Optically pumping hole spins in coupled quantum dot molecules into a steady state of high concurrence entanglement

We present a way to prepare a high concurrence steady state entanglement of two hole spins in a quantum dot molecule. We show that the spontaneous dissipation can be used to induce and stabilize the entanglement with rapid rate. By optical pumping of trion levels, two-qubit singlet state can be automatically generated. We also show that our proposal can synchronously accomplish both initialization and entanglement generation. The effects of acoustic phonons and electron tunneling are also discussed and we find that the main influence is from deformation potential coupling to acoustic phonons in InAs/GaAs quantum dots. At low temperature, we show that concurrence of entanglement can be greater than 0.95 at T=1 K.