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arXiv:1802.09042 · Quantum Information Processing

Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments

S. A. Gerasev, A. V. Fedorova, Edward B. Fel’dman, E. I. Kuznetsova

Published Feb 17, 2018• 2 citations
arXivHTMLPDF
DOI
10.1007/s11128-018-1841-x

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In this work, quantum correlations in two model systems which can be invesitgated by means of solid-state NMR are considered. The first is a two-spin system in NMR spin-locking experiment, where two schemes of spin-locking are considered. Concurrence is calculated for both schemes assuming the initial thermodynamic equilibrium state. Quantum discord is calculated analytically in the high-temperature approximation. The second model system is the spin-1/2 chain with the XY interaction, where the transfer of multiple quantum (MQ) coherences from one end of the chain to another is studied. The conditions under which the density matrix of the receiver is a block-scaled version of the sender’s density matrix are found.
We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1∕21∕21∕2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasiequilibrium state which is established after the time of order ${\ensuremath{\omega}}_{\mathit{loc}}^{\ensuremath{-}1}$ (${\ensuremath{\omega}}_{\mathit{loc}}$ is the dipolar local field) after the MQ NMR experiment. The other method uses an additional resonance ${(\ensuremath{\pi}∕4)}_{y}$ pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.
Abstract Quantum entanglement in two-spin systems in multiple pulse NMR spin locking with dephasing relaxation is studied on the basis of the Lindblad equation. An exact solution for the density matrix of the system for any initial temperature is found. The dependence of the concurrence (which determines quantum entanglement) on the dephasing relaxation rate and the parameters of the multiple pulse sequence is investigated. For different rates of dephasing relaxation, the critical temperature at which entanglement arises is found.