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We derive within a time-dependent scattering formalism expressions for both the current through ac-driven nanoscale conductors and its fluctuations. The results for the time-dependent current, its time average, and, above all, the driven shot noise properties assume an explicit and serviceable form by relating the propagator to a non-Hermitian Floquet theory. The driven noise cannot be expressed in terms of transmission probabilities. The results are valid for a driving of arbitrary strength and frequency. The connection with commonly known approximation schemes such as the Tien-Gordon approach or a high-frequency approximation is elucidated together with a discussion of the corresponding validity regimes. Within this formalism, we study the coherent suppression of current and noise caused by properly chosen electromagnetic fields.
The influence of an electron-vibrational coupling on the laser control of electron transport through a molecular wire that is attached to several electronic leads is investigated. These molecular vibrational modes induce an effective electron-electron interaction. In the regime where the wire electrons couple weakly to both the external leads and the vibrational modes, we derive within a Hartree-Fock approximation a nonlinear set of quantum kinetic equations. The quantum kinetic theory is then used to evaluate the laser driven, time-averaged electron current through the wire-leads contacts. This novel formalism is applied to two archetypical situations in the presence of electron-vibrational effects, namely, (i) the generation of a ratchet or pump current in a symmetrical molecule by a harmonic mixing field and (ii) the laser switching of the current through the molecule.
We study the current and the associated noise for the transport through a two-site molecule driven by an external oscillating field. Within a high-frequency approximation, the time-dependent Hamiltonian is mapped to a static one with effective parameters that depend on the driving amplitude and frequency. This analysis allows an intuitive physical picture explaining the nontrivial structure found in the noise properties as a function of the driving amplitude. The presence of dips in the Fano factor permits a control of the noise level by means of an appropriate external driving.
We investigate the influence of AC driving fields on the coherence properties of one- and two-qubit gate operations. In both cases, we find that for suitable driving parameters, the gate purity improves significantly. A mapping of the time-dependent system-bath model to an effective static model provides analytical results. The resulting purity loss compares favorably with numerical results.
We investigate the influence of a dipole interaction with a classical radiation field on a qubit during a continuous change of a control parameter. In particular, we explore the non-adiabatic transitions that occur when the qubit is swept with linear speed through resonances with the time-dependent interaction. Two classical problems come together in this model: the Landau-Zener and the Rabi problem. The probability of Landau-Zener transitions now depends sensitively on the amplitude, the frequency and the phase of the Rabi interaction. The influence of the static phase turns out to be particularly strong, since this parameter controls the time-reversal symmetry of the Hamiltonian. In the limits of large and small frequencies, analytical results obtained within a rotating-wave approximation compare favourably with a numerically exact solution. Some physical realizations of the model are discussed, both in microwave optics and in magnetic systems.
The noise properties of pump currents through an open double quantum dot setup with non-adiabatic ac driving are investigated. Driving frequencies close to the internal resonances of the double dot-system mark the optimal working points at which the pump current assumes a maximum while its noise power possesses a remarkably low minimum. A rotating-wave approximation provides analytical expressions for the current and its noise power and allows to optimize the noise characteristics. The analytical results are compared to numerical results from a Floquet transport theory.
We derive a master equation for the electron transport through molecular wires in the limit of strong Coulomb repulsion. This approach is applied to two typical situations: First, we study transport through an open conduction channel for which we find that the current exhibits an ohmic-like behaviour. Second, we explore the transport properties of a bridged molecular wire, where the current decays exponentially as a function of the wire length. For both situations, we discuss the differences to the case of non-interacting electrons.
We explore the possibility of inducing in heterostructures driven by an ac gate voltage the coherent current suppression recently found for nanoscale conductors in oscillating fields. The destruction of current is fairly independent of the transport voltage, but can be controlled by the driving amplitude and frequency. Within a tight-binding approximation, we obtain analytical results for the average current in the presence of driving. These results are compared against an exact numerical treatment based on a transfer-matrix approach.
We explore the prospects to control by use of time-dependent fields quantum transport phenomena in nanoscale systems. In particular, we study for driven conductors the electron current and its noise properties. We review recent corresponding theoretical descriptions which are based on Floquet theory. Alternative approaches, as well as various limiting approximation schemes are investigated and compared. The general theory is subsequently applied to different representative nanoscale devices, like the non-adiabatic pumps, molecular gates, molecular quantum ratchets, and molecular transistors. Potential applications range from molecular wires under the influence of strong laser fields to microwave-irradiated quantum dots.
Bistable quantum systems show in parameter regimes with mixed regular/chaotic dynamics a characteristic phenomenon: chaotic tunneling -- coherent transport between regular islands which are separated by a chaotic layer. In this process, quantum mechanical states which are localized in chaotic regions of phase space, serve as a bridge between regular regions. The fact that chaotic states are typically delocalized, results in enhanced tranport -- for the present case in larger tunneling rates. As the appropriate spectral feature, one finds crossings of chaotic singlets with regular (tunnel) doublets. The influence of dissipation and the related decoherence on this tunnel phenomenon is studied in this work. The harmonically driven double well potential served as a model. It turned out that chaotic tunneling is accompanyed by enhanced decoherence and that the dynamics involves by far more than two levels. In the long term limit it results in a staedy flow between all states whose mean energy is below the barrier. While the influence of the driving has been treated exactly within a Floquet formalism, it was for an efficient description of the dissipative effects neccessary to restrict ourselves to weak dissipation. The applicability of the approximations known from literatur, namely Born-Markov and rotating-wave approximation, has been investigated and a modyfied approach based on the Floquet theorem has been derived. Its quality has been studied by means of an exactly solvable model, the parameterically driven harmonic oscillator. For this model system we derived analytical solutions of the different master equations.
We consider the electron transport through driven tight-binding systems. For the theoretical description, a Floquet scattering approach and a Floquet master equation approach are derived. Both formalisms are particularly suited for the exact treatment of non-adiabatic driving. While the scattering approach describes coherent transport exactly, the master equation approach is suitable for a rather direct extension to the case of electron-phonon interaction. Moreover, we derive an expression for the corresponding transport noise which in the driven case depends on the phases of the transmission amplitudes. With these formalisms, we study different situations like the transport through driven molecular wires, the dynamics of coherent quantum ratchets, and the control of current and noise by ac fields.
Coherence control for qubits
(2006)
We study the influence of an external driving field on the coherence properties of a qubit under the influence of bit-flip noise. In the presence of driving, two paradigmatic cases are considered: (i) a field that results for a suitable choice of the parameters in so-called coherent destruction of tunneling and (ii) one that commutes with the static qubit Hamiltonian. In each case, we give for high-frequency driving a lower bound for the coherence time. This reveals the conditions under which the external fields can be used for coherence stabilization.
