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arXiv:quant-ph/0510153 · Physical Review A

Nonseparable Werner states in spontaneous parametric down-conversion

Marco B. Caminati, F. De Martini, Riccardo Perris, Fabio Sciarrino, Veronica Secondi

Published Mar 14, 2006• 24 citations
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Abstract

The multiphoton states generated by high-gain spontaneous parametric down-conversion (SPDC) in the presence of large losses are investigated theoretically and experimentally. The explicit form for the two-photon output state has been found to exhibit a Werner structure very resilient to losses for any value of the nonlinear gain parameter $g$. The theoretical results are found to be in agreement with experimental data obtained by ``entanglement witness'' methods and by the quantum tomography of the state generated by a high-$g$ SPDC.

DOI
10.1103/physreva.73.032312

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The multiphoton states generated by high-gain spontaneous parametric down-conversion (SPDC) in the presence of large losses are investigated theoretically and experimentally. The explicit form for the two-photon output state has been found to exhibit a Werner structure very resilient to losses for any value of the nonlinear gain parameter ggg. The theoretical results are found to be in agreement with experimental data obtained by ``entanglement witness'' methods and by the quantum tomography of the state generated by a high-ggg SPDC.
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Spontaneous parametric down-conversion (SPDC) is the most widely used method to generate higher-order Fock states ($n\ensuremath{\ge}2$). Yet, a consistent performance analysis from fundamental principles is missing. Here, we address this problem by introducing a framework for state fidelity and generation probability under the consideration of losses and multimode emission. With this analysis we show the fundamental limitations of this process as well as a trade-off between state fidelity and generation rate intrinsic to the probabilistic nature of the process. This identifies the parameter space for which SPDC is useful when generating higher-order Fock states for quantum applications. We experimentally investigate the multiphoton regime of SPDC and demonstrate heralded Fock states up to $|n\ensuremath{\rangle}=4$.
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.
A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.
The generation of entangled photons through spontaneous parametric down-conversion (SPDC) is a critical resource for many key experiments and technologies in the domain of quantum optics. Historically, SPDC was limited to the generation of photon pairs. However, the use of the strong nonlinearities in circuit quantum electrodynamics has recently enabled the observation of three-photon SPDC (3P-SPDC). Despite great interest in the entanglement structure of the resultant states, entanglement between photon triplets produced by a 3P-SPDC source has still not been confirmed. Here, we report on the observation of genuine tripartite non-Gaussian entanglement in the steady-state output field of a 3P-SPDC source consisting of a superconducting parametric cavity coupled to a transmission line. We study this non-Gaussian tripartite entanglement using an entanglement witness built from three-mode correlation functions, observing a maximum violation of the bound by 15 standard deviations of the statistical noise. Furthermore, we find strong agreement between the observed and the analytically predicted scaling of the entanglement witness. We then explore the impact of the temporal function used to define the photon mode on the observed value of the entanglement witness.