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arXiv:0903.2903 · Physical Review Letters

Measuring Qutrit-Qutrit Entanglement of Orbital Angular Momentum States of an Atomic Ensemble and a Photon

Ryotaro Inoue, T. Yonehara, Y. Miyamoto, Masato Koashi, Mikio Kozuma

Published Sep 11, 2009• 81 citations
arXivHTMLPDF

Abstract

Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into an ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.

DOI
10.1103/physrevlett.103.110503

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Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into an ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.
Controlling the orbital angular momentum state opens the door to the manipulation of arbitrarily large dimensional quantum state. Here we propose a new method to estimate the Schmidt number of the quantum state. The method enables us to avoid a problem appearing when we estimate the entanglement on the orbital angular momentum of photons using phase holograms. We also report the experimental results on the atoms-photon entanglement which was analyzed by the proposed method. Our experimental results show the possibility of controlling and entangling two remote massive atoms with higher dimensional basis.
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.
Twisted photons can in principle carry a discrete unbounded amount of orbital angular momentum (OAM), which are of great significance for quantum communication and fundamental tests of quantum theory. However, the methods for characterization of the OAM quantum states present a fundamental limit for miniaturization. Metasurfaces can exploit new degrees of freedom to manipulate optical fields beyond the capabilities of bulk optics, opening a broad range of novel and superior applications in quantum photonics. Here we present a scheme to reconstruct the density matrix of the OAM quantum states of single photons with all-dielectric metasurfaces composed of birefringent meta-atoms. We have also measured the Schmidt number of the OAM entanglement by the multiplexing of multiple degrees of freedom. Our work represents a step toward the practical application of quantum metadevices for the measurement of OAM quantum states in free-space quantum imaging and communications.
High-dimensional (HD) entanglement enables an encoding of more bits than in the two-dimensional case and promises to increase communication capacity over quantum channels and to improve robustness to noise. In practice, however, one of the central challenges is to devise efficient methods to quantify the HD entanglement explicitly. Full quantum state tomography is a standard technology to obtain all the information about the quantum state, but it becomes impractical because the required measurements increase exponentially with the dimension in HD systems. Hence, it is highly anticipated that a new method will be found for characterizing the HD entanglement with as few measurements as possible and without introducing unwarranted assumptions. Here, we present and demonstrate a scan-free tomography method independent of dimension, which only requires two measurements for the characterization of two-photon HD orbital angular momentum (OAM) entanglement. Taking Laguerre-Gaussian modes of photons as an example, the density matrices of OAM entangled states are experimentally reconstructed with very high fidelity. Our method is also generalized to the mixed HD OAM entanglement. Our results provide realistic approaches for quantifying more complex OAM entanglement in many scientific and engineering fields such as multiphoton HD quantum systems and quantum process tomography.