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Optical-domain spectral super-resolution enabled by a quantum memory

Mateusz Mazelanik, Adam Leszczyński, Michal P. Parniak

Published Jun 8, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
The concept of temporal imaging draws from the analogy between paraxial propagation of light in space and in dispersive media. So far, temporal imaging has been demonstrated with ultrafast light, corresponding to spectral precision in the THz range. In our quantum memory, we have implemented full spectral and temporal processing capabilities for ultra narrowband photons, which allow us to perform temporal imaging with MHz bandwidth and kHz precision. Implementation of this concept leads to many implications, which give rise to two distinct super-resolved spectroscopy schemes, inspired by recent developments in spatial super-resolved imaging. One scheme takes advantage of elaborate interference in the quantum memory, while the other uses optimized analysis of a homodyne detector traces. Overall, our approach not only brings temporal imaging to the previously untackled regime but also points to a variety of new schemes useful in quantum sensing.
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.
The resolution limits of classical spectroscopy can be surpassed by quantum-inspired methods leveraging the information contained in the phase of the complex electromagnetic field. Their counterpart in spatial imaging has been widely discussed and demonstrated; however, the spectral-domain implementations are few and scarce. We experimentally demonstrate a spectroscopic super-resolution method aimed at broadband light (tens to hundreds of GHz), and based on the spectral-domain analog of image inversion interferometry. In a proof-of-principle experiment, we study the paradigmatic problem of estimating a small separation between two incoherent spectral features of equal brightness, with a small number of photons per coherence time. On the grounds of asymptotic estimation theory, more than a two-fold improvement over the spectral direct imaging is demonstrated in terms of required resources (photons) for a given estimator variance. The setup is based on an actively stabilized Mach–Zehnder-type interferometer with electro-optic time lenses and passive spectral dispersers implementing the inversion. As such, the method promises on-chip integration, good scalability, and further applications, e.g., for mode sorting.
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.