Deliverables
It is well-known that parametric amplification can amplify a signal without degrading it (noise figure equal to 1), provided that it operates in a phase sensitive configuration. In a work performed before the beginning of the QUANTIM project, the NWU group had experimentally shown that this was the case (within the experimental imperfections) for the temporal fluctuations measured at the different points of an image.
UFC, using its recognized expertise on the parametric amplification of images, has studied the pixel to pixel spatial fluctuations on a single shot amplified image by a pulsed, type I, frequency degenerate optical parametric amplifier. The spatial noise figures were experimentally determined in the phase-sensitive and phase insensitive schemes. Both are in good agreement with theory, and UFC recently showed that, as expected, and in the low gain regime, the phase sensitive amplifier does not add noise, while the phase insensitive amplifier leads to the classical 3 dB degradation of the signal to noise ratio.
The experiment and the data processing are very delicate, because of the low level of the signal on each pixel, the absence of the relative phase control and problems of wavefront. They will be improved in the near future in order to observe more easily the quantum spatial effect, and to use it in applications.
UFC has a long experience in the study, both at the experimental and theoretical level, of soliton arrays produced by a mechanism of modulational instability in a in planar waveguide having a Kerr nonlinearity. They have shown at the beginning of the project that quantum noise plays a central role in the spatio-temporal dynamics of these solitons. In collaboration with ENS, they have then theoretically investigated the spatial distribution of quantum fluctuations and correlations in 2D Kerr solitons and soliton arrays.
A first important result has been obtained in the case of the vectorial Kerr single soliton, namely an almost perfect anti-correlation between the fluctuations of the two components of opposite circular polarisations. A significant global and local squeezing was also found, both for the single soliton and for the array of solitons, while correlations between adjacent solitons in the array are very weak in all the studied configurations.
Parametric down conversion produces twin photons which are temporally and spatially perfectly correlated at the quantum level. This effect has been extensively used at the photon counting level in beautiful and famous experiments.
When the pump intensity is raised by a large factor, with the help of intense pulsed lasers, many twin photons are produced, which cannot be counted individually. One obtains on the signal and idler beams quantum correlated images, each having large pixel to pixel fluctuations, but with (almost) identical intensity values in a single shot on the symmetrical pixels of the signal and idler images.
In the high parametric gain regime where roughly 10 to 100 photons were recorded on average on each pixel, the INFM experimental group succeeded in demonstrating such a pixel to pixel quantum correlation in a single shot spatial statistics.
The best spatial noise reduction was about 50% below the standard quantum limit. This important achievement can now be used to information processing
A single mode degenerate OPO generates above threshold a sub-harmonic field with a phase uncertainty of pi, which switches between its two possible solutions when it is perturbed. USTRAT has studied the transverse properties of this device and shown that, when one uses a transverse multimode cavity such a planar cavity instead of a single mode one, the OPO generates complex transverse patterns in which the two solutions co-exist.
They are separated by domain-walls in which the pi-phase shift occurs. Two domain walls may lock to each other, and form cavity solitons, which can further organize themselves in regular soliton arrays. These solitons are stable and can be generated or erased by external causes. USTRAT has shown the importance of quantum noise in inducing the soliton arrays, and of a spatial phase modulation of the pump in both stabilizing their geometry and steering them.
A local squeezing of quantum fluctuations at the exact location of the domain walls has also been predicted. These researches are indications of the potential interest of cavity soliton arrays as a spatial register of information.
Super-resolution techniques have been studied for a long time at the classical level, in the perspective of beating the Rayleigh limit of resolution by using sophisticated deconvolution procedures. Just before the beginning of the QUANTIM project, PHLAM, in collaboration with ENS, had investigated the same techniques at the quantum level, and evaluated the role of quantum noise in the deconvolution technique. They showed that it was possible to improve the performance of super-resolution techniques by injecting non-classical light in very specific transverse modes, namely the eigenmodes of the propagation through the imaging system, called prolate modes.
These investigations were pursued further during the QUANTIM project, in particular with the help of numerical simulations. PHLAM, together with its Russian sub-contractor, discovered the precise scheme of illumination of the object by a regular squeezed light source which produces the requested squeezing of the prolate modes. The simplicity of the scheme brings confidence that quantum-enhanced super-resolution technique can effectively be implemented in an actual experiment
Non linear media have been used for a long time to process images. For example, up-conversion of optical images from the infrared to the visible has been proposed and realized in order to take advantage of the higher quality of CCD detectors in the visible. IMEDEA has investigated this domain at the quantum level, in the specific configuration of vectorial second harmonic generation.
They have shown, both in the intracavity and travelling wave configurations, that the up-conversion of any image to the second harmonic field was possible without distortion by sending the image on one polarisation of the fundamental wave, and a plane wave on the other. Image processing functions like contrast enhancement or contour recognition are possible with this scheme.
Furthermore, they have found that, in some circumstances, the up-conversion operation can be made without adding quantum noise to the initial image.
