We demonstrate the creation and characterization of multiparticle entangled states of neutral atoms with the help of a high finesse cavity.
Our experimental setup consists of a fibre-based high finesse cavity above the surface of an atom chip. It allows us to prepare an ensemble of 87Rb atoms with well-defined atom number. The atoms are trapped in a single antinode of an intracavity standing wave dipole trap and are therefore all equally coupled to the cavity mode. We present a scheme based on a collective, quantum non-destructive (QND) measurement and conditional evolution to create symmetric entangled states and to analyze them at the single-particle level by directly measuring their Husimi Q function. We use this method to create and characterize W states of up to 41 atoms. From the tomography curve of the Q function, we reconstruct the symmetric part of the density matrix via different reconstruction techniques and obtain a fidelity of 0.42.
Furthermore, we have devised an entanglement criterion which only relies on comparing two populations of the density matrix. We use it to infer the degree of multiparticle entanglement in our experimentally created states and find that the state with highest fidelity contains at least 13 entangled particles.