Generation Of Quantum Entangled State

Quantum entanglement is one of the most striking features of quantum physics. Quantum entanglement is a potential resource for quantum information processing, and can be used to test basic problems in quantum mechanics. Quantum entanglement has many applications in both the fields of quantum communication and quantum computation. The two-qubit logic gate which realized quantum computation is usually the two-qubit controlled-not gate(CNOT). Quantum communication can be viewed as the generation, manipulation and measurement of distant entangled states. It is worth showing that it is just owing to the character of the quantum entanglement that the quantum computation and communication are superior to the classical ones. Therefore, qualitative and quantitative studying as well as generating quantum entangled state are quiet important and meaningful. So far there are extensive researches on the generation of quantum entangled state, which has been realized in many physical systems, such as photonic entanglement, entanglement between atoms and field through atom-field interaction, entangled state by capturing ions, entangled state in BEC (Bose-Einstein condensates), and entanglement among quantum spots and so on. This paper introduced and summarized the progress in atomic entangled state, light field entangled state as well as trapped-ion entanglement, and proposed maximal entanglement between two multilevel atoms, the W state of three-mode field entanglement, and the generation of GHZ state multi-field entanglement, as well as scheme about generating entanglement of trapped-ion system. The primary work is as follows: 1)Dynamical character of two four-level Ryberg atoms interacting with single mode light field is analyzed. By utilizing virtual excitation of a cavity field as well as excitation of additional classical field, a effective scheme is also proposed in order to generate a maximal entangled state of two four-level Reberg atoms in off-resonant cavity. Moreover, such a scheme can extend to generate maximal entangled state between two N-level Reberg atoms. When two atoms whose initial states are modified in advance pass the cavity field at the same time, the atoms are actually excited, but there isn't energy exchange between atoms and the field. In this way the quantum information held by the atoms doesn't lose. 2)Through studying dynamics of interaction between a single atom and multi cavity fields, a potential scheme generating GHZ state of multi cavity fields is put forward. Such a scheme, based on resonant interaction between a three-level atom and multi cavity fields, realized by controlling interactive time and measuring atomic state. This scheme can generate entangled GHZ state of multi fields by using not only V-type atoms but also Ξ-type atoms. 3)By investigating dynamics of interaction between a single atom and three-mode cavity field, a scheme is proposed for generating three-mode field W-state in a high-quality cavity without medium. On the basis of the interaction between a four-level atom and a three-mode field, the scheme comes true by controlling interactive time and measuring atomic final state. In addition, such a scheme can prepare W-state of multi-mode field. 4)A scheme is proposed in order to generating coherent state of random trapped-ion composed movement, which is linear distribution in phasic space. Furthermore, the scheme can be used to prepare maximal entangled GHZ state of any trapped-ions, and also realize a two-qubit phase-shift gate. The advantages of this scheme are as follows: it uses only one standing wave whose carrier-wave frequency causes ionic transition is used in this method, in addition all ions'locations are not confined to wave antinode, but everywhere. These advantages bring convenience in experiment. At the same time, the operation time can be short enough provided that laser with enough Rabi frequency is chosen.