Controlling the higher dimensional entanglement between light and cold atoms

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Higher-dimensional bipartite entangled states enable us to achieve more efficient quantum information processing, for example by enhancing optical data traffic in quantum communications compared to usually employed two-dimensional entanglement between qubits. Such higher-dimensional entangled states can be created by using Laguerre-Gaussian (LG) modes, since photons in LG modes carry orbital angular momenta (OAM) which can be utilized to define an infinite-dimensional Hilbert space. Inspired by the pioneering experiment using parametric down-conversion (PDC), various protocols have been demonstrated using the OAM states of photons. However, PDC is a spontaneous process and the generation time of the entangled photons is completely random. Producing higher-dimensional entanglement between two remote long-lived massive atoms is therefore an important step toward the realization of intricate tasks of quantum information. Here, as the first step, we demonstrated higher dimensional entanglement of OAM states between a collective atomic excitation and a photon. Schmidt number for the atom-photon system was estimated to be 3 through the quantum tomography, which means the system was entangled in 3 X 3 dimensional Hilbert space.