Gamma-ray bursts (GRBs) usually occurs in a dense star-forming region with massive circum-burst medium. The small-angle scattering of intense prompt X-ray emission off the surrounding dust grains will have observable consequences, and sometimes can dominate the X-ray afterglow. In most of the previous studies, only Rayleigh-Gans (RG) approximation is employed for describing the scattering process, which works accurately for the typical size of grains (with radius $aleq 0.1,{rm mu m}$) in the diffuse interstellar medium. When the size of the grains may significantly increase as in a more dense region where GRBs would occur, the RG approximation may not be valid enough for modeling detailed observational data. In order to study the temporal and spectral properties of the scattered X-ray emission more accurately with potentially larger dust grains, we provide a practical approach using the series expansions of anomalous diffraction (AD) approximation based on the complicated Mie theory. We apply our calculations to understanding the puzzling X-ray afterglow of recently observed GRB~130925A which showed a significant spectral softening. We find that the X-ray scattering scenarios with either AD or RG approximation adopted could both well reproduce the temporal and spectral profile simultaneously. Given the plateau present in early X-ray light curve, a typical distribution of smaller grains as in the interstellar medium would be suggested for GRB 130925A.
Sensing single nuclear spins is a central challenge in magnetic resonance based imaging techniques. Although different methods and especially diamond defect based sensing and imaging techniques in principle have shown sufficient sensitivity, signals from single nuclear spins are usually too weak to be distinguished from background noise. Here, we present the detection and identification of remote single C-13 nuclear spins embedded in nuclear spin baths surrounding a single electron spins of a nitrogen-vacancy centre in diamond. With dynamical decoupling control of the centre electron spin, the weak magnetic field ~10 nT from a single nuclear spin located ~3 nm from the centre with hyperfine coupling as weak as ~500 Hz is amplified and detected. The quantum nature of the coupling is confirmed and precise position and the vector components of the nuclear field are determined. Given the distance over which nuclear magnetic fields can be detected the technique marks a firm step towards imaging, detecting and controlling nuclear spin species external to the diamond sensor.
We study the topological properties of quantum states for the spinless particle hopping in a Mobius ladder. This system can be regarded as a molecular device possibly engineered from the aromatic Mobius annulenes, which enjoys a pseudo-spin orbital interaction described by a non-Abelian gauge structure. It results from the nontrivial topology of configuration space, and results in various observable effects, such as optical spectral splitting. The transmission spectrum through the Mobius molecular device is calculated to demonstrate a topological effect as a destructive interferences in the conduction band. The induced interaction also leads to an entanglement between the transverse and longitudinal modes for any locally factorized state.
We develop a quantum noise approach to study quantum transport through nanostructures. The nanostructures, such as quantum dots, are regarded as artificial atoms, subject to quasi-equilibrium fermionic reservoirs of electrons in biased leads. Noise operators characterizing the quantum fluctuation in the reservoirs are related to the damping and fluctuation of the artificial atoms through the quantum Langevin equation. The average current and current noise are derived in terms of the reservoir noise correlations. In the white-noise limit, we show that the current and current noise can be exactly calculated by the quantum noise approach, even in the presence of interaction such as Coulomb blockade. As a typical application, the average current and current noise through a single quantum dot are studied.
Exciton levels and fine-structure splitting in laterally-coupled quantum dot molecules are studied. The electron and hole tunneling energies as well as the direct Coulomb interaction are essential for the exciton levels. It is found that fine-structure splitting of the two-lowest exciton levels is contributed from the intra- and inter-dot exchange interactions, both of which are largely influenced by the symmetry and tunnel-coupling between the two dots. As the inter-dot separation is reduced, fine-structure splitting of the exciton ground state is largely increased while those of the excited states are decreased. Moreover, the dependence of the fine-structure splitting in quantum dot molecules on the Coulomb correlation is clearly clarified.
We propose and study a spin-orbit interaction based mechanism to actively cool down the torsional vibration of a nanomechanical resonator made by semiconductor materials. We show that the spin-orbit interactions of electrons can induce a coherent coupling between the electron spins and the torsional modes of nanomechanical vibration. This coherent coupling leads to an active cooling for the torsional modes via the dynamical thermalization of the resonator and the spin ensemble.
