Excitonic entanglement of protected states in quantum dot molecules

The entanglement of an optically generated electron-hole pair in artificial quantum dot molecules is calculated considering the effects of decoherence by interaction with environment. Since the system evolves into a mixed states and due to the complexity of energy level structure, we use the negativity as entanglement quantifier, which is well defined in $d \otimes d^\prime$ composite vector spaces. By a numerical analysis of the non-unitary dynamics of the exciton states, we establish the feasibility of producing protected entangled superpositions by an appropriate tuning of bias electric field, $F$. A stationary state with a high value of negativity (high degree of entanglement) is obtained by fine tuning of $F$ close to a resonant condition between indirect excitons. We also found that when the optical excitation is set approximately equal to the electron tunneling coupling, $\Omega/T_e \sim 1$, the entanglement reaches a maximum value. In front of the experimental feasibility of the specific condition mentioned before, our proposal becomes an useful strategy to find robust entangled states in condensed matter systems.