Quantum interference fringes beating the diffraction limit

Kawabe, Yoshio; Fujiwara, Hideki; Okamoto, Ryo; Sasaki, Keiji; Takeuchi, Shigeki

doi:10.1364/oe.15.014244

Cited by 51 publications

(56 citation statements)

References 21 publications

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“…The visibility of an unentangled OCM, on the other hand, decays exponentially. In doing this, we have also achieved the highest spatial super-resolution to date [10][11][12].In 2000, Boto et al pointed out that entangled states of light offer a way to improve the resolution of interferometers beyond the diffraction limit, which determines the smallest spatial features achievable in classical optical systems [2]. This limit is set by the fringe spacing of the interference pattern created by two beams of wavelength λ meeting at an angle θ, which is λ/(2 sin θ 2 ).…”

mentioning

confidence: 91%

“…The visibility of an unentangled OCM, on the other hand, decays exponentially. In doing this, we have also achieved the highest spatial super-resolution to date [10][11][12].…”

mentioning

confidence: 93%

“…work on N00N states [4,5,[13][14][15][16] and their application in tasks such as quantum lithography and quantum imaging [10][11][12]17]. However, the individual photons in the N00N state cannot be localized to better than λ/2, regardless of the narrow spatial scale of the N-photon correlation fringes [6,7].…”

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confidence: 99%

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Scalable Spatial Superresolution Using Entangled Photons

et al. 2014

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N00N states -maximally path-entangled states of N photons -exhibit spatial interference patterns sharper than any classical interference pattern. This is known as super-resolution. However, even with perfectly efficient number-resolving detectors, the detection efficiency of all previously demonstrated methods to measure such interference decreases exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. Here, we create spatial super-resolution fringes with two-, three-, and fourphoton N00N states, and demonstrate a scalable implementation of the so-called "optical centroid measurement" which provides an in-principle perfect detection efficiency. Moreover, we compare the N00N-state interference to the corresponding classical super-resolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons, while the visibility of our experimentally measured N00N-state super-resolution fringes remains approximately constant with N. Our implementation of the optical centroid measurement is a scalable method to measure high photon-number quantum interference, an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology.Many essential techniques in modern science and technology, from precise position sensing to high-resolution imaging to nanolithography, rely on the creation and detection of the finest possible spatial interference fringes using light. Classically, all such measurements face a fundamental barrier related to the "diffraction limit," which is determined by the wavelength of the light [1], but quantum entanglement can be used to surpass this limit by making the spatial interference fringes sharper (a result referred to as super-resolution) [2,3]. In particular, the N-photon entangled "N00N" state can display an interference pattern N times finer than that of classical light [4,5]. However, N00N states suffer from a weakness that has made their advantage controversial: the probability of all N photons arriving at the same place, and thus the detection efficiency, decreases exponentially with N [6,7]. Here we implement the optical centroid measurement (OCM) proposed by Tsang [8] to completely overcome this problem. A proof-of-principle experiment confirming the underlying concept of the OCM was recently performed [9], but, being limited to only two photons and two 'movable' detectors, it could not probe the scaling properties nor demonstrate the efficiency gain of the OCM. In our experiment, using an array of 11 fixed detectors, we measure two-, three-, and four-photon spatial fringes, and find that their visibility does not degrade with the number of entangled photons, clearly displaying the enhanced efficiency and scalability of the OCM. The visibility of an unentangled OCM, on the other hand, decays exponentially. In doing...

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confidence: 91%

“…The visibility of an unentangled OCM, on the other hand, decays exponentially. In doing this, we have also achieved the highest spatial super-resolution to date [10][11][12].…”

mentioning

confidence: 93%

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Scalable Spatial Superresolution Using Entangled Photons

et al. 2014

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“…Our results show that, given more efficient detectors, the OCM could potentially be scaled to high photon numbers and perhaps provide a means for practical quantum imaging. Our experiment also represents the highest spatial superresolution to date [10][11][12].…”

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confidence: 99%

“…1(a)], the probability of detecting all of the photons at a given position will display spatial fringes with a period of λ=ð2N sinðθ=2ÞÞ, where θ is the angle betweenk 1 andk 2 (assuming jk 1 j ¼ jk 2 j ¼ ð2π=λÞ). The period of the N00N fringes is N times smaller than that of classical fringes, suggesting that N00N states could be used to increase the resolution of optical systems by a factor of N. This observation has led to much subsequent work on N00N states [4,5,[13][14][15][16] and their application in tasks such as quantum lithography and quantum imaging [10][11][12]17]. However, the individual photons in the N00N state cannot be localized to better than λ=2, regardless of the narrow spatial scale of the N-photon correlation fringes [6,7].…”

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confidence: 99%

Scalable Imaging of Superresolution

Matthews¹

2014

Physics

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N00N states-maximally path-entangled states of N photons-exhibit spatial interference patterns sharper than any classical interference pattern. This is known as superresolution. However, even given perfectly efficient number-resolving detectors, the detection efficiency of all previous measurements of such interference would decrease exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. A technique known as the "optical centroid measurement" has been proposed to solve this and has been experimentally verified for photon pairs; here we present the first extension beyond two photons, measuring the superresolution fringes of two-, three-, and four-photon N00N states. Moreover, we compare the N00N-state interference to the corresponding classical superresolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons. Our work represents an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology.

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Pixel Super‐Resolution Interference Pattern Sensing Via the Aliasing Effect for Laser Frequency Metrology

Wan

Zhao

et al. 2023

Laser & Photonics Reviews

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The superposition of several optical beams with large mutual angles results in sub‐micrometer periodic patterns with a complex intensity, phase, and polarization structure. For high‐resolution imaging thereof, one often employs optical super‐resolution methods such as scanning nano‐particle imaging. Here, it is reported that by using a conventional arrayed image sensor in combination with 2D Fourier analysis, the periodicities of light fields much smaller than the pixel size can be resolved in a simple and compact setup, with a resolution far beyond the Nyquist limit set by the pixel size. The ability to resolve periodicities with spatial frequencies of ≈3 µm−1, 15 times higher than the pixel sampling frequency of 0.188 µm−1, is demonstrated. This is possible by analyzing high‐quality Fourier aliases in the first Brillouin zone. In order to obtain the absolute spatial frequencies of the interference patterns, simple rotation of the image sensor is sufficient, which modulates the effective pixel size and allows determination of the original Brillouin zone. Based on this method, wavelength sensing with a resolving power beyond 100,000 without any special equipment is demonstrated.

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Quantum interference fringes beating the diffraction limit

Cited by 51 publications

References 21 publications

Scalable Spatial Superresolution Using Entangled Photons

Scalable Spatial Superresolution Using Entangled Photons

Scalable Imaging of Superresolution

Pixel Super‐Resolution Interference Pattern Sensing Via the Aliasing Effect for Laser Frequency Metrology

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