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We theoretically explore the possibility of creating spin entanglement bysimultaneously coupling two electronic spins to a nuclear ensemble. Bymicroscopically modeling the spin ensemble with a single mode boson field, weuse the time-dependent Fr\"{o}hlich transformation (TDFT) method developed mostrecently [Yong Li, C. Bruder, and C. P. Sun, Phys. Rev. A \textbf{75}, 032302(2007)] to calculate the effective coupling between the two spins. Ourinvestigation shows that the total system realizes a solid state basedarchitecture for cavity QED. Exchanging such kind effective boson in a virtualprocess can result in an effective interaction between two spins. It isdiscovered that a maximum entangled state can be obtained when the velocity ofthe electrons matches the initial distance between them in a suitable way.Moreover, we also study how the number of collective excitations influences theentanglement. It is shown that the larger the number of excitation is, the lessthe two spins entangle each other.Comment: 8 pages, 4 figure

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Creation of entanglement between two electron spins induced by many spin ensemble excitations