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arXiv:quant-ph/0402043 · International Journal of Quantum Information

ANTINORMALLY ORDERED PHOTODETECTION OF CONTINUOUS-MODE FIELD

Koji Usami, Akihisa Tomita, Kazuo Torii Nakamura

Published Mar 1, 2004• 3 citations
arXivHTMLPDF

Abstract

When the electromagnetic field is detected by stimulated emission, rather than by absorption, antinormally ordered photodetection can be realized. One of the distinct features of this photodetection scheme is its sensitivity to zero-point fluctuation due to the existence of the spontaneous emission. We have recently succeeded in experimentally demonstrating the antinormally ordered photodetection by exploiting nondegenerate stimulated parametric down-conversion process. To properly account for the experiment, the detection process needs to be treated with time-dependent and continuous-mode operators because of the broadband nature of the parametric down-conversion process and the wide spectrum of the pump that we used. Here, we theoretically analyze the antinormally ordered intensity correlation of the continuous-mode fields by pursuing the detection process in the Heisenberg picture. It is shown that the excess positive correlation due to zero-point fluctuation reduces because of the frequency-distinguishability of the two emitted photon pairs.

DOI
10.1142/s0219749904000110

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When the electromagnetic field is detected by stimulated emission, rather than by absorption, antinormally ordered photodetection can be realized. One of the distinct features of this photodetection scheme is its sensitivity to zero-point fluctuation due to the existence of the spontaneous emission. We have recently succeeded in experimentally demonstrating the antinormally ordered photodetection by exploiting nondegenerate stimulated parametric down-conversion process. To properly account for the experiment, the detection process needs to be treated with time-dependent and continuous-mode operators because of the broadband nature of the parametric down-conversion process and the wide spectrum of the pump that we used. Here, we theoretically analyze the antinormally ordered intensity correlation of the continuous-mode fields by pursuing the detection process in the Heisenberg picture. It is shown that the excess positive correlation due to zero-point fluctuation reduces because of the frequency-distinguishability of the two emitted photon pairs.
We have measured antinormally ordered Hanbury Brown-Twiss correlations for coherent states of the electromagnetic field by using a stimulated parametric down-conversion process. Photons were detected by stimulated emission, rather than by absorption, so that the detection responded not only to actual photons but also to zero-point fluctuations via spontaneous emission. The observed correlations were distinct from normally ordered ones as they showed excess positive correlations, i.e., photon bunching effects, which arose from the thermal nature of zero-point fluctuations.
In a recent paper [I. I. Arkhipov, Phys. Rev. A 98, 021803 (2018)], it was shown that one can completely identify the nonclassicality of single- and two-mode Gaussian states by means of certain nonclassicality witnesses which are based on intensity moments up to the third order of optical fields, provided that an appropriate coherent displacement is applied to a given Gaussian state. Here, we utilize a mathematical equivalence between the description of the coherent displaced Gaussian states generated in the spontaneous parametric processes and the Gaussian states generated in the corresponding stimulated parametric processes. Resorting to that equivalence, we study and compare the power of those nonclassicality witnesses in the detection of the nonclassicality of the two-mode Gaussian states generated in both the spontaneous and stimulated second subharmonic and down-conversion processes and which are subsequently subject to a beam splitter. We demonstrate that by means of an appropriate induced stimulated emission, one can completely identify the nonclassicality of the considered Gaussian states in comparison to the case of the spontaneous emission. This is important from the experimental point of view, as the stimulated emission can be easily implemented in running optical experiments, and such method can exploit just simple linear detectors.
The properties of a photon counter functioning by stimulated emission---rather than by absorption---of photons in an external field are examined. A possible scheme for such a quantum counter is described, and it is shown that correlation measurements performed with a number of quantum counters correspond to antinormally ordered products of field operators. These correlations, unlike the normally ordered ones, are always positive definite and depend explicitly on the number of radiation modes per unit volume to which the counter is coupled. It is shown that the antinormally ordered correlations carry useful information about the field only when the average photon occupation number per mode is large. A general expression for the probability that the quantum counter registers nnn counts in a certain time interval is derived and is shown to be related in an interesting way to the corresponding expression for the photoelectric detector. The variance of the probability distribution is evaluated for some simple states of the field.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the regime in which stimulation occurs at the single-photon level has hitherto remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by a weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we observe a clear enhancement that cannot be accounted for by spontaneous processes or accidental coincidences alone, and is consistent with stimulation involving the seed and the generated photon pair. These results provide time-domain evidence of seed-induced three-photon correlations and suggest new ways to engineer and probe multi-photon states for quantum imaging, sensing, and information processing.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the elementary physical mechanism of stimulation by individual photons has remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by an ultra-weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we access the regime in which the single-photon component of the seed can stimulate the emission of a photon pair, giving rise to a temporally correlated three-photon event. We observe a clear enhancement that cannot be explained by spontaneous processes or accidental coincidences alone, providing time-domain evidence of the fundamental stimulation mechanism at the single-photon level. Beyond its fundamental significance, these results suggest new ways to characterize seed–PDC mode overlap, phase matching, and weak nonlinear coupling in regimes where bright stimulated-emission measurements are not appropriate. Multimode and interferometric extensions could enable correlation-based imaging and phase-sensitive spectroscopy.