Quantum Entanglement Of Trapped-ion Systems And Its Applications In Quantum Information

Ion trap has been widely used in various fields of scientific and technical re-searches. Especially, the technology of ion trap supplies experimental support forquantum computing and quantum communication theories, which implies importantapplications of the high technology. Since Cirac and Zoller proposed the scheme ofquantum computation in ion trap in 1995, the theoretical studying and experimen-tal exploring of quantum information processing in ion trap have obtained strikingachievements. Physical scientist in experiment can manipulate and control not onlythe internal electronic states, but also the external motional states with very highprecision by coupling the trapped ions to laser field, which makes trapped-ion sys-tem ideally suited for quantum computing, quantum communication and so on underwell-controlled conditions. In the thesis, we focus on the study of preparation of theentangled states, teleportation of unknown quantum states, quantum computation andpreparation of non-classical states in the trapped-ion systems. The main innovativeresults are as follows:1. A simple scheme is proposed to produce the GHZ state of three hot trapped ionsfor testing quantum nonlocality. The scheme can directly be generalized to producethe GHZ state of N hot trapped ions. The distinct advantages of the scheme are thatit is insensitive to heating of vibrational mode and there is no need to address singleion, which is of importance in the view of experiment. Furthermore, the scheme isvery simple, in the whole preparation process there is only one step.2. An effective scheme has been proposed to teleport an unknown single ionicinternal state and an unknown ionic entangled internal state in the trapped-ion system.The scheme can be generalized to teleport N-ion electronic entangled GHZ class state. The distinct advantages of the scheme are that it is insensitive to heating of vibrationalmode, Bell states (other entangled states) can be exactly distinguished via detectingthe ionic state(states) and the success probability for the teleportation can reach 1.3. In the system with a two-level ion confined both in a linear trap and in ahigh-Q single mode cavity, a simple scheme is presented to realize the basic two-qubit logic gates such as the quantum phase gate(QPG), the SWAP gate and thecontrolled-NOT(CNOT) gate beyond the Lamb-Dicke(LD) limit. Three kinds of two-qubit quantum phase gates are realized, i.e. the QPG operation involving the cavitymode as well as the vibrational mode of the trapped ion, the QPG operation involvingthe internal states as well as the vibrational mode of the trapped ion and the QPGoperation involving the internal states of the trapped ion as well as the cavity mode.Neither the LD approximation nor the auxiliary atomic level is needed in the scheme.The logic gates involving the cavity mode as well as the vibrational mode of the trappedion is insensitive to spontaneous emission and the logic gates involving the internalstates as well as the vibrational mode of the trapped ion is insensitive to the decay ofthe cavity, which is an important feature for the practical implementation of quantumcomputing. Experimental feasibility for achieving the scheme is also discussed.4. A simple and efficient scheme is proposed to generate two-mode nonclassicalstates of a quantum system, which is composed of the one-dimension trapped-ionmotion and a single-cavity field mode. The two-mode nonclassical states include two-mode SU(2) Schrodinger-cat states, entangled coherent states, and the squeezed catstates. The distinct feature of the scheme is that it operates in the strong-excitationregime(Ω＞＞ν), which greatly enhance operation speed.5. A fast procedure is presented to produce the quantum-interference states forthe collective motion of N trapped ions using a single standing-wave field resonant with the ionic carrier frequency. The distinct feature of the scheme is that the numberN of the trapped ions in principle may be an arbitrary integer, the required time onlylhnited by the available laser intensity. In addition, as long as the field is spatiallyhomogeneous over the trapped ions, the only parameter that depends on N, in themodel, is the time the laser pulse is applied. Thus the scheme should help to buildlarger mesoscopic quantum superposition in trapped ions, to study experimentallydecoherence proceasses.