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arXiv:2311.10574 · Optics Letters

Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection

Wiktor Krokosz, Mateusz Mazelanik, Michał Lipka, Marcin Jarzyna, Wojciech Wasilewski, Konrad Banaszek, Michal P. Parniak

Published Jan 17, 2024• 6 citations
arXivHTMLPDF

Abstract

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

DOI
10.1364/ol.514659

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Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.
Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies to fully exploit information already present in the field is to perform a quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ an optical quantum memory with spin-wave storage and an embedded processing capability to implement a time-inversion interferometer for input light, projecting the optical field in the symmetric-antisymmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
Existing super-resolution methods of optical imaging hold a solid place as an application in multiple sciences, but many new developments allow beating of diffraction limit in better and more subtle ways. An avenue was opened by suggesting to fully exploit information already present in the field by performing quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ optical quantum memory with spin-wave storage and an embedded processing capability to implement a timeinversion interferometer for input light, projecting the optical field in the symmetricanti-symmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20.1 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.
Super-resolution imaging holds a solid place in biological and chemical sciences, but many new developments allow the beating of diffraction (Rayleigh) limit in better and more subtle ways. The modern understanding of the Rayleigh limit comes from information theory where it is identified as vanishing information about the separation of two sources for small separations - the Rayleigh curse. The surprising observation [1] that the quantum Cramer-Rao bound (CRB), which identifies maximum information available in the optical field, does not vanish even for zero separation, led to so-called quantum-inspired superresolution methods that suggest to fully exploit information already present in the field by performing tailored measurements [1]. Such an approach is starkly different approach compared with methods relying on nonlinear processes such as STED or specific emission statistics.
Quantum metrology has been shown to surpass classical limits of correlation, resolution, and sensitivity. It has been introduced to interferometric radar schemes, with intriguing preliminary results. Even quantum-inspired detection of classical signals may be advantageous in specific use cases. Following ideas demonstrated so far only in the optical domain, where practically no thermal background photons exist, we realize room-temperature microwave frequency super-resolved phase measurements with trillions of photons, while saturating the Cramer-Rao bound of sensitivity. We experimentally estimate the interferometric phase using the expectation value of the parity operator by two methods. We achieve superresolution up to 1200 times better than the wavelength with 25-ns integration time and 56-dB SNR.