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The reversal of the time evolution of the local polarization in an interacting spin system involves a sign change of the effective dipolar Hamiltonian which refocuses the "spin diffusion" process generating a polarization echo. Here, the attenuation of these echo amplitudes as a function of evolution time is presented for cymantrene and ferrocene polycrystalline samples, involving one and two five spin rings per molecule respectively. We calculate the fraction of polarization which is not refocused because only the secular part of the dipolar Hamiltonian is inverted. The results indicate that, as long as the spin dynamics is restricted to a single ring, the non-inverted part of the Hamiltonian is not able by itself to explain the whole decay of the polarization echoes. A cross over from exponential (cymantrene) to Gaussian (ferrocene) attenuation is experimentally observed. This is attributed to an increase of the relative importance of the spin dynamics, as compared with irreversible interactions, which favors dynamical irreversibility.

Quantum Information Processing relies on coherent quantum dynamics for a precise control of its basic operations. A swapping gate in a two-spin system exchanges the degenerate states |↑, ↓ and |↓, ↑ . In NMR, this is achieved turning on and off the spin-spin interaction b = ∆E that splits the energy levels and induces an oscillation with a natural frequency ∆E/ℏ. Interaction of strength /τSE, with an environment of neighboring spins, degrades this oscillation within a decoherence time scale τ φ . While the experimental frequency ω and decoherence time τ φ were expected to be roughly proportional to b/ and τSE respectively, we present here experiments that show drastic deviations in both ω and τ φ . By solving the many spin dynamics, we prove that the swapping regime is restricted to ∆EτSE ℏ. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/τ φ ∝ (b/ ) 2 τ SE . The transition between quantum dynamical phases occurs when ω ∝ (b/ℏ) 2 − (k/τ SE ) 2 becomes imaginary, resembling an overdamped classical oscillator. Here, 0 ≤ k 2 ≤ 1 depends only on the anisotropy of the systemenvironment interaction, being 0 for isotropic and 1 for XY interactions. This critical onset of a phase dominated by the Quantum Zeno effect opens up new opportunities for controlling quantum dynamics.

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An ingenious pulse sequence devised by Zhang, S., Meier, B. H., and Ernst, R. R., 1992, Phys. Rev. Lett., 69, 2149 reverses the time evolution ('spin diffusion') of the local polarization in a dipolar coupled ' H spin system. This refocusing originates a polarization echo, whose amplitude attenuates by increasing the time tR elapsed until the dynamics are reversed. Different functional attenuations are found for a set of dipolar coupled systems: ferrocene, (C5H&Fe, cymantrene, (C,H,)Mn(CO),, and cobaltocene, (C5H5)2Co. To control a relevant variable involved in this attenuation a pulse sequence has been devised to progressively reduce the dipolar dynamics. Since it reduces the evolution of the polarization echo it is referred to as the REPE sequence. Two extreme behaviours were found while characterizing the materials. In systems with a strong source of relaxation and slow dynamics the attenuation follows an exponential law (cymantrene). In systems with strong dipolar dynamics the attenuation is mainly Gaussian. By the application of the REPE sequence the characteristic time of the Gaussian decay is increased until the presence of an underlying dissipative mechanism is revealed (cobaltocene). For ferrocene, however, the attenuation remains Gaussian within the experimental timescale. These two types of behaviour suggest that the many-body quantum dynamics present an extreme intrinsic instability which, in the presence of small perturbations, leads to the onset of irreversibility. This experimental conclusion is consistent with the tendencies displayed by the numerical solutions of model systems. IntroductionNuclear spin dynamics, often called spin diffusion, is a powerful tool [l] for analysing both the local and long range structure in solids. Since the spin diffusion rate depends on the internuclear dipolar interactions, it contains useful information on the spatial proximity of the nuclei and on the dimensionality of the interaction network [2]. Therefore, there is a great interest in new pulse sequences applicable to a broad range of systems. This is the case of the pulse sequence devised by Zhang, Meier and Ernst (ZME) [3] which creates a locd polarization (LP) in a homonuclear spin system (I spins) and detects its later evolution. A central point of this sequence is that it uses the presence of rare S spins to label each of the I spins directly bonded to them. Therefore, no spectral resolution of I spins is required. This sequence has been applied successfully to several systems with different purposes [4-71, and it has been generalized [8] to be used under magic-angle spinning (MAS), increasing its potential applications. On the other hand, it allows one to monitor the formation of a polurizution echo (PE) [3] when, by external means, the LP

Two centres A and B connected by one or more sets of bridging states (pathways) define a graph in the space of states. The Hamiltonian is decimated in this space and the problem is reduced to that of two sites with corrected energies E , and E, and an effective interaction VAB. The goal of the method is to make evident how the pathways should be modified in order to tune the resulting coupling. The condition for maximum coupling is i', = EB (resonance) and is related to a generalised reflection-inversion symmetry while the coupling minimises if VAB = 0 (anti-resonance). This is a non-trivial situation allowed by the topology of the system which occurs when two or more pathways interfere destructively. The effects of resonances and anti-resonances in electron transfer and other applications are discussed.

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