Geometric phase gate based on the ac Stark shift

Abstract

We present an alternate derivation of the geometric phase gate based on the ac Stark shift for two qubits coupled to a shared cavity mode. Our derivation differs from the standard one in that the qubit---light coupling occurs purely as an ac Stark shift, rather than a state-dependent force. We derive expressions for the geometric phases induced on the qubit states arising from the displacement of coherent light. Simple analytic expressions are obtained for sinusodial driving of the cavity field.