In this paperwe propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques and currently developed approaches of phase control, a feasible proposal for implementation of a geometric phase gate is presented, where the conditional phase shift (Berry phase) is achieved by adiabatically and cyclically changing the parameters of the driving fields. Here we find that the geometric phase acquired is related to the way how the relative phase is modulated. In the second scheme, the system Hamiltonian is adiabatically changed in a noncyclic manner, so that the acquired conditional phase is not a Berry phase. A detailed analysis of the experimental feasibility and the effect of decoherence is also given. The proposed schemes provide new perspectives for adiabatic manipulation of interacting Rydberg systems with tailored phase modulation.
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