Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem

We present a remarkable finding that a recently discovered [G. S. Uhrig, Phys. Rev. Lett. 98, 100504 (2007)] series of pulse sequences, designed to optimally restore coherence to a qubit in the spin-boson model of decoherence, is in fact completely model-independent and generically valid for arbitrary dephasing Hamiltonians given sufficiently short delay times between pulses. The series maximizes qubit fidelity versus number of applied pulses for sufficiently short delay times because the series, with each additional pulse, cancels successive orders of a time expansion for the fidelity decay. The "magical" universality of this property, which was not appreciated earlier, requires that a linearly growing set of "unknowns" (the delay times) must simultaneously satisfy an exponentially growing set of nonlinear equations that involve arbitrary dephasing Hamiltonian operators.Comment: Published in PRL, revise

Localization in one-dimensional incommensurate lattices beyond the Aubry-Andr\'e model

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schr\"odinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.Comment: 5 pages, 6 figure

Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-Andr\'e models

We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous Aubry-Andr\'e and noninteracting Anderson model. For the case with deterministic disordered potential induced by a secondary incommensurate lattice (i.e. the Aubry-Andr\'e model), we identify a class of self dual models, for which the boundary between localized and extended eigenstates are determined analytically by employing a generalized Aubry-Andr\'e transformation. We also numerically investigate the localization properties of non-dual models with next-nearest-neighbor hopping, Gaussian, and power-law decay hopping terms. We find that even for these non-dual models, the numerically obtained mobility edges can be well approximated by the analytically obtained condition for localization transition in the self dual models, as long as the decay of the hopping rate with respect to distance is sufficiently fast. For the disordered potential with genuinely random character, we examine scenarios with next-nearest-neighbor hopping, exponential, Gaussian, and power-law decay hopping terms numerically. We find that the higher order hopping terms can remove the symmetry in the localization length about the energy band center compared to the Anderson model. Furthermore, our results demonstrate that for the power-law decay case, there exists a critical exponent below which mobility edges can be found. Our theoretical results could, in principle, be directly tested in shallow atomic optical lattice systems enabling non-nearest-neighbor hopping.Comment: 18 pages, 24 figures updated with additional reference

Spin-polarized transport in inhomogeneous magnetic semiconductors: theory of magnetic/nonmagnetic p-n junctions

A theory of spin-polarized transport in inhomogeneous magnetic semiconductors is developed and applied to magnetic/nonmagnetic p-n junctions. Several phenomena with possible spintronic applications are predicted, including spinvoltaic effect, spin valve effect, and giant magnetoresistance. It is demonstrated that only nonequilibrium spin can be injected across the space-charge region of a p-n junction, so that there is no spin injection (or extraction) at low bias.Comment: Minor Revisions. To appear in Phys. Rev. Let

A number conserving theory for topologically protected degeneracy in one-dimensional fermions

Semiconducting nanowires in proximity to superconductors are among promising candidates to search for Majorana fermions and topologically protected degeneracies which may ultimately be used as building blocks for topological quantum computers. The prediction of neutral Majorana fermions in the proximity-induced superconducting systems ignores number-conservation and thus leaves open the conceptual question of how a topological degeneracy that is robust to all local perturbations arises in a number-conserving system. In this work, we study how local attractive interactions generate a topological ground-state near-degeneracy in a quasi one-dimensional superfluid using bosonization of the fermions. The local attractive interactions opens a topological quasiparticle gap in the odd channel wires (with more than one channel) with end Majorana modes associated with a topological near-degeneracy. We explicitly study the robustness of the topological degeneracy to local perturbations and find that such local perturbations result in quantum phase slips which split of the topological degeneracy by an amount that does not decrease exponentially with the length of the wire, but still decreases rapidly if the number of channels is large. Therefore a bulk superconductor with a large number of channels is crucial for true topological degeneracy.Comment: 11 pages, 2 figure

Magnetic field-assisted manipulation and entanglement of Si spin qubits

Architectures of donor-electron based qubits in silicon near an oxide interface are considered theoretically. We find that the precondition for reliable logic and read-out operations, namely the individual identification of each donor-bound electron near the interface, may be accomplished by fine-tuning electric and magnetic fields, both applied perpendicularly to the interface. We argue that such magnetic fields may also be valuable in controlling two-qubit entanglement via donor electron pairs near the interface.Comment: 4 pages, 4 figures. 1 ref and 1 footnote adde