Two-Photon Diffraction and Quantum Lithography

D’Angelo, Milena; Chekhova, Maria V.; Shih, Yanhua

doi:10.1103/physrevlett.87.013602

Cited by 639 publications

(492 citation statements)

References 9 publications

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“…In the field of quantum-enhanced measurements, entanglement may be employed to enhance the precision of the measurement beyond the Heisenberg limit (Giovannetti et al, 2004(Giovannetti et al, , 2006Mitchell et al, 2004). Similarly, the spatial resolution may be enhanced in quantum imaging applications Pittman et al, 1995), quantum-optical coherence tomography (Abouraddy et al, 2002;Esposito, 2016;Nasr et al, 2003), as well as in quantum lithographic applications (Boto et al, 2000;D'Angelo et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear optical signals and spectroscopy with quantum light

2016

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Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties -known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators in the joint field plus matter phase space. These are distinct from Glauber's photon counting formalism which use normally ordered products of ordinary operators in the field space. One notable advantage for spectroscopy applications is that entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems.

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Section: Introductionmentioning

confidence: 99%

Nonlinear optical signals and spectroscopy with quantum light

2016

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“…St, 42.50.Dv, In modern quantum optics, there is a great variety of proposals trying to improve different aspects of the image formation process, commonly summarized by the field of quantum imaging. Today, this fast growing field ranges from early Ghost imaging [1], sub-wavelength phase measurements [2,3] to quantum lithography [4,5,6], quantum microscopy [7,8,9, 10] and many more (see e.g. [11]).…”

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confidence: 99%

Sub-Rayleigh quantum imaging using single-photon sources

et al. 2009

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We propose a technique capable of imaging a distinct physical object with sub-Rayleigh resolution in an ordinary far-field imaging setup using single-photon sources and linear optical tools only. We exemplify our method for the case of a rectangular aperture and two or four single-photon emitters obtaining a resolution enhanced by a factor of two or four, respectively.PACS numbers: 42.50. St, 42.50.Dv, In modern quantum optics, there is a great variety of proposals trying to improve different aspects of the image formation process, commonly summarized by the field of quantum imaging. Today, this fast growing field ranges from early Ghost imaging [1], sub-wavelength phase measurements [2,3] to quantum lithography [4,5,6], quantum microscopy [7,8,9, 10] and many more (see e.g. [11]). Though all proposals commonly aim to overcome the classical boundaries of image formation, only few improve the spatial resolution itself, i.e. the ability to image a physical object while overcoming the Rayleigh [12] or Abbe limit [13] of classical optics.So far, in quantum imaging sub-classical resolution has been achieved by using sources of entangled photons [5,8], but it was also shown recently that initially uncorrelated light can be used for that purpose [10,14]. All those methods exploit second (or N th) order correlations between two (or N ) photons, i.e. quantum interferences between two-(or N -) photon amplitudes, to surmount the classical boundaries. Hereby, it is yet a challenge to implement sub-Rayleigh quantum imaging using linear optical tools only.In this letter, we propose a method of imaging a physical object, e.g. an aperture, beyond the classical Rayleigh resolution using linear optics. Our scheme involves N uncorrelated single photon emitters serving as a nonclassical light source and N detectors performing correlation measurements. By placing the N detectors at different positions in the Fourier plane of the object we avoid the use of multiphoton absorption techniques. Moreover, using a lens in the Fourier plane our setup is also capable to reproduce the object in the image plane of the lens. We exemplify our method for the case of two single photon emitters. By exploiting two-photon interferences we show that this scheme allows to image the object with sub-Rayleigh resolution, i.e., with a resolution enhanced by a factor of two with respect to the classical case. In the same way, sub-Rayleigh resolution enhanced by a factor of four is obtained for N = 4 emitters and using N = 4 detectors. By extending this scheme, we show that the same results are also obtained for different objects, e.g., in case of a grating with N slits.Only recently, first experiments were able to observe higher order interferences of photons emitted by single trapped atoms [15,16,17,18]. These observations stand in a long line of experiments using single photon sources to investigate interference phenomena of single-and multi-photon amplitudes. After the early demonstration of first-oder interferences of light scattered by two ions [22], t...

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“…This is so because the NOON state shows a de Broglie wavelength of λ/N for the N -photon interference. D'Angelo et al [17] demonstrated the feasibility of the scheme for N = 2.…”

Section: Introductionmentioning

confidence: 99%

Projection measurement of the maximally entangledN-photon state for a demonstration of theN-photon de Broglie wavelength

Sun

Guo

2006

Phys. Rev. A

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We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N = 4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.

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Two-Photon Diffraction and Quantum Lithography

Cited by 639 publications

References 9 publications

Nonlinear optical signals and spectroscopy with quantum light

Nonlinear optical signals and spectroscopy with quantum light

Sub-Rayleigh quantum imaging using single-photon sources

Projection measurement of the maximally entangledN-photon state for a demonstration of theN-photon de Broglie wavelength

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