Entanglement Evolution in a Heisenberg Spin Dimer

The transitory and steady-state entanglement of a two-qubit XY Heisenberg magnetic spin system immersed in an external magnetic field are analyzed in terms of the entanglement measure of concurrence. The dependence of the system entanglement on coupling strength, decay rate, and applied magnetic field is numerically simulated for two distinct models of system evolution involving decoherence to the environment. An applied magnetic field was found to consistently reduce the system entropy. The external magnetic field increases entanglement for small strength, and if too strong, it reduces the entanglement. The maximum entanglement is formed from a balance of external magnetic field and the decay rate. The transitory level of entanglement in the system is found to oscillate with a frequency that is proportional to the magnetic field strength before reaching steady-state entanglement. It was found that collective decay produces more entanglement than individual decay.