Perfect pattern formation of neutral atoms in an addressable optical lattice

We propose a physical scheme for formation of an arbitrary pattern of neutral atoms in an addressable optical lattice. We focus specifically on the generation of a perfect optical lattice of simple orthorhombic structure with unit occupancy, as required for initialization of a neutral atom quantum computer. The scheme employs a compacting process that is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that selectively moves the atoms in one internal state along the lattice principal axis. Realizations of these elementary operations and their physical limitations are analyzed. The complexity of the compacting scheme is analyzed and we show that this scales linearly with the number of lattice sites per row of the lattice. Neutral atoms trapped in an optical lattice constitute an attractive system for implementation of scalable quantum computation f1-3g, simulation of many-body systems f4g, and implementation of topological quantum computing f5-9g. In standard optical lattices, small lattice constants present a serious obstacle to implementing quantum compu- tation, since it is difficult to address individual qubits with an external field. An optical lattice with a large lattice constant is in principle addressable, and can allow for the quantum state manipulation of individual atoms by an optical field. High addressability and controllability and low decoherence make addressable lattices promising candidates for large- scale quantum computer implementation. The present work focuses on preparation of the initializa- tion of an addressable optical lattice for the purposes of quantum computing. The objective is a perfectly filled, regu- lar optical lattice, with each site occupied by a single atom in its motional ground state and in a specific internal state. We consider one-dimensional s1Dd, orthorhombic two- dimensional s2Dd, and three-dimensional s3Dd lattices. After loading and laser-cooling atoms in the optical lattice, half the sites have a single atom and half are vacant. In order to use this system for scalable quantum computation, a perfect lat- tice with each site occupied by a single atom is required. We propose here an efficient, feasible scheme forcompacting the optical lattice, i.e., for removing vacant sites to the edge of the lattice, thus creating a smaller lattice, but one more suit- able for quantum computation. The scheme presented here can as well be used to make arbitrary patterns of neutral atoms in an addressable optical lattice. These include lattices with fractional occupation, a specific translational and rotational lattice symmetry, a bro- ken symmetry, and heteroatomic patterns. Another important property of the scheme is that it can be applied recursively to reach any desired accuracy of the pattern formation. After a large number of elementary operations, the lattice can be cooled and imaged again. The remaining defects can be eliminated by repeating the compacting scheme. This recur- sion increases the total pattern formation time by the total duration of additional cooling and imaging cycles, but does not result in any increase in the scaling of the pattern forma- tion, i.e., the algorithmic complexity of the scheme is un- changed. The possibility of preparing any homoatomic or heteroatomic pattern of neutral atoms to an arbitrarily high degree of perfection makes this scheme attractive for initial- ization of quantum simulations of condensed phase systems, in addition to initialization of quantum computation.