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Coherence conditions for groups of Rydberg atoms

We investigate the excitation of a collection of cold atoms to Rydberg states. By a direct numerical solution of Schrödinger's equation, we are able to compute various interesting properties of the many-body wavefunction. The high polarizability of Rydberg atoms allows them to support large dipole moments which in turn can interact with each other over long ranges. If the interaction energy between excited atoms is large enough, the resultant energy shift will move the two excitation states out of resonance, thus effectively blocking a two excitation state from occurring. One particular topic investigated is the quantum phase gate, where both groups of atoms are within a blockade radius Rb and subjected to a π − 2π − π sequence of pulses. We examine the regime where the groups are neither totally within nor totally outside the blockade radius. Our results explore the tolerance in variation of intergroup lattice distances for a series of quantum gates.