Low perturbation limit decoherence analyzed by scaling the Double Quantum Hamiltonian

Abstract

By varying the magnitude of the effective interaction between spins in relation to the perturbations, we study the decoherence behavior in a connected proton system. Making use of the Magnus expansion, we introduce a NMR pulse sequence that generates an average Hamiltonian with Double Quantum terms multiplied by a scaling factor, $\delta$, with the possibility to take positive and negative values. The performance of the pulse sequence for different values of the scaling factors was validated in polycrystalline adamantane, by observing the evolution of the polarization. A time reversal procedure, accessible through the change of sign in the controlled Hamiltonian, was necessary to observe multiple quantum coherences. The spin counting develops a characteristic growth in two species of clusters for the scaled time. The influence of the scaling factor on the reversibility was observed through the behavior of the Loschmidt echoes, which decayed faster as the scaling factor increases. From the analysis of dynamics and its reversibility, we extracted characteristic times for the spin diffusion, $T_2^{\delta }$ and the intrinsic decoherence decay, $T_3^{\delta }$ for each scaling factor $\delta$, and perturbation time scale, $T_{\Sigma }$. Observing the dependence of reversibility vs. perturbation rates, both normalized with the spin diffusion rate, we find that in the limit of low perturbations, $T_2^{\delta }/T_3^{\delta }$ deviates from the linear dependence on $T_2^{\delta }/T_{\Sigma }$ that corresponds to strong perturbation. The asymptotic value $T_2/T_3\approx 0.15$ as $T_2^{\delta }/T_{\Sigma }$ vanishes, gives evidence that the main source of irreversibility is the intrinsic decoherence associated to the chaotic many-body dynamics of the system.