Formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution

We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state. The structure is described by a two-level spinless Anderson model where the levels are coupled to two leads held at different chemical potentials. The problem is solved by a numerically exact hierarchical master equation technique and the results are compared to approximate ones obtained from Born-Markov theory. The methods allow us to study the time evolution up to times of order 104 of the bare hybridization time, enabling eludication of the role of the initial state on the transient dynamics, coherent charge oscillations and an interaction-induced renormalization of energy levels. We find that when the system carries a single electron on average the formation of the steady state is strongly influenced by the coherence between the dots. The latter can be sizeable and, indeed, larger in the presence of a bias voltage than it is in equilibrium. Moreover, the interdot coherence is shown to lead to a pronounced difference in the population of the dots.