Studies On The Quantum Logic Gate With Potential Trap Ions+cavity Field System

Since the pioneering works of P.W.Shor and L.K.Grover, quantum computing has attracted much attention, the quantum computer can solve some problems much more efficient than classical computer. Some physical systems, such as nuclear magnetic resonan, cecavity quantum electron dynamics, coupled quantum dots, cold trapped ions. In the last few years, as the development of technology of CQED and the trapped ions, many efforts have been paid to combine the CQED and trapped-cold-ions. Indeed, there have been also a few experimental studies concerning the trapped ions in the optical cavity. These experimental developments imply that realizing quantum computing with the trapped-ion-cavity systems is feasible.In this paper we propose two kinds quantum computing scheme with two-level trapped ions without using the auxiliary atomic levels in a single cavity, we use two fifferent methods to realize quantum logic gates, in the experiment this two kinds scheme have their owe advantages. The first scheme is to use rotating wave approximation method to determine the effective Hamitonnian of the system, in this scheme it is the most important that the laser-ion interaction is beyond the Lamb-Dicke limit, witch helps reduce ion trap noise and improve the cooling rate. The second scheme is operated in the large-detuning regime, wherein the cavity field is only virtually excited. Thus, it is insensitive to the cavity decay, and greatly reduces the requirement for the quality factor of the cavity.Finally, in our two proposals two-qubit quantum phase gate, involving only two internal atomic levels of two trapped ions in a cavity, could be achieved by only one step operation, this is particularly important for the physical implementation of quantum computing. It is well-known that, due to the practical existence of decoherence, the more operation steps imply the longer the computing time. Therefore, it is a critical issue to cut down the number of operation steps during the quantum computing. Our proposed two scheme is experimental feasible, is more simple and effective.