I The Self-Imaging Phenomenon and its Applications

Patorski, Krzysztof

doi:10.1016/s0079-6638(08)70084-2

Cited by 400 publications

(274 citation statements)

References 219 publications

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“…They are separated by the equal distance of L = 38 cm, which is the Talbot length L T = d 2 /λ dB for a typical de Broglie wavelength of λ dB = 2.6 pm. The first grating acts as a periodic array of narrow slit sources, the second one as the diffracting element, and the third grating is used as a scanning detection mask, which modulates the molecular density pattern produced by the Talbot-Lau interference effect [15,16]. The transmitted molecules are ionized by a blue laser beam (wavelength 488 nm, 6.6 µm waist), and their intensity I is recorded as a function of the lateral displacement of the third grating.…”

Section: Figmentioning

confidence: 99%

Decoherence of matter waves by thermal emission of radiation

Hackermüller

Hornberger

Brezger

et al. 2004

Nature

315

356

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Emergent quantum technologies have led to increasing interest in decoherence -the processes that limit the appearance of quantum effects and turn them into classical phenomena. One important cause of decoherence is the interaction of a quantum system with its environment, which 'entangles' the two and distributes the quantum coherence over so many degrees of freedom as to render it unobservable. Decoherence theory [1][2][3][4] has been complemented by experiments using matter waves coupled to external photons [5][6][7] or molecules [8], and by investigations using coherent photon states [9], trapped ions [10] and electron interferometers [11,12]. Large molecules are particularly suitable for the investigation of the quantumclassical transition because they can store much energy in numerous internal degrees of freedom; the internal energy can be converted into thermal radiation and thus induce decoherence. Here we report matter wave interferometer experiments in which C 70 molecules lose their quantum behaviour by thermal emission of radiation. We find good quantitative agreement between our experimental observations and microscopic decoherence theory. Decoherence by emission of thermal radiation is a general mechanism that should be relevant to all macroscopic bodies.In this Letter we investigate the decoherence of molecular matter waves. We change the internal temperature of the molecules in a controlled way before they enter a near-field interferometer, and observe the corresponding reduction of the interference contrast. The idea behind this effort is to demonstrate a most fundamental decoherence mechanism that we encounter in the macroscopic world: All large objects, but also molecules of sufficient complexity, are able to store energy and to interact with their environment via thermal emission of photons. It is generally believed that warm macroscopic bodies emit far too many photons to allow the observation of de Broglie interferences, whereas individual atoms or molecules can be sufficiently well isolated to exhibit their quantum nature. However, there must be a transition region between these two limiting cases. Interestingly, as we show in this study, C 70 fullerene molecules have just the right amount of complexity to exhibit perfect quantum interference in our experiments [13] at temperatures below 1000 K, and to gradually lose all their quantum behaviour when the internal temperature is increased up to 3000 K. We can thus trace the quantum-to-classical transition in a controlled and quantitative way. The complexity of large molecules adds a novel quality with respect to previously performed experiments with atoms [5][6][7]: the energy in molecules may be equilibrated in many internal degrees of freedom during the free flight, and a fraction of the vibrational energy will eventually be reconverted into emitted photons. Therefore the internal dynamics of the molecule is also relevant for the quantum behaviour of the centre-of-mass state. In contrast to resonance fluorescence, which was investigated wit...

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Section: Figmentioning

confidence: 99%

Decoherence of matter waves by thermal emission of radiation

Hackermüller

Hornberger

Brezger

et al. 2004

Nature

315

356

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“…This verifies that electron beams diffracted by nanostructures remain coherent after propagating farther than the Talbot length zT = 2d 2 /λ = 1.2 mm, and hence is a proof of principle for the function of a Talbot-Lau interferometer for electrons. Distorted fringes due to a phase object demonstrates an application for this new type of electron interferometer.Near-field interference effects that result in self-similar images of a periodic structure were noticed by Talbot in 1836, and later described as Fourier images [1,2,3]. One remarkable feature is that revivals in image visibility occur periodically as the plane of observation is separated from the periodic structure.…”

mentioning

confidence: 96%

“…Partially coherent waves are required to observe self-images of a single grating (the Talbot effect). However, a related phenomenon (the Lau effect) occurs with incoherent light if two gratings are used [3,4,5]. Fringes are then formed behind the second grating, and the fringe visibility oscillates as a function of grating separation.…”

