Quantum Entanglement Of The Atom And Superconducting Qubits Systems Interacting With The Field

Quantum information science is a new and interdisciplinary subject created by thecombination of quantum mechanics and information science. This information sciencefocus on the study of information encoding, transmission, processing and extraction bymeans of the quantum state. This field has become a hot area of physics research in recentyears. Quantum entanglement is one of the most striking features of quantum mechan-ics. In the field of quantum information, quantum entanglement, as a physical resource,plays an important role in quantum teleportation, quantum dense coding, entanglementswapping and quantum computing. Therefore, the research of quantum entanglement isof great theoretical significance and wide application prospects. This work is dedicated tothe study of entanglement swapping, quantum entanglement of the system describing theinteraction between atoms or superconducting qubit with quantized field, entanglementsudden death and the generation of entanglement. The main results are as follows:Entanglement swapping in two independent Jaynes-Cummings models has been in-vestigated and the feasibility of experimental realization has been addressed. The in-?uence of the initial state of the atom and the o?-resonant atom-field interaction on theatom-field, atom-atom entanglement and the occupation probabilities of the atom-atomstates has been examined. It is shown that one can directly infer the atom-atom entan-glement from the atom-field correlations in the case of resonance. At some interactiontimes, the maximally entangled state of two atoms can be obtained. The atomic coher-ence decreases the amount of entanglement between the atom and the field and the degreeof the atom-atom entanglement. Moreover, the large detuning decreases the degree of theatom-field entanglement.The property of linear entropy of the atom in k-photon JCM with the Stark Shift andKerr-like medium has been examined. The e?ects of the nonlinear Kerr effect and theStark shift on the dynamical behavior of the linear entropy have been investigated. Forthe field initially in coherent state, the linear entropy for two-photon transition evolvesperiodically. In the presence of Kerr-like medium the degree of entanglement betweenthe atom and the field decreases. When the field is initially in the even coherent state,the evolution period of the atomic linear entropy becomes comparatively smaller. Thise?ect results from the interference of quantum mechanical superposition of two coherent states. The effect of the Stark shift on the linear entropy is negative. In case of four-photontransition it is observed that in the absence of Kerr-like medium, the atom is completelydisentangled from the field at some interaction time. The atom and the field almost retaina partial entanglement in the time evolution process in the presence of Kerr-like medium.The temporal evolution of the linear entropy and concurrence of two superconduct-ing charge qubits interacting with quantized field has been investigated. It is shown thatthe linear entropy almost tends to zero at the half of the revival time where the two chargequbits are disentangled with the field. The relative phase of two qubits'levels decreasesthe degree of entanglement between the two qubits and the field. The more oscillationsof the linear entropy are observed when the field is initially in even coherent state. Thise?ect is due to the interference between the two coherent states in the superposition state.The long-living and maximum entanglement between the two qubits is obtained when therelative phase is equal toπ/2.The dynamical properties of entanglement between two two-level atoms that are s-patially separated from each other and pass through a thermal state or Fock state cavityone after another have been examined. In the case of thermal state cavity, we found thatthe entanglement between the two separable atoms is created when the two atoms are ini-tially in excited states. Moreover, the threshold time for the creation of the entanglementis dependent on the atomic coherence and becomes longer as the mean photon numberincreases. In the case of Fock state cavity, the threshold time for the creation of the en-tanglement is independent on the atomic coherence of the first atom. The threshold timebecomes shorter as the photon number increases. Moreover, we can observe the atomicmotion leads to the periodic evolution of the atom-atom entanglement and an increase inparameter p results in not only a shortening of the evolution period of the time behaviorof concurrence but also a decrease in the amplitude of the atom-atom entanglement.The system which consists of two identical two-level atoms trapped in spatially sep-arated cavities connected by an optical fiber has been examined. The e?ect of cavity-fibercoupling strength and the amplitude of the atom on the time evolution of entanglementhas been discussed. The entanglement between the two atoms exhibits the periodic be-havior with the time under the condition of the large cavity-fiber coupling strength limit.The threshold time and maximal entanglement for the creation of the entanglement canbe controlled by the cavity-fiber coupling strength. That is, it seems that the proposal mayprovide us with a potential way to control and manipulate the entanglement by changingcavity-fiber coupling strengths and the amplitudes of the atom. The entanglement dynamics between two atoms for one of them in a two-photonJaynes-Cummings cavity and the other isolated completely have been investigated. Thebiggest advantage of this model is that one can control the entanglement between atomsdue to the isolated atoms. The in?uence of the initial atomic states and the initial meanphoton number of the field on the time evolution of the atom-atom entanglement has beendiscussed. It is shown that the phenomenon of sudden death of entanglement occurs andthe length of the death time interval is independent of the initial state of the atoms. Theatom-atom entanglement exhibits periodic behavior at long time scale. The reason of thisbehavior is the periodicity of the matrix elements of the reduced density matrix.