Intracavity parametric generation is one of the most efficient ways of producing single mode non-classical light in the continuous wave regime and with a low power pump. If one wants to produce in an analogous way multimode non-classical light, or amplify images in the cw regime, one must use optical cavities having transverse degenerate modes, such as planar, confocal or semi-confocal cavities. ENS, in collaboration with INFM for the theoretical part, has undertaken the study of such devices.
At the beginning of the QUANTIM project, they showed that they were able to produce complex optical patterns on the signal and idler modes that were correlated at the quantum level even though they had different shapes, and they ascertained the multimode character of these patterns at the quantum level. When operating in the frequency degenerate mode, the system was then shown to amplify weak images in a phase sensitive way, with a maximum gain of approximately 3, and to generate a quantum correlation between its two polarisation components.
It has been known for a long time, and experimentally demonstrated, that the sensitivity of optical measurements performed on the global intensity, or on the global phase, of a light beam can be improved by using single mode non-classical states of light, such as sub-Poissonian or squeezed states. This is no longer true for measurements performed in optical images, in which one only monitors a change in the transverse distribution of the light.
Just before the beginning of the project, ENS had shown theoretically that the simplest of these measurements, that of the position of the centre of a beam, could be also improved beyond the standard quantum limit by using a multi-mode non-classical light, namely the mixing of a Gaussian coherent beam with a squeezed vacuum state in a transverse mode of specific shape. This mixing actually creates a perfect quantum correlation between the intensities measured on the different pixels of the detector. During the QUANTIM project this effect was experimentally demonstrated, in a common work between ENS and the ANU (Canberra, Australia), using the very efficient squeezed light generators developed at ANU.
In a first experiment, ENS and ANU were able to improve the measurement of the displacement in a given direction of the transverse plane of a 0.5 mm diameter beam well below the standard quantum noise limit, at the angstrom level, using a split detector and a two-mode non-classical light. In a second experiment, using a quadrant detector and a three-mode non-classical light, they could measure simultaneously the two transverse coordinates of the beam centre below the standard quantum noise limit.
Meanwhile the theoretical understanding of such measurements in images advanced, and the transverse mode responsible for the noise in a measurement of any quantity derived from the combination of the intensities measured on different pixels was identified. This opens the possibility of improving many image processing and analysis functions, such as pattern recognition, image segmentation, or wavefront analysis.
The idea of entangled two-photon imaging (ghost imaging") was conceived some time ago by Klishko and inspired a number of beautiful experiments in the mid nineties. As is well known, spontaneous parametric down-conversion consists of an emission of correlated pairs of signal and idler photons. One inserts in the signal arm an object that one intends to observe. The image of this object is obtained in a rather paradoxical way, without using a pixellised detector, but instead a single, non imaging, detector on the signal beam.
On the other hand, one inserts a pixellised detector (i.e. a camera) in the idler arm where there is no object. The entangled imaging technique realizes the observation of the object by detecting the coincidences between the measured photons on the signal and idler beams. The BU group gave, at the beginning of this project, a comprehensive theory of this phenomenon which allowed INFM and BU to make further progress in its understanding. It was for example shown by INFM that one could also produce the same imaging in the continuous variable regime, i.e. by using the correlation between photocurrents, and that both the near field and the far field images could be imaged in the same experimental set-up. Following R. Boyd's experiment which was able to obtain a near field image using classically correlated beams, and not twin photons, a lively worldwide discussion started on the precise assignment of classical and quantum features in "two-photon imaging".
These investigations led INFM to a very surprising and spectacular result: the discovery that the same imaging technique could be made, both in the near field and in the far field, by using classical correlated beams, such as a thermal beam divided in two parts on a beam splitter, instead of quantum correlated beams.
In the spring of 2004, the INFM group succeeded in making an experiment demonstrating the reconstruction of the image, both in the near and far field, in a ghost imaging scheme based on the classical correlation between two thermal-like light beams.
In the domain of single mode light described by continuous variables (field quadratures), specific quantum information protocols have been proposed, then experimentally implemented, such as quantum cryptography, quantum teleportation or quantum dense coding. One of the aims of the QUANTIM project was to investigate how these protocols could be extended into the domain of images, and in which respect the intrinsic parallelism peculiar to imaging could be used in these protocols. PHLAM, and especially the Saint Petersburg group, subcontractor of PHLAM, in collaboration with INFM, has extensively studied this problem.
They have shown how to prepare in an optimal way a spatially multimode entangled beam, which is the extension to the image problem of the EPR correlated state needed in the single mode teleportation, and how to use a pixellised detection and modulation scheme to exactly imprint, both in phase in amplitude, any input image on a different output beam.
The scheme has indeed a lot of similarities with the usual holographic technique, with the advantage that, in the quantum teleportation scheme, no quantum noise is added by the image reproduction device. A similar analysis is currently made for the problem of dense coding
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