Unconventional Geometric Quantum Phase Gate for Trapped Ions Based on the Squeeze Operator

A scheme for generating a geometric phase gate (GPG) with the squeeze operator is proposed in a system of trapped ions by using two standing wave lasers illuminating two ions simultaneously. A geometric phase is acquired by using a vibration mode undergoing a cyclic squeezing process in the phase space. This scheme gives an alternative effective way for a GPG in trapped ions, and it is realizable with current experimental techniques.