Evolution of multiple quantum coherences with scaled dipolar Hamiltonian.

In this article, we introduce a pulse sequence which allows the monitoring of multiple quantum coherences distribution of correlated spin states developed with scaled dipolar Hamiltonian. The pulse sequence is a modification of our previous Proportionally Refocused Loschmidt echo (PRL echo) with phase increment, in order to verify the accuracy of the weighted coherent quantum dynamics. The experiments were carried out with different scaling factors to analyze the evolution of the total magnetization, the time dependence of the multiple quantum coherence orders, and the development of correlated spins clusters. In all cases, a strong dependence between the evolution rate and the weighting factor is observed. Remarkably, all the curves appeared overlapped in a single trend when plotted against the self-time, a new time scale that includes the scaling factor into the evolution time. In other words, the spin system displayed always the same quantum evolution, slowed down as the scaling factor decreases, confirming the high performance of the new pulse sequence.

Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians.

We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.