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

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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, show a sharp decline for a relatively large Lamb–Dicke parameter value of η L = η c =0.2, and are seen to decrease further with increase in number of initial state vibrational quanta m.