Ultra-cold atoms trapped by light, with their robust quantum coherence and controllability, provide an attractive system for quantum information processing and for simulation of complex problems in condensed matter physics. Many quantum information processing schemes require that individual qubits be manipulated and deterministically entangled with one another, a process that would typically be accomplished by controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress toward this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. We have used an optical lattice of double-well potentials to isolate and manipulate arrays of paired atoms, inducing controlled entangling interactions within each pair. Our experiment is the first realization of proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation represents the first demonstration of the essential component of a quantum SWAP gate in neutral atoms. The half implementation of SWAP, the sqrt(SWAP) gate, is entangling, and together with single qubit rotations form a set of universal gates for quantum computation.
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