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arXiv:0804.2425 · New Journal of Physics

Spatiotemporal correlations in entangled photons generated by spontaneous parametric down conversion

Clara I. Osorio, Alejandra Valencia, Juan P Torres

Published Nov 10, 2008• 46 citations
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Abstract

In most configurations aimed at generating entangled photons based on spontaneous parametric down conversion (SPDC), the generated pairs of photons are required to be entangled in only one degree of freedom. Any distinguishing information coming from the other degrees of freedom that characterize the photon should be suppressed to avoid correlations with the degree of freedom of interest. However, this suppression is not always possible. Here, we show how the frequency information available affects the purity of the two-photon state in space, revealing a correlation between the frequency and the space degrees of freedom. This correlation should be taken into account to calculate the total amount of entanglement between the photons.

DOI
10.1088/1367-2630/10/11/113012

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In most configurations aimed at generating entangled photons based on spontaneous parametric down conversion (SPDC), the generated pairs of photons are required to be entangled in only one degree of freedom. Any distinguishing information coming from the other degrees of freedom that characterize the photon should be suppressed to avoid correlations with the degree of freedom of interest. However, this suppression is not always possible. Here, we show how the frequency information available affects the purity of the two-photon state in space, revealing a correlation between the frequency and the space degrees of freedom. This correlation should be taken into account to calculate the total amount of entanglement between the photons.
The generation of paired photons entangled in the spatial degree of freedom, i.e., in orbital angular momentum, offers a convenient physical resource to investigate the nature of entanglement in a multidimensional Hilbert space with controllable dimensionality. The two main physical processes that generate pairs of photons which show correlations in orbital angular momentum are (a) spontaneous parametric down-conversion (SPDC), and (b) Raman transitions induced in atomic ensembles. One question naturally arises: what kinds of correlations exist between the orbital angular momentum of the generated photons? The answer might be different if we consider the whole quantum state of the generated photons, i.e., all possible directions where the pairs of photons can be emitted, or if we consider only a small section of the full set of directions.
Entanglement generated by Spontaneous Parametric Down Conversion (SPDC) involves multiple, often mutually correlated degrees of freedom. These degrees of freedom are often treated independently, overlooking the intrinsic correlation between them. We focus on the spatial spectral correlations that, if left uncontrolled, introduce distinguishability and reduce coherence, undermining applications such as high-dimensional OAM encoding. We analyze the spatio spectral structure of the biphoton and identify source configurations enabling a strong reduction of such correlations. We then quantify how spatial spectral coupling degrades OAM spatial purity, mapping high-purity regions as functions of OAM order, crystal length, and pump/collection waists. The resulting design parameters enable engineering bright, high purity OAM entangled sources, reducing the need for loss-introducing filtering and therefore supporting scalable high-dimensional photonic quantum technologies.
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.
Here we report our efforts in the characterization and engineering of spatio-temporally [1] entangled photon states. We use photon pairs obtained from spontaneous parametric down-conversion (SPDC) and present a novel way to reconstruct the complex spectral wavefunction from information obtained in a two-dimensional Hong-Ou-Mandel experiment [2]. This represents a novel and straightforward way to access otherwise hidden information in the wavefunction. Furthermore, the choice of the detection mode gives us some control over the spatio-temporal structure of the wavefunction.
Spontaneous parametric down conversion (SPDC)-based sources of photonic entangled states are usually generated using coherent pump fields. For temporal, spatial, and polarization degree of freedom, the down-converted light entanglement is limited by the coherence of the pump in the same degree of freedom. However, the effect of pump coherence on the entanglement in a different degree of freedom remains largely unexplored. Here we experimentally demonstrate the generation of polarization entanglement from SPDC pumped by a light emitting diode (LED), a spatiotemporally incoherent pump. The two-photon state is found to have a concurrence of 0.562 and purity of 0.647.