The role of interactions, tunneling and harmonic confinement on the adiabatic loading of bosons in an optical lattice

We calculate entropy-temperature curves for interacting bosons in unit filled optical lattices for both homogeneous and harmonically trapped situations, and use them to understand how adiabatic changes in the lattice depth affect the temperature of the system. In a translationally invariant lattice, the zero tunneling limit facilitates a rather detailed analytic description. Unlike the non-interacting bosonic system which is always cooled upon adiabatic loading for low enough initial temperature, the change in the excitation spectrum induced by interactions can lead to heating. Finite tunneling helps to reduce this heating. Finally, we study the spatially inhomogeneous system confined in a parabolic potential and show that the presence of the trap can significantly reduce the final available temperature, due to the non-vanishing superfluid component at the edge of the cloud which is present in trapped systems.Comment: 9 pages and 6 figures. Two typos in Sec.IIIA were corrected and some references were update

Spin-orbit effects in nanowire-based wurtzite semiconductor quantum dots

We study the effect of the Dresselhaus spin-orbit interaction on the electronic states and spin relaxation rates of cylindrical quantum dots defined on quantum wires having wurtzite lattice structure. The linear and cubic contributions of the bulk Dresselhaus spin-orbit coupling are taken into account, along with the influence of a weak external magnetic field. The previously found analytic solution for the electronic states of cylindrical quantum dots with zincblende lattice structures with Rashba interaction is extended to the case of quantum dots with wurtzite lattices. For the electronic states in InAs dots, we determine the spin texture and the effective g-factor, which shows a scaling collapse when plotted as a function of an effective renormalized dot-size dependent spin-orbit coupling strength. The acoustic-phonon-induced spin relaxation rate is calculated and the transverse piezoelectric potential is shown to be the dominant one.Comment: 12 pages, 5 figure

Signatures of molecular correlations in the few-electron dynamics of coupled quantum dots

We study the effect of Coulomb interaction on the few-electron dynamics in coupled semiconductor quantum dots by exact diagonalization of the few-body Hamiltonian. The oscillation of carriers is strongly affected by the number of confined electrons and by the strength of the interdot correlations. Single-frequency oscillations are found for either uncorrelated or highly correlated states, while multi-frequency oscillations take place in the intermediate regime. Moreover, Coulomb interaction renders few-particle oscillations sensitive to perturbations in spatial directions other than that of the tunneling, contrary to the single-particle case. The inclusion of acoustic phonon scattering does not modify the carrier dynamics substantially at short times, but can damp oscillation modes selectively at long times.Comment: 4 pages, 5 figures, RevTex4 two-column format, to appear in Phys. Rev.

Spin relaxation near the metal-insulator transition: dominance of the Dresselhaus spin-orbit coupling

We identify the Dresselhaus spin-orbit coupling as the source of the dominant spin-relaxation mechanism in the impurity band of doped semiconductors. The Dresselhaus-type (i.e. allowed by bulk-inversion asymmetry) hopping terms are derived and incorporated into a tight-binding model of impurity sites, and they are shown to unexpectedly dominate the spin relaxation, leading to spin-relaxation times in good agreement with experimental values. This conclusion is drawn from two complementary approaches employed to extract the spin-relaxation time from the effective Hamiltonian: an analytical diffusive-evolution calculation and a numerical finite-size scaling.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Triplet-Singlet Spin Relaxation in Quantum Dots with Spin-Orbit Coupling

We estimate the triplet-singlet relaxation rate due to spin-orbit coupling assisted by phonon emission in weakly-confined quantum dots. Our results for two and four electrons show that the different triplet-singlet relaxation trends observed in recent experiments under magnetic fields can be understood within a unified theoretical description, as the result of the competition between spin-orbit coupling and phonon emission efficiency. Moreover, we show that both effects are greatly affected by the strength of the confinement and the external magnetic field, which may give access to very long-lived triplet states as well as to selective population of the triplet Zeeman sublevels.Comment: 5 pages, 3 figures. Closely related to recent experiments in cond-mat/060972

An SPQR-tree-like embedding representation for level planarity

An SPQR-tree is a data structure that efficiently represents all planar embeddings of a biconnected planar graph. It is a key tool in a number of constrained planarity testing algorithms, which seek a planar embedding of a graph subject to some given set of constraints. We develop an SPQR-tree-like data structure that represents all level-planar embeddings of a biconnected level graph with a single source, called the LP-tree, and give a simple algorithm to compute it in linear time. Moreover, we show that LP-trees can be used to adapt three constrained planarity algorithms to the level-planar case by using them as a drop-in replacement for SPQR-trees