Entanglement of dipolar coupling spins

Entanglement of dipole-dipole interacting spins 1/2 is usually investigated when the energy of interaction with an external magnetic field (the Zeeman energy) is greater than the energy of dipole interactions by three orders. Under this condition only a non-equilibrium state of the spin system, realized by pulse radiofrequence irradiations, results in entanglement. The present paper deals with the opposite case: the dipolar interaction energy is the order of magnitude or even larger than the Zeeman one. It was shown that entanglement appears under the thermodynamic equilibrium conditions and the concurrence reaches the maximum when the external field is directed perpendicular to the vector connecting the nuclei. For this direction of the field and a system of two spins with the Hamiltonian accounting the realistic dipole-dipole interactions in low external magnetic field, the exact analytical expression for concurrence was also obtained. The condition of the entanglement appearance and the dependence of concurrence on the external magnetic field, temperature, and dipolar coupling constant were studied.Comment: 9 pages, 5 figure

Low temperature MQ NMR dynamics in dipolar ordered state

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at a low temperatures. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance ({\pi}/4)_{y}-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. The both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensitive to the spin number in the molecule while the PS method gives very similar time dependencies of the intensities of MQ coherences for different spin numbers. It is shown that the use of the dipolar ordered initial state has the advantage of exciting the highest order MQ coherences in clusters of 4m identical spins, where m=1,2,3..., that is impossible to do with the standard MQ method. MQ NMR methods based on the dipolar ordered initial states at low temperatures complement the standard NMR spectroscopy for better studying structures and dynamic processes in solids.Comment: 12 pages, 4 figures will be published in Solid State Nuclear Magnetic Resonance (2013

Design of a low cost earth resources system

The author has identified the following significant results. Survey results indicated that users of remote sensing data in the Southeastern U.S. were increasingly turning to digital processing techniques. All the states surveyed have had some involvement in projects using digitally processed data. Even those states which do not yet have in-house capabilities for digital processing were extremely interested in and were planning to develop such capabilities

Multiple Quantum NMR and Entanglement Dynamics in Dipolar Coupling Spin

We investigate numerically the time dependence of the multiple quantum coherences and entanglement in linear chains up to nine nuclear spins of 1/2 coupled by the dipole-dipole interactions. Two models are considered: (1) a spin chain with nearest-neighbor dipole -dipole interactions; (2) a more realistic model with interactions between all spins. It is shown that the entangled states appear between remote particles which do not interact directly (model 1), while the interaction between all spins (model 2) not always results in entanglement between remote spins.Comment: 14 pages, 3 figures. accepted for publication in Physical Review