NMR polarization echoes in a nematic liquid crystal

Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an 'infinite' network. By contrast, the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.

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.

Quantum decoherence and quasi-equilibrium in open quantum systems with few degrees of freedom: application to 1H NMR of nematic liquid crystals

Explanation of decoherence and quasi-equilibrium in systems with few degrees of freedom demands a deep theoretical analysis that considers the observed system as an open quantum system. In this work, we study the problem of decoherence of an observed system of quantum interacting particles, coupled to a quantum lattice. Our strategy is based on treating the environment and the system-environment Hamiltonians fully quantum mechanically, which yields a representation of the time evolution operator useful for disentangling the different time scales underlying in the observed system dynamics. To describe the possible different stages of the dynamics of the observed system, we introduce quantum mechanical definitions of essentially isolated, essentially adiabatic, and thermal-contact system-environment interactions. This general approach is then applied to the study of decoherence and quasi-equilibrium in proton nuclear magnetic resonance ((1)H NMR) of nematic liquid crystals. A summary of the original results of this work is as follows. We calculate the decoherence function and apply it to describe the evolution of a coherent spin state, induced by the coupling with the molecular environment, in absence of spin-lattice relaxation. By assuming quantum energy conserving or non-demolition interactions, we identify an intermediate time scale, between those controlled by self-interactions and thermalization, where coherence decays irreversibly. This treatment is also adequate for explaining the buildup of quasi-equilibrium of the proton spin system, via the process we called eigen-selectivity. By analyzing a hypothetical time reversal experiment, we identify two sources of coherence loss which are of a very different nature and give rise to distinct time scales of the spin dynamics: (a) reversible or adiabatic quantum decoherence and (b) irreversible or essentially adiabatic quantum decoherence. Local irreversibility arises as a consequence of the uncertainty introduced by the coupling with an infinite quantum environment. The reversible part can be represented by a semiclassical model, similar to standard line-shape adiabatic models. By exploiting the separation existing between the time scales of the spin coherences and the irreversible decoherence, we present a novel technique to obtain the orientational molecular distribution function for a nematic liquid crystal. The procedure is based on the comparison of the observed coherence time evolution and numerical calculation under the adiabatic quantum decoherence approach. As an example, it is used the experimental free induction decay from a nematic PAA(d6) sample to extract such an orientational distribution. This is the first theoretical description of the experimental liquid crystal NMR signal in the time domain. On the contrary, the irreversible decoherence is intrinsically full-quantum mechanical, as it is governed by the commutation properties of the environment and the spin-lattice Hamiltonians. Consistently, it depends on the molecular correlation in a decisive way, since it vanishes under a mean-field model for the molecular dynamics. The results of this work can contribute to the understanding of the open question of the applicability of the spin-temperature concept in spin systems with few degrees of freedom.

Decoherence of multiple quantum coherences generated from a dipolar ordered state

Starting from the hypothesis that the decay of coherent signals observed in 1H NMR experiments is driven by quantum interference, irreversible decoherence, and nonidealities in the experiment, we design an experiment to isolate and identify the irreversible attenuation of multiple-quantum coherences toward quasiequilibrium states of dipolar order in nematic liquid crystals (LCs). The experiment combines the well-known "magic sandwich" pulse sequence with preparation of dipolar ordered states and encoding of multiple-quantum coherences. The spin system composed of the dipole-coupled protons of a LC molecule provides an example of a small cluster of strongly interacting spins. We study decoherence rates under a sequence that reverses time evolution with the secular dipolar Hamiltonian to compensate coherent evolution of a closed quantum system. In this way, the time scale is made evident where irreversible decoherence takes place, providing insight into the nature of the processes responsible for the attainment of quasiequilibrium. The behavior of single- and double-quantum-coherence amplitudes with reversal time is interpreted as evidence of the quantum character (as opposed to stochastic character) of the processes that drive irreversible decoherence. The experimental method proposed is useful for probing the action of the environment on materials with quantum information processing potential.

Solid-state NMR studies of the molecular structure of Taxol

Solid-state 13C{1H} cross-polarization/magic angle spinning spectroscopy (CP/MAS) has been utilized to extract the molecular structure information of Taxol, which is an anti-tumor therapeutic medicine extracted from the yew bark. The 13C signals have chemical shift values quite consistent with those measured in solution phase, and the overall chemical shift range is over 200 ppm. Notably, most of the 13C resonances of the taxane ring have two clearly resolved spectral components except the resonance peaks of C-15, C-16 and C-17, which are located at the central part of the taxane ring. On the basis of our NMR data, we propose that these doublets originate from two slightly different molecular conformations of the taxane ring and still the central part of the ring remains structurally similar. Furthermore, it is demonstrated that the 13C chemical shift difference deduced from the doublet splittings can serve as a direct measure of the structural difference between the two conformations, which could possibly correlate with the anti-tumor activity of Taxol.