Evaluating the role of perturbations versus the intrinsic coherent dynamics in driving to equilibrium is of fundamental interest to understand quantum many-body thermalization, in the quest to build ever complex quantum devices. Here we introduce a protocol that scales down the coupling strength in a quantum simulator based on a solid-state nuclear spin system, leading to a longer decay time T2, while keeping perturbations associated to control error constant. We can monitor quantum information scrambling by measuring two powerful metrics, out-of-time-ordered correlators (OTOCs) and Loschmidt Echoes (LEs). While OTOCs reveal quantum information scrambling involving hundreds of spins, the LE decay quantifies, via the time scale T3, how well the scrambled information can be recovered through time reversal. We find that when the interactions dominate the perturbation, the LE decay rate only depends on the interactions themselves, T3 ∝ T2, and not on the perturbation. Then, in an unbounded many-spin system, decoherence can achieve a perturbation-independent regime, with a rate only related to the local second moment of the Hamiltonian.

A suitable NMR experiment in a one-dimensional dipolar coupled spin system allows one to reduce the natural many-body dynamics into effective one-body dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by monitoring the excitation of NMR many-body superposition states: the multiple-quantum coherences. The observed effective one-dimensionality of HAp relies on the quasi one-dimensional structure of the dipolar coupled network that, as we show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is also probed through a Loschmidt echo experiment, where the time reversal is implemented on the double-quantum Hamiltonian, HDQ ∝ IWe contrast the decoherence of adamantane, a standard threedimensional system, with that of HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth exponential law.

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We present an improved approach for the study of the evolution of spin correlations and decoherence in multiple quantum nuclear magnetic resonance experiments. The infinite system, constituted by the protons of a polycrystalline adamantane sample, evolves under a double quantum Hamiltonian. The distribution of multiple quantum coherence orders is represented by a contribution of spin clusters with different sizes that exchange spins, increasing their size with the evolution time. A cluster with nearly exponential growth at all times is observed, in agreement with previous models. Remarkably, a small cluster that stabilizes in a size corresponding to 18 correlated spins is revealed. In addition, by performing a renormalization of the obtained data with the experimental Loschmidt echo, the contribution of the different clusters to the observable signal is determined. This procedure accounts for the effect of decoherence on the evolution of the system, and allows setting the range of confidence of the experimental data. Our analysis confirms the natural hint that, correlated states involving higher coherence orders are far more sensitive to the uncontrolled decoherent interactions, than those involving lower orders.