Two experiments that use nonlinear crystals to control the spatial distribution of photons in optical images bring the field of quantum imaging closer to maturity. Quantum information processing could ultimately benefit.
God, it seems, plays dice. Randomness lies at the root of many quantum effects: in the arrival times of the photons on a detector, for example; or, if the intensity is such that the photons cannot be distinguished individually, in the temporal fluctuations of the current generated in the detector by those photons. In the past two decades, physicists have found ways to tame this ‘quantum noise’, and to master, at least in some instances, the temporal distribution of photons.
Two papers now show that it is also pos-sible to control photons' spatial distribution. Writing in Physical Review Letters, Mosset and colleagues1 provide the first experimental demonstration of an optical device that amplifies an image without increasing the spatial distribution of where the photons hit. In a contribution to the same journal last year, Jedrkiewicz et al.2 used a similar device to produce two images with photons that are identically distributed in space.
Because of the quantum nature of light, the amplification of an optical signal is not a simple multiplication of the input signal by the gain. For very large gains, the signal-to-noise ratio at the output is a factor of two smaller than that at the input3. Fortunately, a special class of amplifiers that is not doomed to degrade the signal being amplified does exist. The ‘degenerate parametric amplifier’ is one of these (Fig. 1a). This amplifier consists of a crystal that responds in a nonlinear manner when it is subjected to an intense ‘pump’ beam, the electric field E of which varies cosinusoidally with time t as E=E0cos(πft). (E0 is the maximum amplitude of the wave, and f is the frequency of its oscillation.) An optical input signal at a frequency f/2 can be amplified while propagating in this crystal without changing the signal-to-noise ratio — that is, without degrading the quality of the information channel3. The drawback of this type of amplifier compared with a more conventional one is that it is ‘phase-sensitive’: only cosinusoidally varying fields of the form E=E0cos(πft) are amplified, whereas sinusoidally varying fields E=E0sin(πft) are attenuated.
The first experimental demonstration of this ‘noiseless amplification’ was made in 1993 for single-channel signals (those that have a single frequency and a fixed transverse shape), such as are used in optical telecommunications4, and in 1999 for signals of an arbitrary transverse shape — images5.
The novel aspect of the work of Mosset et al.1 is its emphasis on spatial, rather than temporal, quantum noise. Spatial quantum fluctuations appear only in images, not in single-channel signals. They are related to the degree of randomness that exists in the distribution of photons composing a beam of light carrying an image; this distribution is measured in the plane transverse to the direction of propagation. In essence, the authors show that images are not degraded by additional spatial quantum fluctuations when they are amplified by a degenerate parametric amplifier.
Mosset and colleagues used an intense pulsed laser as the pump beam for the nonlinear crystal of the amplifier, and took photographs of the amplified image during a single pulse. The output image, a slit of rectangular shape (Fig. 1b), exhibits strong spatial intensity fluctuations from one pixel to the next. To quantify the importance of this spatial noise, the authors took averages of it over the pixels composing the recorded image. They measured the signal-to-noise ratio in the image with and without amplification, and found that it was not degraded when the parametric amplifier was operated in the phase-sensitive regime; that is, when the field varied cosinusoidally.
This seemingly simple experiment posed many experimental challenges. Quantifying pixel-to-pixel fluctuations reliably at the quantum level, for example, requires delicate calibration and control of the spatial homogeneity of the detection system. Furthermore, the size of the pixels on which the spatial fluctuations are measured must be carefully adjusted.
Jedrkiewicz et al.2 had already used a nonlinear crystal to produce identical twin images by taking advantage of a process known as parametric down-conversion. This effect, in which a single incoming photon of the pump beam is split by a crystal into two photons whose combined energy and momentum is equal to that of the original photon, has featured in many spectacular quantum-optical experiments performed in the low-intensity regime, where photons can still be counted individually6. Jedrkiewicz and colleagues used a very intense pulsed laser as a pump, so that the twin photons generated could not be counted individually on each pixel of the detector. They showed that, even though the two generated images exhibited strong pixel-to-pixel quantum fluctuations, these fluctuations were identical in the two images. Their device thus produces twin images instead of twin photons.
The experiments of Mosset et al.1 and Jedrkiewicz et al.2 are notable achievements in the rapidly developing domain of quantum imaging7, which deals with the spatial ordering of photons, even in instances where a macroscopic, uncountable number of photons is produced. Other experiments8, using different techniques, have shown that photons inside a beam can be ordered four by four in the transverse plane, and that this kind of light can be used to improve the accuracy of beam positioning on the nanoscale.
Such studies open the way to the observation of a phenomenon known as spatial quantum entanglement9,10, which extends to images the entangled states that were introduced in a famous paper by Einstein, Podolsky and Rosen11. This specific quantum feature, in which two images form a single quantum object — even when they are very far away from each other — is a prerequisite for implementing quantum information protocols not only in time-varying signals, but also in an optical image considered as a quantum object in its own right. The pay-off, some time in the future, could be the development of highly parallel quantum-information processors.
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