Fast quantum logic gates with trapped ions interacting with external laser and quantized cavity field beyond the Lamb-Dicke regime

A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic times, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of $\eta_{L}=\eta_{c}=0.2$, and is seen to decrease further with increase in number of initial state vibrational quanta $m$.