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

Quantum correlations are investigated theoretically in a two-spin system with the dipole-dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of $pi/2$-pulses only and the delays between the pulses can differ. The second scheme contains $varphi$-pulses ($0<varphi<pi$) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between $pi/2$-pulses at arbitraty temperatures. Entanglement emerges after several periods of the pulse sequence in the second scheme at $varphi=pi/4$ at milliKelvin temperatures. The necessary number of the periods increases with increasing temperature. We demonstrate the dependence of entanglement on the number of the periods of the multiple-pulse sequence. Quantum discord is obtained for the first scheme of the multiple-pulse spin-locking experiment at different temperatures.