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      Propagation of Time-Nonlocal Quantum Master Equations for Time-Dependent Electron Transport

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          Abstract

          Time-resolved electron transport in nano-devices is described by means of a time-nonlocal quantum master equation for the reduced density operator. Our formulation allows for arbitrary time dependences of any device or contact parameter. The quantum master equation and the related expression for the electron current through the device are derived in fourth order of the coupling to the contacts. It is shown that a consistent sum up to infinite orders induces level broadening in the device. To facilitate a numerical propagation of the equations we propose to use auxiliary density operators. An expansion of the Fermi function in terms of a sum of simple poles leads to a set of equations of motion, which can be solved by standard methods. We demonstrate the viability of the proposed propagation scheme and consider electron transport through a double quantum dot.

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          Most cited references 19

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          Quantum Computation with Quantum Dots

          We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a newly derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments which would provide an initial demonstration of the desired non-equilibrium spin dynamics are proposed.
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            Driven coherent oscillations of a single electron spin in a quantum dot

            The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.
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              Time-dependent transport in interacting and non-interacting mesoscopic systems

              We consider a mesoscopic region coupled to two leads under the influence of external time-dependent voltages. The time dependence is coupled to source and drain contacts, the gates controlling the tunnel- barrier heights, or to the gates which define the mesoscopic region. We derive, with the Keldysh nonequilibrium Green function technique, a formal expression for the fully nonlinear, time-dependent current through the system. The analysis admits arbitrary interactions in the mesoscopic region, but the leads are treated as noninteracting. For proportionate coupling to the leads, the time-averaged current is simply the integral between the chemical potentials of the time-averaged density of states, weighted by the coupling to the leads, in close analogy to the time-independent result of Meir and Wingreen (PRL {\bf 68}, 2512 (1992)). Analytical and numerical results for the exactly solvable non-interacting resonant-tunneling system are presented.
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                Author and article information

                Journal
                01 March 2011
                Article
                1103.0185

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                15 pages, 4 figures
                cond-mat.mes-hall

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