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.

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

Influence of disorder on the ferromagnetism in diluted magnetic semiconductors

Influence of disorder on the ferromagnetic phase transition in diluted (III,Mn)V semiconductors is investigated analytically. The regime of small disorder is addressed, and the enhancement of the critical temperature by disorder is found both in the mean field approximation and from the analysis of the zero temperature spin stiffness. Due to disorder, the spin wave fluctuations around the ferromagnetically ordered state acquire a finite mass. At large charge carrier band width, the spin wave mass squared becomes negative, signaling the breakdown of the ferromagnetic ground state and the onset of a noncollinear magnetic order.Comment: Replaced with revised version. 10 pages, 3 figure

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.

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.

The transfer dilemma

Abstract In this paper we provide an overview of research on transfer, highlighting its main tenets. Then we look at interviews of two fifth grade students learning about mathematical concepts regarding operations on positive and negative quantities. We attempt to focus on how their learning is influenced by their prior knowledge and experience. We take the position that transfer is a theory of learning and we attempt to show that it cannot provide a solid foundation for explaining such examples of learning

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

Quantum Correlations in Two-Boson Wavefunctions

We present the Schmidt decomposition for arbitrary wavefunctions of two indistinguishable bosons, extending the recent studies of entanglement or quantum correlations for two fermion systems [J. Schliemann et al., Phys. Rev. B {\bf 63}, 085311 (2001) and quant-ph/0012094]. We point out that the von Neumann entropy of the reduced single particle density matrix remains to be a good entanglement measure for two identical particles.Comment: in press at Phys. Rev.

Spin susceptibilities, spin densities and their connection to spin-currents

We calculate the frequency dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interaction. The resonances of the susceptibilities depends on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.Comment: 6 pages, revtex4 styl

Quantum-Hall Quantum-Bits

Bilayer quantum Hall systems can form collective states in which electrons exhibit spontaneous interlayer phase coherence. We discuss the possibility of using bilayer quantum dot many-electron states with this property to create two-level systems that have potential advantages as quantum bits.Comment: 4 pages, 4 figures included, version to appear in Phys. Rev. B (Rapid Communications