Cavity Carving of Atomic Bell States

Abstract

We demonstrate entanglement generation of two neutral atoms trapped inside an optical cavity. Entanglement is created from initially separable two-atom states through carving with weak photon pulses reflected from the cavity. A polarization rotation of the photons heralds the entanglement. We show the successful implementation of two different protocols and the generation of all four Bell states with a maximum fidelity of (90 ± 2)%. The protocol works for any distance between cavitycoupled atoms, and no individual addressing is required. Our result constitutes an important step towards applications in quantum networks, e.g. for entanglement swapping in a quantum repeater.Entanglement is a central ingredient of quantum physics. It was long debated until groundbreaking experiments with entangled photons [1,2] Here we follow this proposal and show entanglement of two atomic qubits within one cavity QED node from which photons are reflected and detected with polarization-sensitive counters. As the scheme is insensitive to fluctuating photon numbers, we employ weak coherent laser pulses and use photon detection as a herald. Combined with atomic state rotations, we produce entangled states from an initially separable atom pair state, and show the creation of all four maximally entangled Bell states. Our scheme features several distinct advantages that distinguish it from other entanglement schemes [8,9,18,19]. Most notably, the interaction strength between two atoms coupled to the optical cavity does not depend on distance. Also, individual addressing of the two atoms is not required, rendering the technique robust, e.g., against focusing and pointing errors of the laser used for atomic state rotations. Moreover, the entangling protocol is fast, limited only by the duration of the atomic state rotation and the light pulses. The minimum pulse duration is determined by the cavity linewidth.Following [20], we call our technique carving. An initially separable state of two atoms undergoes a common projective measurement with probabilistic outcome. For an appropriately chosen projection subspace, the part of a two-atom wavefunction in that subspace can be entangled. If the measurement yields the orthogonal outcome, the atoms are not entangled and the attempt will cos (θ/2)|↑ j − e iφ sin (θ/2)|↓ j are coherent spin states defined by the spherical coordinates θ and φ on the generalized Bloch sphere. The initial distribution (left sphere) is rotated around the y-axis (middle sphere) before the |↓↓ and |↑↑ components are carved out. After the carving step, the poles are not populated anymore and the maximally entangled Bell-state |Ψ + is prepared (right sphere). The color code is normalized on each sphere and Q increases from dark to bright. be discarded. Specifically, each of the two atoms carries a qubit encoded in the states |↑ and |↓ . Starting with an initially separable two-atom state |↓↓ , a global π/2 rotation prepares 1 2 (|↑↑ − |↑↓ − |↓↑ + |↓↓ ). A projective measurement ("carving") allows us to probabilistically re...

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