Full Quantum Treatment of Rabi Oscillation Driven by a Pulse Train and Its Application in Ion-Trap Quantum Computation

Rabi oscillation of a two-level system driven by a pulse train is a basic process involved in quantum computation. We present a full quantum treatment of this process and show that the population inversion of this process collapses exponentially, has no revival phenomenon, and has a dual-pulse structure in every period. As an application, we investigate the properties of this process in ion-trap quantum computation. We find that in the Cirac-Zoller computation scheme, when the wavelength of the driving field is of the order 10^-6 m , the lower bound of failure probability is of the order 10^-2 after about 10² controlled-NOT gates. This value is approximately equal to the generally-accepted threshold in fault-tolerant quantum computation.