Geometric phase gate with trapped ions in thermal motion by adiabatic passage

We propose a scheme for implementing two-qubit geometric phase gate via the adiabatic evolution for trapped ions in thermal motion, leveraging on the stimulated Raman adiabatic passage with the geometric phase mechanism. Evolution along a dark state makes our scheme not only immune from decoherence due to spontaneous emission from excited states, but also rid off the dynamical phase. Furthermore, due to the opposite detuning of the driving lasers, the vibrational states of the trapped ions are only virtually excited during the operations, so our scheme is also insensitive to the occupation number of the vibrational mode.