Entanglement Of The Coupled System Of Two Superconducting Quantum Bits And Binomial Optical Field

In recent years, quantum computation and quantum communication technology have been developed greatly. Based on the controlled quantum systems as hardware the quantum computing can be used to do scientific computing, quantum simulation and quantum information processing. Quantum computation is more advanced than classical computation. As the core component of the superconducting quantum devices, Josephson junction possesses a great potential in quantum information technology because of its integration, good controllability and the convenient to be embedded into the electronic circuits, good application prospects have been shown in quantum information technology. In addition, as the physical resource to realize quantum information, quantum entanglement plays an important role in the quantum state preparation, quantum communication, quantum encoding, quantum computation and so on. Nowadays, a lot of research on the coupling and entanglement between superconducting quantum bits and quantum optical field has been done, and some important progresses have been achieved.In this paper, we have mainly explored the entanglement evolution properties between the two charge quantum bits and the optical field of the interacting system of the two superconducting charge quantum bits coupled by a large Josephson junction and binomial optical field, and the entanglement properties between the two charge quantum bits.Firstly, we have studied the linear entropy evolution properties of the superconducting quantum bits of the interacting system of the two coupled superconducting charge quantum bits and binomial optical field. The obtained results show that, in the initial moment, two superconducting charge quantum bits in the maximally entangled state, and the optical field in the binomial field, when the two bits and the optical field began to interact, entanglement can immediately generate between the field and the bits, linear entropy will reach the maximum value gradually. Subsequently, the time evolution of the linear entropy begin to collapse and recover, at about the half time of the recovery cycle the linear entropy tends to zero, i.e. no entanglement between the two quantum bits and binomial optical field. With the increasing of the optical field parameters, the time evolution of the linear entropy begin to oscillate, as a whole the oscillations begin to move evenly, the maximum value of the linear entropy almost remains the same, but the duration of the maximum value become short. With the increase of the relative phase between the two charge quantum bits, the entanglement between the two bits and the optical field become weak, and the probability of the case of the two bits simultaneously in the excited state become small.Secondly, we have studied the time evolution of concurrence entanglement of the two superconducting charge quantum bits of the interacting system of the two coupled superconducting charge quantum bits and binomial optical field. The time evolution of entanglement between the two charge quantum bits shows oscillatory behavior, and the oscillation amplitude decreases with time; At some time, the concurrence entanglement of the two quantum bits is zero, i.e. no entanglement between the two quantum bits. With the increase of the optical field parameters, the time evolution of concurrence entanglement oscillates rapidly. For the two superconducting charge quantum bits, concurrence entanglement reach the corresponding peak values at the cross points of the excited state and ground state probability curve.