Quantum Logic Gates with Ion Trap in an Optical Cavity

The time evolution of ionic internal states for trapped cold ions interacting with external laser in a harmonic oscillator potential, and a potential with a small nonlinear component varying as x⁶, modeled through a q-deformed harmonic oscillator, is briefly discussed. The entanglement of ionic internal states and center of mass vibrational states results in collapse and revival of population inversion. For deformation parameter, τ = 0.004(q = e^τ), the population inversion shows an extremely well behaved collapse and revival pattern. Next a simple application where entanglement is used for implementing quantum logic gates with ion trap placed inside an optical cavity, is presented. It is found that faster ionic state manipulation times can be obtained by working beyond the Lamb-Dicke regime.