We present a method to determine the decay of multiparticle quantum correlations as quantified by the geometric measure of entanglement under the influence of decoherence. With this, we compare the robustness of entanglement in Greenberger-Horne-Zeilinger ͑GHZ͒, cluster, W, and Dicke states of four qubits and show that the Dicke state is the most robust. Finally, we determine the geometric measure analytically for decaying GHZ and cluster states of an arbitrary number of qubits. The decoherence of quantum states is a process in quantum dynamics that is relevant for the discussion of fundamental issues like the transition from quantum to classical physics ͓1͔. Also from a practical point of view decoherence phenomena have to be studied as they occur in experiments involving entanglement and their suppression is of vital importance for any implementation of quantum information processing.Due to this importance, the influence of decoherence on the entanglement of multiparticle systems has been studied from several perspectives ͓2,3͔. These investigations concerned either the lifetime of entanglement or the entanglement properties of the bipartite system which arise if the multiparticle system is split into two parts. The lifetime of entanglement, however, gives no quantitative information about the decay of entanglement ͓3͔. Moreover, as a highly entangled multiparticle state may be separable with respect to each bipartition ͓4͔, considering bipartite aspects only may not lead to a full understanding of the decoherence process. It is therefore highly desirable to investigate a full multipartite entanglement measure under the influence of decoherence. Unfortunately, all known entanglement measures for multiparticle entanglement are defined via complicated optimization procedures ͓5͔, which makes it practically impossible to compute them for a given mixed quantum state.In this paper we present a method to investigate the decay of quantum correlations which can be used to overcome these difficulties. We study different four-qubit states and use our method to compare their robustness against decoherence, using a phenomenological model described below. Our approach allows us to compute the entanglement for Greenberger-Horne-Zeilinger ͑GHZ͒ and cluster states of an arbitrary number of qubits and thereby to investigate the scaling behavior for these states under decoherence. As we will further see, our results can be directly tested in nowadays experiments with photons or trapped ions. Finally, from the viewpoint of pure quantum information theory, our results represent one of the few cases where the computation of a relevant entanglement measure for mixed states can be performed ͓6͔.We consider the following situation: a pure quantum state ͉ ͘ is prepared at time t = 0 and in the presence of noise evolves to a mixed state ͑t͒. Our task is to quantitatively investigate the time evolution of the entanglement E͑t͒ = E͓ ͑t͔͒ and its dependence on the initial state and the number of qubits.As entanglement quantifier, we use t...

Semiconductor devices have been scaled to the point that transport can be dominated by only a single dopant atom. As a result, in a Si Fin Field Effect Transistor Kondo physics can govern transport when one electron is bound to the single dopant. Orbital (valley) degrees of freedom, apart from the standard spin, strongly modify the Kondo effect in such systems. Owing to the small size and the s-like orbital symmetry of the ground state of the dopant, these orbital degrees of freedom do not couple to external magnetic fields which allows to tune the symmetry of the Kondo effect. Here we study this tunable Kondo effect and demonstrate experimentally a symmetry crossover from a SU(4) ground state to a pure orbital SU(2) ground state as a function of magnetic field. Our claim is supported by theoretical calculations that unambiguously show that the SU(2) symmetric case corresponds to a pure valley Kondo effect of fully polarized electrons.PACS numbers: 71.27.+a, 71.30.+h, 73.23.Hk,72.15.Qm The resistance of metals with magnetic impurities anomalously increases as one decreases the temperature. This Kondo effect [1] can be explained as the screening of the localized spin of the magnetic impurity by the spins of the de-localized electrons in the metal. As a consequence of this screening, the localized spin and the itinerant ones form a many-body singlet with binding energy T K , which defines the low temperature scale at which Kondo physics appears. A few years ago, it was shown that quantum dots (QDs) [2] behave as Kondo impurities. The transport properties of QDs in the Kondo regime are quite remarkable: starting from an insulating QD in the Coulomb blockade regime at high temperatures, the linear conductance reaches the maximum unitary value of a perfect quantum conductor,2 /h as the temperature is reduced well below. At finite bias voltages V b , Kondo physics manifests as a zero-bias anomaly in the dI/dV b curves whose width is roughly given by T K . The Kondo effect in QDs originates from quantum fluctuations of the charge residing in the QD: electrons can transit through virtual states on a time-scale which is shorter than allowed by the Heisenberg uncertainty principle [1]. This mechanism generates effective spin flips which in turn lead to Kondo physics. Importantly, the role of the electron spin can be replaced by any other quantum degree of freedom such as e.g. orbital momentum [3][4][5][6][7][8][9], giving rise to exotic Kondo effects. Furthermore, the simultaneous presence of both a spin-and an orbital-degeneracy leads to an SU(4)-Kondo effect, where SU(4) refers to the symmetry of the corresponding Kondo ground state [3][4][5][6][7][8][9].In the past, SU(4) Kondo symmetry has been predicted to arise in parallel double quantum dot systems [3], but so far it has only been clearly observed in carbon nanotubes [5] and in single dopant devices in Si [9]. Si is a good candidate for observing SU(4) Kondo physics due to its six-fold valley (orbital) degeneracy of the conduction band and orbital effects are th...

The Kondo effect has been observed in a single gate-tunable atom. The measurement device consists of a single As dopant incorporated in a silicon nanostructure. The atomic orbitals of the dopant are tunable by the gate electric field. When they are tuned such that the ground state of the atomic system becomes a (nearly) degenerate superposition of two of the silicon valleys, an exotic and hitherto unobserved valley Kondo effect appears. Together with the "regular" spin Kondo, the tunable valley Kondo effect allows for reversible electrical control over the symmetry of the Kondo ground state from an SU(2) to an SU(4) configuration.

We derive a general scattering-matrix formula for the pumped current through a mesoscopic region attached to a normal and a superconducting lead. As applications of this result we calculate the current pumped through ͑i͒ a pump in a wire, ͑ii͒ a quantum dot in the Coulomb blockade regime, and ͑iii͒ a ballistic double-barrier junction, all coupled to a superconducting lead. Andreev reflection is shown to enhance the pumped current by up to a factor of 4 in the case of equal coupling to the leads. We find that this enhancement can still be further increased for slightly asymmetric coupling.

We calculate the energy spectrum and eigenstates of a graphene sheet that contains a circular deformation. Using time-independent perturbation theory with the ratio of the height and width of the deformation as the small parameter, we find that due to the curvature the wave functions for the various states acquire unique angular asymmetry. We demonstrate that the pseudomagnetic fields induced by the curvature result in circulating probability currents.