Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1

We study the entanglement spectra of bilayer quantum Hall systems at total filling factor nu=1. In the interlayer-coherent phase at layer separations smaller than a critical value, the entanglement spectra show a striking similarity to the energy spectra of the corresponding monolayer systems around half filling. The transition to the incoherent phase can be followed in terms of low-lying entanglement levels. Finally, we describe the connection between those two types of spectra in terms of an effective temperature leading to relations for the entanglement entropy which are in full analogy to canonical thermodynamics.Comment: New findings in Eqs.(5)-(8) and pertaining discussion, and addendum to the title, version as publishe

Perturbative regimes in central spin models

Central spin models describe several types of solid state nanostructures which are presently considered as possible building blocks of future quantum information processing hardware. From a theoretical point of view, a key issue remains the treatment of the flip-flop terms in the Hamiltonian in the presence of a magnetic field. We systematically study the influence of these terms, both as a function of the field strength and the size of the spin baths. We find crucial differences between initial states with central spin configurations of high and such of low polarizations. This has strong implications with respect to the influence of a magnetic field on the flip-flop terms in central spin models of a single and more than one central spin. Furthermore, the dependencies on bath size and field differ from those anticipated so far. Our results might open the route for the systematic search for more efficient perturbative treatments of central spin problems.Comment: 7 pages, 3 figure

Hyperfine induced spin and entanglement dynamics in Double Quantum Dots: A homogeneous coupling approach

We investigate hyperfine induced electron spin and entanglement dynamics in a system of two quantum dot spin qubits. We focus on the situation of zero external magnetic field and concentrate on approximation-free theoretical methods. We give an exact solution of the model for homogeneous hyperfine coupling constants (with all coupling coefficients being equal) and varying exchange coupling, and we derive the dynamics therefrom. After describing and explaining the basic dynamical properties, the decoherence time is calculated from the results of a detailed investigation of the short time electron spin dynamics. The result turns out to be in good agreement with experimental data.Comment: 10 pages, 8 figure

Nuclear spin state narrowing via gate--controlled Rabi oscillations in a double quantum dot

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $\ket{\uparrow\downarrow}$--state and the $\ket{\downarrow\uparrow}$--state of the two--electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $\ket{\uparrow\downarrow}$--state and to perform a $\sqrt{\mathrm{SWAP}}$ operation with unit fidelity.Comment: v1:9 pages, 1 figure; v2: 13 pages, 2 figures, added section on measurement, to appear in Phys. Rev.

Bi-partite mode entanglement of bosonic condensates on tunneling graph

We study a set of $L$ spatial bosonic modes localized on a graph $\Gamma.$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $\Gamma.$ We analyze how, in the exact many-body eigenstates of the system i.e., Bose-Einstein condensates over single-particle eigenfunctions, the bi-partite quantum entanglement of a lattice vertex with respect to the rest of the graph depends on the topology of $\Gamma.$Comment: 3 Pages LaTeX, 2 Figures include

Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.Comment: 10 pages, 3 figure

Dissipation effects in spin-Hall transport of electrons and holes

We investigate the spin-Hall effect of both electrons and holes in semiconductors using the Kubo formula in the correct zero-frequency limit taking into account the finite momentum relaxation time of carriers in real semiconductors. This approach allows to analyze the range of validity of recent theoretical findings. In particular, the spin-Hall conductivity vanishes for vanishing spin-orbit coupling if the correct zero-frequency limit is performed.Comment: 5 pages, no figures, version to appear in Phys. Rev.

Focusing of Spin Polarization in Semiconductors by Inhomogeneous Doping

We study the evolution and distribution of non-equilibrium electron spin polarization in n-type semiconductors within the two-component drift-diffusion model in an applied electric field. Propagation of spin-polarized electrons through a boundary between two semiconductor regions with different doping levels is considered. We assume that inhomogeneous spin polarization is created locally and driven through the boundary by the electric field. The electric field distribution and spin polarization distribution are calculated numerically. We show that an initially created narrow region of spin polarization can be further compressed and amplified near the boundary. Since the boundary involves variation of doping but no real interface between two semiconductor materials, no significant spin-polarization loss is expected. The proposed mechanism will be therefore useful in designing new spintronic devices

Spin decay and quantum parallelism

We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find striking dependencies on the type of the initial state of the nuclear spin system. Simple product states show a profoundly different behavior than randomly correlated states whose time evolution provides an illustrative example of quantum parallelism and entanglement in a decoherence phenomenon.Comment: 6 pages, 4 figures included, version to appear in Phys. Rev.

Examining how teachers use graphs to teach mathematics during a professional development program

There are urgent calls for more studies examining the impact of Professional Development (PD) programs on teachers’ instructional practices. In this study, we analyzed how grades 5-9 mathematics teachers used graphs to teach mathematics at the start and end of a PD program. This topic is relevant because while many studies have investigated students’ difficulties with graphs, there is limited research on how teachers use graphs in their classrooms and no research on how PD impacts the way teachers use graphs in class to teach mathematics. Participant teachers took three graduate level semester-long courses focused on mathematics and student mathematical thinking. The program provided teachers with multiple opportunities for exploration and discussion, systematic feedback, contexts for collaboration and collegial sharing, and extended follow-up support. We analyzed all lessons where teachers used graphs in class at the start and end of the program, finding that teachers’ use of graphs was qualitatively more sophisticated in the end lessons. Results suggest that the features of the PD program had a positive effect on teachers’ classroom practices regarding the use of graphs