Optimizing the fast Rydberg quantum gate

The fast phase gate scheme, in which the qubits are atoms confined in sites of an optical lattice, and gate operations are mediated by excitation of Rydberg states, was proposed by Jaksch et al. [Phys. Rev. Lett. $85,$ 2208 (2000)]. A potential source of decoherence in this system derives from motional heating, which occurs if the ground and Rydberg states of the atom move in different optical lattice potentials. We propose to minimize this effect by choosing the lattice photon frequency $\omega ,$ so that the ground and Rydberg states have the same frequency-dependent polarizability $\alpha \left(\omega \right).\mathrm{}$ The results are presented for the case of Rb.