Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

Abstract

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor 𝜃 and relative coupling strength R=g 1/g 2 on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ a ),C(ρ f ),S(ρ a )) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate 𝜃 and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.