The Cohomology of Transitive Lie Algebroids

For a transitive Lie algebroid A on a connected manifold M and its a representation on a vector bundle F, we study the localization map Y^1: H^1(A,F)-> H^1(L_x,F_x), where L_x is the adjoint algebra at x in M. The main result in this paper is that: Ker Y^1_x=Ker(p^{1*})=H^1_{deR}(M,F_0). Here p^{1*} is the lift of H^1(\huaA,F) to its counterpart over the universal covering space of M and H^1_{deR}(M,F_0) is the F_0=H^0(L,F)-coefficient deRham cohomology. We apply these results to study the associated vector bundles to principal fiber bundles and the structure of transitive Lie bialgebroids.Comment: 17pages, no figure

Floquet spin states in graphene under ac driven spin-orbit interaction

We study the role of periodically driven time-dependent Rashba spin-orbit coupling (RSOC) on a monolayer graphene sample. After recasting the originally $4\times 4$ system of dynamical equations as two time-reversal related two-level problems, the quasi-energy spectrum and the related dynamics are investigated via various techniques and approximations. In the static case the system is a gapped at the Dirac point. The rotating wave approximation (RWA) applied to the driven system unphysically preserves this feature, while the Magnus-Floquet approach as well as a numerically exact evaluation of the Floquet equation show that this gap is dynamically closed. In addition, a sizable oscillating pattern of the out-of-plane spin polarization is found in the driven case for states which completely unpolarized in the static limit. Evaluation of the autocorrelation function shows that the original uniform interference pattern corresponding to time-independent RSOC gets distorted. The resulting structure can be qualitatively explained as a consequence of the transitions induced by the ac driving among the static eigenstates, i.e., these transitions modulate the relative phases that add up to give the quantum revivals of the autocorrelation function. Contrary to the static case, in the driven scenario, quantum revivals (suppresions) are correlated to spin up (down) phases.Comment: 10 pages, 8 figures. Typos corrected. Accepted for publication in PR

Hybrid quantum repeater based on resonant qubit-field interactions

We propose a hybrid quantum repeater based on ancillary coherent field states and material qubits coupled to optical cavities. For this purpose, resonant qubit-field interactions and postselective field measurements are determined which are capable of realizing all necessary two-qubit operations for the actuation of the quantum repeater. We explore both theoretical and experimental possibilities of generating near-maximally-entangled qubit pairs ($F>0.999$) over long distances. It is shown that our scheme displays moderately low repeater rates, between $5 \times 10^{-4}$ and $23$ pairs per second, over distances up to $900$ km, and it relies completely on current technology of cavity quantum electrodynamics.Comment: 18 pages, 13 figures, corrected according to published Erratu