  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.