mentioning

confidence: 99%

Electron interferometry with nanogratings

Cronin

McMorran

2006

Phys. Rev. A

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We present an electron interferometer based on near-field diffraction from two nanostructure gratings. Lau fringes are observed with an imaging detector, and revivals in the fringe visibility occur as the separation between gratings is increased from 0 to 3 mm. This verifies that electron beams diffracted by nanostructures remain coherent after propagating farther than the Talbot length zT = 2d 2 /λ = 1.2 mm, and hence is a proof of principle for the function of a Talbot-Lau interferometer for electrons. Distorted fringes due to a phase object demonstrates an application for this new type of electron interferometer.Near-field interference effects that result in self-similar images of a periodic structure were noticed by Talbot in 1836, and later described as Fourier images [1,2,3]. One remarkable feature is that revivals in image visibility occur periodically as the plane of observation is separated from the periodic structure. The visibility of self-images is maximized at half-integer multiples of the Talbot distance z T = 2d 2 /λ, with d being the period of the structure and λ the wavelength of the light or de Broglie waves illuminating the structure. Partially coherent waves are required to observe self-images of a single grating (the Talbot effect). However, a related phenomenon (the Lau effect) occurs with incoherent light if two gratings are used [3,4,5]. Fringes are then formed behind the second grating, and the fringe visibility oscillates as a function of grating separation. These Lau fringes have maximum visibility on a distant screen when the gratings are separated by nd 2 /λ, with n being an integer. In a Talbot-Lau interferometer, Lau fringes are detected with the aid of a third grating, but the fringes can also be observed directly on a screen, thus making a Lau interferometer as shown in Figure 1.Here we present a Lau interferometer for electrons based on two nanostructure gratings that each have a period of d = 100 nm. With medium energy (5 keV) electrons that have a de Broglie wavelength of λ = 17 pm, the Talbot length is 1.16 mm. An imaging detector 80 cm beyond the gratings was used to observe the Lau fringes shown in Figure 2, and the fringe visibility as a function of grating separation is plotted in Figure 3. If the fringes are analyzed with a third grating (even a digital grating in the image processing can achieve this purpose), then this apparatus serves as a Talbot-Lau interferometer. However, even more information is gained by studying images of the Lau fringes directly.Interferometers based on the Talbot and Lau effects have found applications in light optics [3,5,6], in atom optics [7,8,9,10,11], and more recently with x-rays [12]. Yet even though electron interferometry is a mature field [13,14,15], neither Lau nor Talbot-Lau interferometer designs have been operated with electrons until now.Perhaps the chief reason that Talbot-Lau interferometers have not previously been created for electrons is that suitable periodic structures have not been available. Crystals with a lattice peri...

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“…The experiment can be performed despite the imperfect quality of the grating due to the fact that the Talbot effect reproduces the self-image with modified quality from the grating [30,31]. This is a well-known effect.…”

Section: Discussionmentioning

confidence: 99%

Single Exposure Imaging of Talbot Carpets and Resolution Characterization of Detectors for Micro- and Nano- Patterns

Kim¹,

Danylyuk²,

Brocklesby³

et al. 2016

Journal of the Optical Society of Korea

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In this paper, we demonstrate a self-imaging technique that can visualize longitudinal interference patterns behind periodically-structured objects, which is often referred to as Talbot carpet. Talbot carpet is of great interest due to ever-decreasing scale of interference features. We demonstrate experimentally that Talbot carpets can be imaged in a single exposure configuration revealing a broad spectrum of multi-scale features. We have performed rigorous diffraction simulations for showing that Talbot carpet print can produce ever-decreasing structures down to limits set by mask feature sizes. This demonstrates that large-scale pattern masks may be used for direct printing of features with substantially smaller scales. This approach is also useful for characterization of image sensors and recording media.

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I The Self-Imaging Phenomenon and its Applications

Cited by 400 publications

References 219 publications

Decoherence of matter waves by thermal emission of radiation

Decoherence of matter waves by thermal emission of radiation

Electron interferometry with nanogratings

Single Exposure Imaging of Talbot Carpets and Resolution Characterization of Detectors for Micro- and Nano- Patterns

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