Tunable Nongeometric Phase Gates for Two Hot Ions via Adiabatic Evolution of Dark States

We propose a scheme for implementing nongeometric phase gates for two trapped ions via adiabatic passage of dark states. During the operation, the vibrational mode is only virtually excited, thus the scheme is insensitive to heating. Furthermore, the spontaneous emission is suppressed since the ions are always in the electronic ground states. The scheme is robust against small fluctuations of parameters, and the conditional phase is tunable.