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arXiv:0804.3257 · Physical Review A

Spatial entanglement of paired photons generated in cold atomic ensembles

Clara I. Osorio, S. Barreiro, Morgan W. Mitchell, Juan P. Torres

Published Nov 3, 2008• 11 citations
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Abstract

Cold atomic ensembles can mediate the generation of entanglement between pairs of photons. Photons with specific directions of propagation are detected, and the entanglement can reside in any of the degrees of freedom that describe the whole quantum state of the photons: polarization, spatial shape, or frequency. We show that the direction of propagation of the generated photons determines the spatial quantum state of the photons and, therefore, the amount of entanglement generated. When photons generated in different directions are combined, this spatially distinguishing information can degrade the quantum purity of the polarization or frequency entanglement.

DOI
10.1103/physreva.78.052301

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Cold atomic ensembles can mediate the generation of entanglement between pairs of photons. Photons with specific directions of propagation are detected, and the entanglement can reside in any of the degrees of freedom that describe the whole quantum state of the photons: polarization, spatial shape, or frequency. We show that the direction of propagation of the generated photons determines the spatial quantum state of the photons and, therefore, the amount of entanglement generated. When photons generated in different directions are combined, this spatially distinguishing information can degrade the quantum purity of the polarization or frequency entanglement.
Recently, atomic ensemble and single photons were successfully entangled by using collective enhancement [D. N. Matsukevich et al., Phys. Rev. Lett. 95, 040405 (2005)], where atomic internal states and photonic polarization states were correlated in a nonlocal manner. Here, we experimentally clarified that in an ensemble of atoms and a photon system, there also exists an entanglement concerned with spatial degrees of freedom. Generation of higher-dimensional entanglement between remote atomic ensemble and an application to condensed matter physics are also discussed.
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.
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.
Correlated light generated from atomic ensembles can have a central role in prominent quantum information protocols, such as long-distance quantum communication. Here we present our studies on three topics involving the generation of correlated light with four-wave mixing (FWM) in a cold atomic ensemble for applications in quantum communications with high capacity. We experimentally investigate the generation of light with seeded FWM in cold cesium atoms and the time correlations of photon pairs generated with spontaneous FWM. We theoretically investigate the correlations in orbital angular momentum of photon pairs generated with spontaneous FWM for a range of experimental geometries. These studies represent foundational work toward the control and measurement of high-dimensional entanglement in the orbital angular momentum degree of freedom photon pairs for use in high-dimensional quantum communication.
We propose a scheme for transferring entanglement from one photonic degree of freedom to another through Raman interactions between a photon pair in cavity modes and atomic ensemble. The condition for deterministically generating the entanglement encoded in frequency or both frequency and polarization is obtained. The scheme could be immune to the photon loss originating from cavity-mode damping, spontaneous emission, and the dephasing due to atomic thermal motion. For current techniques, there are no major difficulties for this scheme to be realized experimentally.