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Unformatted text preview: Implementations using optical lattices Hyochul Kim 1. Introduction Neutral atom is one of promising candidates for quantum information pro- cessing because they are very weakly coupled to the environment, so decoher- ence can be controlled well. Specially in Bose-Einstein condensation (BEC), it can be controlled in all quantum-mechanical degrees of freedom. All the atoms in BEC show identical quantum properties, so it is an ideal testing bed for fundamental quantum physics and quantum computing scheme. (1 , 2 , 3) 2. Optical traps for neutral atoms Optical lattices are periodic trapping potentials which are created by in- terference of traveling laser beams yielding standing laser waves in each direction. With three pairs of standing laser waves, three dimensional con- fined potential atomic trap can be realized. This potential comes from the interaction of the light field with the light-induced dipole moment of the atom, so called ac-Stark effect. This potential which traps the atom is proportional to the laser field intensity and inversely proportional to the detuning( = w- w ) of the laser light( w ) relative to the atomic transi- tion frequency( w ).when w > w , a repulsive potential is created while for w < w , an attractive potential is realized. 3. Superfluids and Mott insulators The behaviour of bosonic atoms with repulsive interactions in a periodic potential can be expressed through Bose-Hubbard hamiltonian H =- J <i,j> a + i a j + 1 2 U i n i ( n i- 1) a + i and a i describe the creation and annihilation operators for a boson on the i th lattice site and n i counts the number of bosons of the i th lattice site. J is a tunnel coupling between neighbouring potential wells and U is a repulsion between two atoms on a single lattice site. When the optical lattice is shallow, the kinetic energy dominates. This regime is called superfluid state, and Hamiltonian is H SF =- J <i,j> a + i a j 1 On the other hand, when the lattice potential is deep enough, barrier height is high, so we can only consider the interaction energy of two particles in the same lattice site. This regime is called Mott Insulating limit....
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- Fall '09