Quantum entanglement and transport in a non-equilibrium interacting double-dot system: the curious role of degeneracy

We study quantum entanglement and its relation to transport in a non-equilibrium interacting double dot system connected to electronic baths. The dynamical properties in the non-interacting regime are studied using an exact numerical approach whereas the steady state properties are obtained following the well-known non-equilibrium Green's function (NEGF) approach. By means of mutual information and concurrence we explore the connection between the quantum correlations in the system and the current flowing through the dots. It is observed that entanglement between the dots is heavily influenced by the degeneracy or the lack thereof, of the dot levels. In the non-degenerate case, the concurrence falls sharply when the applied bias crosses a certain critical value. In contrast when the dot energy levels are degenerate, the concurrence reaches a very high asymptotic value of 1/2. When interactions are switched on, the degeneracy is lifted, and once again concurrence falls to zero beyond a critical value of the applied bias. Lastly it is observed that the concurrence can be made to reach almost the value of 1.0 if the chemical potential in both baths are made very large (while keeping the sign the same) provided the dot levels are kept degenerate within the non-interacting limit. A combination of NEGF method, brute-force numerics and asymptotics are employed to corroborate our findings.