In our recent Letter [1] we proposed the use of ac-driven double quantum dots as bipolar spin filters. As described in the Letter, an important requirement in order to have spin-dependent pumping and filtering is to break the spin degeneracy by means of an external magnetic field. While this breaking of degeneracy is effective for one-electron and two-electron states, there are remaining degeneracies in the three-electron sector which were not considered. Importantly, the degeneracy between the three-electron states (L # , R T ), one electron down in the left dot and the triplet T "" in the right dot, and (L " , R T 0 ) one electron up in the left dot and the triplet T 0 1= 2 p "# #" in the right dot, is not broken if L z R z , L z , and R z being the Zeeman splitting in each dot. We erroneously omitted the second state, (L " , R T 0 ), in our density matrix calculation and, as a result, our claim that the current at the frequency ! " is fully spin-up polarized is incorrect. The rest of the results or conclusions of the Letter remain valid.We have performed new calculations including the triplet T 0 and found that the spin-up polarization, P " I " =I " I # , at ! ! " is P " 70% for L z = R z 1. Full spin-up polarization can be recovered by introducing inhomogeneities in the Zeeman splitting, L z Þ R z . In particular, we recover P " 100% for L z = R z 0:6. We thank Tristan Meunier and Bjoern Trauzettel for pointing this oversight out to us.[1] E. Cota, R. Aguado, and G. Platero, Phys. Rev. Lett., 94, 107202 (2005).

Recently it has been shown that ac-driven double quantum dots can act as spin pumps and spin filters. By calculating the current through the system for each spin polarization, by means of the time evolution of the reduced density matrix in the sequential tunneling regime (Born-Markov approximation), we demonstrate that the spin polarization of the current can be controlled by tuning the parameters (amplitude and frequency) of the ac field. Importantly, the pumped current as a function of the applied frequency presents a series of peaks which are uniquely associated with a definite spin polarization. We discuss how excited states participating in the current allow the system to behave as a bipolar spin filter by tuning the ac frequency and intensity. We also discuss spin relaxation and decoherence effects in the pumped current and show that measuring the width of the current vs frequency peaks allows to determine the spin decoherence time T2.

We propose and analyze a new scheme of realizing both spin filtering and spin pumping by using ac-driven double quantum dots in the Coulomb blockade regime. By calculating the current through the system in the sequential tunneling regime, we demonstrate that the spin polarization of the current can be controlled by tuning the parameters (amplitude and frequency) of the ac field. We also discuss spin relaxation and decoherence effects in the pumped current.

We study the role of dissipation and structural defects on the time evolution of quantum dot arrays with mobile charges under external driving fields. These structures, proposed as quantum dot cellular automata, exhibit interesting quantum dynamics which we describe in terms of equations of motion for the density matrix. Using an open system approach, we study the role of asymmetries and the microscopic electron-phonon interaction on the general dynamical behavior of the charge distribution (polarization) of such systems. We find that the system response to the driving field is improved at low temperatures (and/or weak phonon coupling), before deteriorating as temperature and asymmetry increase. In addition to the study of the time evolution of polarization, we explore the linear entropy of the system in order to gain further insights into the competition between coherent evolution and dissipative processes.

We study the pumping of spin-polarized electrons in a double quantum dot system with up to two electrons per dot, via an applied AC field and a constant magnetic field. The behaviour of the current through the double-dot system is studied as a function of the AC field and coupling to the leads, using a Markov master equation approach for the time evolution of the reduced density matrix. For up to two electrons in the system, we find that the formation of a spin-triplet state blocks the current through the device, and analyse possible solutions. When we incorporate three-and four-particle states, with up to two opposite spin electrons per dot, we find a regime where the pumping of spin-polarized electrons is realized through double occupancy states in each dot. This property is robust against spin-relaxation and decoherence processes which are taken into account phenomenologically. Finally we study the effects of applying a pulsed AC field and the possibility of the resolution of Rabi oscillations.