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The Rayleigh's criterion infamously imposes a minimum separation between two incoherent sources for them to be distinguishable via classical methods. In this work, we demonstrate the emergence of two-photon beats from the interference of a…

Quantum Physics · Physics 2025-05-23 Salvatore Muratore , Danilo Triggiani , Vincenzo Tamma

Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially…

Quantum Physics · Physics 2016-09-07 Mankei Tsang , Ranjith Nair , Xiao-Ming Lu

The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is…

Quantum Physics · Physics 2007-05-23 Thomas Legero , Tatjana Wilk , Markus Hennrich , Gerhard Rempe , Axel Kuhn

The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon…

Quantum Physics · Physics 2009-11-10 T. Legero , T. Wilk , A. Kuhn , G. Rempe

We demonstrate the ultimate sensitivity allowed by quantum physics in the estimation of the time delay between two photons by measuring their interference at a beam-splitter through frequency-resolving sampling measurements. This…

Quantum Physics · Physics 2023-04-25 Danilo Triggiani , Giorgos Psaroudis , Vincenzo Tamma

Abstract Superresolution has been demonstrated to overcome the limitation of the Rayleigh's criterion and achieve significant improvement of the precision in resolving the separation of two incoherent optical point sources. However, in…

Quantum Physics · Physics 2024-12-06 Junyan Li , Shengshi Pang

The Rayleigh criterion determines the resolution limit of a periodogram, which is the minimum frequency separation required to barely resolve two sinusoids. Failing to consider the Rayleigh criterion may result in incorrect interpretations…

Instrumentation and Methods for Astrophysics · Physics 2025-08-27 V. Ramirez Delgado , J. S. Caicedo Vivas , S. Dodson-Robinson , C. Haley

Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSF), namely in the subdiffraction limit. Recently,…

Quantum Physics · Physics 2019-01-09 Sisi Zhou , Liang Jiang

The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing…

Quantum Physics · Physics 2025-10-22 Junyan Li , Shengshi Pang

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright…

Quantum Physics · Physics 2017-12-13 J. Rehacek , Z. Hradil , B. Stoklasa , M. Paur , J. Grover , A. Krzic , L. L. Sanchez-Soto

Optical sensing schemes that rely on two-photon interference provide a powerful platform for precision metrology, although they are inherently constrained by a trade-off between dynamic range and measurement precision. To overcome this…

We present a sensing scheme for estimating the frequency difference of two non-entangled photons. The technique consists of time-resolving sampling measurements at the output of a beam splitter. With this protocol, the frequency shift…

Quantum Physics · Physics 2025-12-10 Luca Maggio , Danilo Triggiani , Paolo Facchi , Vincenzo Tamma

Coherence spectroscopy has been intensively studied over the last several decades for various applications in science and engineering. The Rayleigh criterion defines the resolution limit of an interferometer, where many-wave interference…

Quantum Physics · Physics 2024-05-22 Byoung S. Ham

We establish a simple method to assess the quantum Fisher information required for resolving two incoherent point sources with an imaging system. The resulting Cram\'er-Rao bound shows that the standard Rayleigh limit can be surpassed by…

Quantum Physics · Physics 2016-06-28 Martin Paur , Bohumil Stoklasa , Zdenek Hradil , Luis L. Sanchez-Soto , Jaroslav Rehacek

We obtain the multiple-parameter quantum Cram\'er-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth.…

Quantum Physics · Physics 2017-07-05 Shan Zheng Ang , Ranjith Nair , Mankei Tsang

We consider imaging of two partially coherent sources and derive the ultimate quantum limits for estimating the separation, location, relative intensity, and coherence factor. We show that super-resolution in the separation is achievable…

Quantum Physics · Physics 2026-05-20 Joaquín López-Suárez , Michalis Skotiniotis

The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond…

Quantum Physics · Physics 2019-01-09 Mankei Tsang

Conventional incoherent imaging based on measuring the spatial intensity distribution in the image plane faces the resolution hurdle described by the Rayleigh diffraction criterion. Here, we demonstrate theoretically using the concept of…

The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. An important figure of merit for sensing time dependent signals is the spectral…

Quantum Physics · Physics 2019-12-05 Tuvia Gefen , Amit Rotem , Alex Retzker

We have constructed an efficient source of photon pairs using a waveguide-type nonlinear device and performed a two-photon interference experiment with an unbalanced Michelson interferometer. Parametric down-converted photons from the…

Quantum Physics · Physics 2009-11-06 Kaoru Sanaka , Karin Kawahara , Takahiro Kuga
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