measurement systems for engineering applications.
To overcome the limit of diffraction while achieving the superresolution technique, solid immersion lenses are the key optical elements for data storage and nanophotonics applications. Recent demonstrations have shown how different nanostructures (such as elliptical solid immersion lenses) are used in diverse fields of increasing resolution in the presence of a structured Gaussian beam. By applying twisted beams such as angular momentum beams (Laguerre- Gaussian) and spatial higher-order Gaussian beams (Hermite- Gauss), we can attain a sharp near-field focal spot pattern, which is considerably better than the conventional solid immersion lens structure in ~mm scale specifically for imaging beyond diffraction limit. Our computation results present a resolution of ~27 nm under a specific Hermite -Gauss mode illumination on a pyramidal shape nanolens structure. By numerical simulations, tolerance has been confirmed with a slight variation in beam size and geometrical modification to make the model compatible with fabrication errors. This narrow bandwidth intensity distribution can be utilized for scanning the sample with higher resolution, especially in the field of quantum technology.
Tracking small transverse displacements of an optical beam with ultra-high accuracy is a fundamental problem underlying numerous important applications ranging from pointing, acquisition and tracking for establishing a lasercom link, to atomic force microscopy for imaging with atomic-scale resolution. Determining what is the optimal quantum-optical probe and the best achievable sensitivity of measuring a small transverse optical beam displacement, is the fundamental question central to these sensing schemes. By mapping this problem to an array of nested Mach-Zehnder interferometers, we explicitly construct the optimal probe state. It is entangled across the spatial modes allowed within the Fresnel number product of the propagation geometry, and entangled across the temporal modes within the time-bandwidth product of the optical probe. We show that the optimal sensitivity of measuring the beam displacement achieves a Heisenberg limited scaling over both the number of temporal modes and the average number of photons transmitted per mode. Surprisingly, we discover a sub-Heisenberg limited scaling over the number of available spatial modes. To qualify the quantum enhancement, we also establish the optimal sensitivity of a classical-light probe, which gives shot-noise limit over both the number of temporal modes and the number of photons per mode, and Heisenberg limited scaling over the number of spatial modes. Finally, we construct an explicit design for quantum-enhanced beam tracking, which uses a Gaussian (multi-mode-entangled squeezed-state) probe and a Gaussian (multi-mode homodyne) receiver.
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect alignment with the centroid of the object. Both inhibit the practical application of these methods, as uniform motion and/or relative jitter destroy their assumptions. Here, we show that measuring intensity in the Fourier plane enables super-resolution without any of the issues of image-based methods. We start with the shift-invariance of the Fourier transform and the observation that the two-point position problem x1,x2 in the near field corresponds to the single-point wavenumber problem k=2π/(x2−x1) in the far field. We consider the full range of mutual coherence and show that for fully coherent sources, the Fourier method saturates the quantum limit, i.e. it gives the best possible measurement. Similar results hold for sub-Rayleigh constellations of N sources, which can act collectively as a spatially averaged metasurface and/or individually as elements of a phased-array antenna. The theory paves the way to merge Fourier optics with super-resolution techniques, enabling experimental devices that are both simpler and more robust than previous designs.
The resolution of imaging devices is ultimately limited by the diffraction of light. This limit can be circumvented by exploiting near-field phenomena, non-linearities of the sample or specific illumination schemes, which led to the recent explosion of optical super-resolution techniques. However, it would be desirable to reach the nanoscale in the most general way possible, with far-field linear imaging of uniformly illuminated samples. In the last few years, the answer to that came with the field of quantum-inspired super-resolution (QISR), where quantum metrological techniques were used to find novel measurement schemes that, beyond the conventional direct imaging of light, would achieve higher precisions. Interestingly, these ideas would always in some way or another involve transverse spatial modes of light. This thesis presents our work on the subject, with novel theoretical and experimental results. Firstly, we develop the traditional theory of QISR, with has mostly focused on either the estimation of separation of two point sources or on geometric moments of samples. Then, we introduce our own results on optical imaging of general distributions of point sources, in a step to take QISR from toy examples to real imaging scenarios. Secondly, we apply all the concepts studied on a experimental, proof-of-principle implementation of a QISR scheme dubbed Hermite-Gaussian Microscopy (HGM), which uses heterodyne detection with several Hermite-Gaussian modes as local oscillator in order to reconstruct the object sample and achieve super-resolution. We report the techniques necessary for the manipulation of spatial modes of light, as well as our results, where we demonstrated 2D imaging with twofold resolution enhancement beyond the diffraction limit.
Free-electron quantum optics has recently emerged as a promising platform for coherent electron-light interactions, yet its potential for quantum-enhanced metrology remains largely unexplored. Here, we investigate the fundamental precision limit of coupling-strength estimation in multi-electron photon-induced near-field electron microscopy (PINEM), demonstrating that the quantum Fisher information scales quadratically with electron number. We then propose an experimentally accessible scheme combining squeezed-light probing and optical homodyne detection that attains Heisenberg scaling with respect to electron number, provided the electrons exhibit nonzero inter-electron coherence, while surpassing conventional PINEM sensing in photon-number enhancement as well. We further analyze the effect of imperfect electron preparation, showing that electron phase noise is converted into a fluctuating optical displacement and eventually limits the precision. To overcome this limitation, an auxiliary optical mode coupled to the same electron ensemble measures the displacement noise in the signal mode, allowing its conditional suppression and recovery of the Heisenberg scaling. Our work establishes multi-electron coherence as a resource for free-electron quantum metrology and opens the route to precision measurements of nanoscale electron-light interactions.