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arXiv:0807.0130 · Physical Review A

Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble

Qunfeng Chen, Bao‐Sen Shi, Yong-Sheng Zhang, Guang‐Can Guo

Published Nov 6, 2008• 92 citations
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Abstract

In this paper, we experimentally demonstrate that the photon pairs generated via spontaneous four-wave mixing in a hot atomic ensemble are in entangled orbital angular momentum (OAM) states. The density matrix of the OAM states of the photon pair is reconstructed, from which the fidelity to the maximal entangled state and the concurrence are estimated to be about 0.89 and 0.81, respectively. The experimental result also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.

DOI
10.1103/physreva.78.053810

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In this paper, we experimentally demonstrate that the photon pairs generated via spontaneous four-wave mixing in a hot atomic ensemble are in entangled orbital angular momentum (OAM) states. The density matrix of the OAM states of the photon pair is reconstructed, from which the fidelity to the maximal entangled state and the concurrence are estimated to be about 0.89 and 0.81, respectively. The experimental result also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
Constructing a quantum memory for a photonic entanglement is vital for realizing quantum communication and network. Because of the inherent infinite dimension of orbital angular momentum (OAM), the photon's OAM has the potential for encoding a photon in a high-dimensional space, enabling the realization of high channel capacity communication. Photons entangled in orthogonal polarizations or optical paths had been stored in a different system, but there have been no reports on the storage of a photon pair entangled in OAM space. Here, we report the first experimental realization of storing an entangled OAM state through the Raman protocol in a cold atomic ensemble. We reconstruct the density matrix of an OAM entangled state with a fidelity of 90.3%±0.8% and obtain the Clauser-Horne-Shimony-Holt inequality parameter S of 2.41±0.06 after a programed storage time. All results clearly show the preservation of entanglement during the storage.
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.
We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the down-converted photons. We investigate the two-dimensional state subspace defined by the OAM states ±ℓ and superpositions thereof, with ℓ=1, 2, ..., 30. We find that the reconstructed density matrix, even for OAMs up to around ℓ=20, is close to that of a maximally entangled Bell state with a fidelity in the range between F =0.979 and F =0.814. This demonstrates that, although the single count-rate diminishes with increasing ℓ, entanglement persists in a large dimensional state space.