Distributed manipulation of two-qubit entanglement with coupled continuous variables

We study the dynamics of two qubits separately sent through two coupled resonators, each initially containing a coherent-state field. We present analytical arguments and numerically approximate solutions for the qubit-field system under different two-qubit initial states, photon-hopping strengths, and detunings. In the far off-resonant regime, the maximal entanglement of two qubits can be generated with the initial qubit state in which one qubit is in the excited state and the other is in the ground state, and the initially maximal two-qubit entanglement can be frozen and fully revived even for large mean photon number. When the qubits are both initially in their excited states or ground states, qubit–qubit entanglement birth and death apparently appear in the regime where the photon-hopping strength is close to qubit-field detuning, and its peaks do not decrease monotonically as the interaction time increases. It is interesting to observe that when there is photon hopping between two fields, the field–field entanglement can be larger than 1 and increases as the initial amplitude of the coherent state grows. Our present setup is fundamental for distributed quantum information processing and applicable to different physical qubit-resonator systems.