The realization of Bose-Einstein condensation in a dilute vapour and the development of optical lattices have been among the highlights of the past decade in Atomic Physics. Merging these tools together opens up new possibilities in the coherent manipulation of the quantum state of matter.
This proposal focuses on engineering entangled states of a many-particle system, starting from neutral atoms in the quantum-degenerate regime trapped in the nodes of an optical lattice potential. Externally-controlled, spin-dependent transport is introduced as the key tool to manipulate individual quantum states, and its relevance for implementing a quantum walk algorithm is pointed out.
When supplemented with coherent collisions, this might allow to implement and study fundamental quantum gates with the specific goal to process quantum information across the lattice. Starting from the Moti state, maximally entangled states could be generated, which pose a challenge for both the experimentalist and the theorist on how to characterize them.
Finally, we describe how a Feshbach resonance can be used to speed-up the efficiency of quantum gates, and to engineer fundamental states of condensed matter, such as Laughlin states of the Quantum Hall Hamiltonian or a Tonks gas of impenetrable bosons.
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