We propose a way to manifestly reduce the entropy of a finite system of atoms to arbitrarily small values. First, the locations of vacancies of laser-cooled atoms in a deep optical lattice are measured. Then, the distribution is efficiently compacted using a combination of site-specific atomic state nips and state-sensitive lattice site translations. In the final state, the central region of the lattice has exactly one atom per site in its vibrational ground state. This is a good initial state for a quantum computer. The process can be understood to be an experimentally viable Maxwell demon with a memory.
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