Spin qubits based on interacting spins in double quantum dots have been demonstrated successfully. Readout of the qubit state involves a conversion of spin to charge information, which is universally achieved by taking advantage of a spin blockade phenomenon resulting from Pauli's exclusion principle. The archetypal spin blockade transport signature in double quantum dots takes the form of a rectified current. At present, more complex spin qubit circuits including triple quantum dots are being developed. Here we show, both experimentally and theoretically, that in a linear triple quantum dot circuit the spin blockade becomes bipolar with current strongly suppressed in both bias directions and also that a new quantum coherent mechanism becomes relevant. In this mechanism, charge is transferred non-intuitively via coherent states from one end of the linear triple dot circuit to the other, without involving the centre site. Our results have implications for future complex nanospintronic circuits.

We analyze coherent spin phenomena in triple quantum dots in triangular configuration under crossed dc and ac magnetic fields. In particular, we discuss the interplay between Aharonov-Bohm current oscillations, coherent electron trapping and spin blockade under two-electron spin resonance configurations. We demonstrate an unexpected antiresonant behaviour in the current, allowing for both removal and restoration of maximally entangled spin blockaded states by tuning the ac field frequency. Our theoretical predictions indicate how to manipulate spin qubits in a triangular quantum dot array. PACS numbers:Electronic transport through mesoscopic systems can become correlated not only by charge interaction but also by the spin degree of freedom. A dramatic combination of both can be found in systems where strong Coulomb interaction limits the population to a small number of electrons (Coulomb blockade) and where Pauli exclusion principle avoids certain internal transitions -spin blockade (SB). This was first observed as a rectification effect in the current through a double quantum dot (DQD) 1 . Recent experiments have taken advantage of SB to achieve qubit operations in a double dot by electric gate control 2 or by electron spin resonance (ESR) 3 . It consists in inducing transitions between the electron's spinup and spin-down states, which are splitted by the Zeeman energy coming from a dc magnetic field, B dc . Different mechanisms have been considered: crossed dc and ac magnetic fields (B ac ), where the ac frequency is resonant with the Zeeman splitting 4,5 , effective B ac induced by ac electric fields in the presence of spin-orbit interaction 6 , slanting Zeeman fields 7 or hyperfine interaction 8 .Lately, a next step towards quantum dot arrays has been reached: tunnel spectroscopy measurements with triple quantum dots (TQD), both in series 9 and in triangular configurations 10 have been achieved. Theoretical works in these systems 11,12 analyze their eigenstates and stability diagram, as well as the effect of a magnetic field penetrating the structure. TQDs with strongly correlated electrons have also been investigated in the Kondo regime 13 and have been proposed as spin entanglers 14 . Additionally, these systems show a more peculiar property which is intrinsic to three-level systems, namely coherent population trapping, which is a well-known effect in quantum optics and which was observed in threelevel atoms excited by two resonant laser fields 15 . There, the electronic wave function evolves towards an eigenstate superposition, a so-called dark state, which is decoupled from the laser fields and therefore it manifests as an antiresonance in the emission spectrum. An analogy in transport has been made when coherent superpositions avoid transport by interference between tunneling events. These dark states can be achieved by driv-FIG. 1: (Color online) Coherent processes in a triangular TQD, with one electron confined in the dot connected to the drain. ∆1 = ∆2 = ∆3, where ∆i is the Zeeman splitting in dot i. ...

We examine the low-energy physics of graphene in the presence of a circularly polarized electric field in the terahertz regime. Specifically, we derive a general expression for the dynamical polarizability of graphene irradiated by an ac electric field. Several approximations are developed that allow one to develop a semianalytical theory for the weak field regime. The ac field changes qualitatively the single and many electron excitations of graphene: undoped samples may exhibit collective excitations (in contrast to the equilibrium situation), and the properties of the excitations in doped graphene are strongly influenced by the ac field. We also show that the intensity of the external field is the critical control parameter for the stability of these excitations.

We analyze transport through both a double quantum dot and a triple quantum dot with inhomogeneous Zeeman splittings in the presence of crossed dc and ac magnetic fields. We find that strongly spin-polarized current can be achieved by tuning the relative energies of the Zeeman-split levels of the dots, by means of electric gate voltages: depending on the energy level detuning, the double quantum dot works either as spin-up or spin-down filter. We show that a triple quantum dot in series under crossed dc and ac magnetic fields can act not only as spin-filter but also as spin-inverter.

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