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arXiv:1002.2043 · Physical Review A

Quantum-to-classical transition via fuzzy measurements on high-gain spontaneous parametric down-conversion

Chiara Vitelli, Nicolò Spagnolo, Lorenzo Toffoli, Fabio Sciarrino, F. De Martini

Published Mar 29, 2010• 32 citations
arXivHTMLPDF

Abstract

We consider the high-gain spontaneous parametric down-conversion in a noncollinear geometry as a paradigmatic scenario to investigate the quantum-to-classical transition by increasing the pump power, that is, the average number of generated photons. The possibility of observing quantum correlations in such a macroscopic quantum system through dichotomic measurement will be analyzed by addressing two different measurement schemes, based on different dichotomization processes. More specifically, we will investigate the persistence of nonlocality in an increasing size $\frac{n}{2}$-spin singlet state by studying the change in the correlations form as $n$ increases, both in the ideal case and in presence of losses. We observe a fast decrease in the amount of Bell's inequality violation for increasing system size. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about ${10}^{3}$. Our results shed light on the practical extreme difficulty of observing nonlocality by performing such a dichotomic fuzzy measurement.

DOI
10.1103/physreva.81.032123

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We consider the high-gain spontaneous parametric down-conversion in a noncollinear geometry as a paradigmatic scenario to investigate the quantum-to-classical transition by increasing the pump power, that is, the average number of generated photons. The possibility of observing quantum correlations in such a macroscopic quantum system through dichotomic measurement will be analyzed by addressing two different measurement schemes, based on different dichotomization processes. More specifically, we will investigate the persistence of nonlocality in an increasing size n2\frac{n}{2}2n​-spin singlet state by studying the change in the correlations form as nnn increases, both in the ideal case and in presence of losses. We observe a fast decrease in the amount of Bell's inequality violation for increasing system size. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about 103{10}^{3}103. Our results shed light on the practical extreme difficulty of observing nonlocality by performing such a dichotomic fuzzy measurement.
We analyze the high gain spontaneous parametric down‐conversion in a non collinear geometry as a paradigmatic scenario to investigate the observation of nonlocal properties when the size of the system is increased while keeping fixed the measurement resolution. We observe theoretically a fast decrease in the amount of Bell’s inequality violation when the number of particles is increased, due to the low resolution of the measurement apparatus. This theoretical analysis is supported by the experimental observation of macro‐macro correlations with an average number of photons of about 103. Our results enlighten the practical extreme difficulty of observing non‐locality by performing such a dichotomic fuzzy measurement.
We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic ``vacuum'' seed field. We analytically show that the second-order spatiotemporal correlations of the field generated from the DFG process replicate those of the signal field from SPDC. Specifically, for low gain, the model is consistent with the quantum calculation of the signal photon's reduced density matrix; and for high gain, the model's predictions are in good agreement with our experimental measurements of the far-field intensity profile, orbital angular momentum spectrum, and wavelength spectrum of the SPDC field for increasing pump strengths. We further theoretically show that the model successfully captures second-order SU(1,1) interference and induced coherence effects in both gain regimes. Intriguingly, the model also correctly predicts the linear scaling of the interference visibility with object transmittance in the low-gain regime---a feature that is often regarded as a quintessential signature of the nonclassicality of induced coherence. Our model may not only lead to fundamental insights into the classical-quantum divide in the context of SPDC and induced coherence, but can also be a useful theoretical tool for numerous experiments and applications based on SPDC.
We consider travelling-wave parametric down-conversion in the high-gain regime and present the experimental demonstration of the quantum character of the spatial fluctuations in the system. In addition to showing the presence of sub-shot noise fluctuations in the intensity difference, we demonstrate that the peak value of the normalized spatial correlations between signal and idler lies well above the line marking the boundary between the classical and the quantum domain. This effect is equivalent to the apparent violation of the Cauchy-Schwartz inequality, predicted by some of us years ago, which represents a spatial analogue of photon antibunching in time. Finally, we analyse numerically the transition from the quantum to the classical regime when the gain is increased and we emphasize the role of the inaccuracy in the determination of the symmetry center of the signal/idler pattern in the far-field plane.
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.
We consider travelling-wave parametric down-conversion in the high-gain regime and present the experimental demonstration of the quantum character of the spatial fluctuations in the system. In addition to showing the presence of sub-shot noise fluctuations in the intensity difference, we demonstrate that the peak value of the normalized spatial correlations between signal and idler lies well above the line marking the boundary between the classical and the quantum domain. This effect is equivalent to the apparent violation of the Cauchy–Schwartz inequality, predicted by some of us years ago, which represents a spatial analogue of photon antibunching in time. Finally, we analyse numerically the transition from the quantum to the classical regime when the gain is increased and we emphasize the role of the inaccuracy in the determination of the symmetry centre of the signal–idler pattern in the far-field plane.
Parametric down-conversion (PDC) is mostly known in the low-gain (spontaneous) regime, in which the correlated photon pairs are produced. Spontaneous PDC (SPDC) plays a very important role for quantum optics as a variety of quantum states is produced via SPDC. In the high-gain case PDC leads to generation of bright states having up to hundreds mW mean power. With such states almost any nonlinear optical interaction or light-matter interaction becomes more efficient. Even being macroscopically bright, the produced states maintain nonclassical properties as, for example, the fluctuations of electric field quadratures are squeezed below the shot-noise level. The high-gain PDC could be used not only in the same applications as SPDC, it also can provide new ones. Apart from that the high-gain PDC has many remarkable spectral and statistical properties, which are in the focus of this work. The description starts from the PDC generation in normal and anomalous group velocity dispersion ranges. The spectrum and mode content of high-gain PDC is considered as well as their change with the parametric gain are demonstrated. Then, there are the interference effects emerging from the PDC correlations presented, namely the macroscopic analogue of the Hong-Ou-Mandel interference. In addition, it is shown how spatial and temporal walk-off matching could be used for the generation of giant narrowband twin beams. Finally, the statistical properties of high-gain PDC are reviewed as well as their use for multiphoton effects is demonstrated. Photon-number fluctuations of PDC are studied via normalized correlation functions and probability distributions. These fluctuations enhance the generation efficiency for multiphoton effects by orders of magnitude and lead to tremendously fluctuating light described by heavy-tailed photon-number probability distributions.