Transport through a double quantum dot in the sequential- and co- tunneling regimes

We study transport through a double quantum dot, both in the sequential tunneling and cotunneling regimes. Using a master equation approach, we find that, in the sequential tunneling regime, the differential conductance $G$ as a function of the bias voltage $\Delta\mu$ has a number of satellite peaks with respect to the main peak of the Coulomb blockade diamond. The position of these peaks is related to the interdot tunnel splitting and the singlet-triplet splitting. We find satellite peaks with both {\em positive} and {\em negative} values of differential conductance for realistic parameter regimes. Relating our theory to a microscopic (Hund-Mulliken) model for the double dot, we find a temperature regime for which the Hubbard ratio (=tunnel coupling over on-site Coulomb repulsion) can be extracted from $G(\Delta\mu)$ in the cotunneling regime. In addition, we consider a combined effect of cotunneling and sequential tunneling, which leads to new peaks (dips) in $G(\Delta\mu)$ inside the Coulomb blockade diamond below some temperature scales, which we specify.Comment: 16 pages, 10 figure

L-Drawings of Directed Graphs

We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive $x$- and $y$-coordinates and edges consist of two segments, one exiting the source vertically and one entering the destination horizontally. We study the problem of computing L-drawings using minimum ink. We prove its NP-completeness and provide a heuristics based on a polynomial-time algorithm that adds a vertex to a drawing using the minimum additional ink. We performed an experimental analysis of the heuristics which confirms its effectiveness.Comment: 11 pages, 7 figure

Parametrized Complexity of Weak Odd Domination Problems

Given a graph $G=(V,E)$, a subset $B\subseteq V$ of vertices is a weak odd dominated (WOD) set if there exists $D \subseteq V {\setminus} B$ such that every vertex in $B$ has an odd number of neighbours in $D$. $\kappa(G)$ denotes the size of the largest WOD set, and $\kappa'(G)$ the size of the smallest non-WOD set. The maximum of $\kappa(G)$ and $|V|-\kappa'(G)$, denoted $\kappa_Q(G)$, plays a crucial role in quantum cryptography. In particular deciding, given a graph $G$ and $k>0$, whether $\kappa_Q(G)\le k$ is of practical interest in the design of graph-based quantum secret sharing schemes. The decision problems associated with the quantities $\kappa$, $\kappa'$ and $\kappa_Q$ are known to be NP-Complete. In this paper, we consider the approximation of these quantities and the parameterized complexity of the corresponding problems. We mainly prove the fixed-parameter intractability (W$[1]$-hardness) of these problems. Regarding the approximation, we show that $\kappa_Q$, $\kappa$ and $\kappa'$ admit a constant factor approximation algorithm, and that $\kappa$ and $\kappa'$ have no polynomial approximation scheme unless P=NP.Comment: 16 pages, 5 figure

Dynamic response of 1D bosons in a trap

We calculate the dynamic structure factor S(q,omega) of a one-dimensional (1D) interacting Bose gas confined in a harmonic trap. The effective interaction depends on the strength of the confinement enforcing the 1D motion of atoms; interaction may be further enhanced by superimposing an optical lattice on the trap potential. In the compressible state, we find that the smooth variation of the gas density around the trap center leads to softening of the singular behavior of S(q,omega) at Lieb-1 mode compared to the behavior predicted for homogeneous 1D systems. Nevertheless, the density-averaged response remains a non-analytic function of q and omega at Lieb-1 mode in the limit of weak trap confinement. The exponent of the power-law non-analyticity is modified due to the inhomogeneity in a universal way, and thus, bears unambiguously the information about the (homogeneous) Lieb-Liniger model. A strong optical lattice causes formation of Mott phases. Deep in the Mott regime, we predict a semi-circular peak in S(q,\omega) centered at the on-site repulsion energy, omega=U. Similar peaks of smaller amplitudes exist at multiples of U as well. We explain the suppression of the dynamic response with entering into the Mott regime, observed recently by D. Clement et al., Phys. Rev. Lett. v. 102, p. 155301 (2009), based on an f-sum rule for the Bose-Hubbard model.Comment: 24 pages, 11 figure

All-Electrical Quantum Computation with Mobile Spin Qubits

We describe and discuss a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Static electric fields are used to implement a universal set of quantum gates, via the spin-orbit and exchange couplings. Initialization and measurement can be performed either by spin injection from/to ferromagnets, or by using spin filters and mesoscopic spin polarizing beam-splitters. The vulnerability of this proposal to various sources of error is estimated by numerical simulations. We also assess the suitability of various materials currently used in nanotechnology for an actual implementation of our model.Comment: 10 pages, 6 figs, RevTeX

Measurement efficiency and n-shot read out of spin qubits

We consider electron spin qubits in quantum dots and define a measurement efficiency e to characterize reliable measurements via n-shot read outs. We propose various implementations based on a double dot and quantum point contact (QPC) and show that the associated efficiencies e vary between 50% and 100%, allowing single-shot read out in the latter case. We model the read out microscopically and derive its time dynamics in terms of a generalized master equation, calculate the QPC current and show that it allows spin read out under realistic conditions.Comment: 5 pages, 1 figur

Phonon-induced decay of the electron spin in quantum dots

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time $T_2$ is as large as the spin relaxation time $T_1$, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, $T_2=2T_1$ for arbitrarily large Zeeman splittings, in contrast to the naively expected case $T_2\ll T_1$. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that $T_2=2T_1$ for all spin-orbit mechanisms in leading order in the electron-phonon interaction.Comment: 5 pages, 1 figur

Theory of Spin Hall Magnetoresistance from a Microscopic Perspective

We present a theory of the spin Hall magnetoresistance of metals in contact with magnetic insulators. We express the spin-mixing conductances, which govern the phenomenology of the effect, in terms of the microscopic parameters of the interface and the spin-spin correlation functions of the local moments on the surface of the magnetic insulator. The magnetic field and temperature dependence of the spin-mixing conductances leads to a rich behaviour of the resistance due to an interplay between the Hanle effect and spin mixing at the interface. Our theory provides a useful tool for understanding the experiments on heavy metals in contact with magnetic insulators of different kinds, and it predicts striking behaviours of magnetoresistance.Comment: 8 pages, four figure

Electron Spins in Artificial Atoms and Molecules for Quantum Computing

Achieving control over the electron spin in quantum dots (artificial atoms) or real atoms promises access to new technologies in conventional and in quantum information processing. Here we review our proposal for quantum computing with spins of electrons confined to quantum dots. We discuss the basic requirements for implementing spin-qubits, and describe a complete set of quantum gates for single- and two-qubit operations. We show how a quantum dot attached to leads can be used for spin filtering and spin read-out, and as a spin-memory device. Finally, we focus on the experimental characterization of the quantum dot systems, and discuss transport properties of a double-dot and show how Kondo correlations can be used to measure the Heisenberg exchange interaction between the spins of two dots.Comment: 13 pages, 8 figures, Invited Review (Semiconductor Spintronics, Special Issue of SST