Refocalization sequences in nuclear magnetic resonance (NMR) can in principle reverse the coherent evolution under the secular dipolar Hamiltonian of a closed system. We use this experimental strategy to study the effect of irreversible decoherence on the signal amplitude attenuation in a single-crystal hydrated salt where the nuclear spin system consists of the set of hydration water proton spins having a strong coupling within each pair and a much weaker coupling with other pairs. We study the experimental response of attenuation times with temperature, crystal orientation with respect to the external magnetic field, and rf pulse amplitudes. We find that the observed attenuation of the refocalized signals can be explained by two independent mechanisms: (a) evolution under the nonsecular terms of the reversion Hamiltonian, and (b) an intrinsic mechanism having the attributes of irreversible decoherence induced by the coupling with a quantum environment. To characterize (a) we compare the experimental data with the numerical calculation of the refocalized NMR signal of an artificial, closed spin system. To describe (b) we use a model of the irreversible adiabatic decoherence of spin pairs coupled with a phonon bath which allows evaluating an upper bound for the decoherence times. This model accounts for both the observed dependence of the decoherence times on the eigenvalues of the spin-environment Hamiltonian, and the independence from the sample temperature. This result, then, supports the adiabatic decoherence induced by the dipole-phonon coupling as the explanation for the observed irreversible decay of reverted NMR signals in solids.
Refocalization sequences in nuclear magnetic resonance (NMR) can in principle reverse the coherent evolution under the secular dipolar Hamiltonian of a closed system. We use this experimental strategy to study the effect of irreversible decoherence on the signal amplitude attenuation in a single-crystal hydrated salt where the nuclear spin system consists of the set of hydration water proton spins having a strong coupling within each pair and a much weaker coupling with other pairs. We study the experimental response of attenuation times with temperature, crystal orientation with respect to the external magnetic field, and rf pulse amplitudes. We find that the observed attenuation of the refocalized signals can be explained by two independent mechanisms: (a) evolution under the nonsecular terms of the reversion Hamiltonian, and (b) an intrinsic mechanism having the attributes of irreversible decoherence induced by the coupling with a quantum environment. To characterize (a) we compare the experimental data with the numerical calculation of the refocalized NMR signal of an artificial, closed spin system. To describe (b) we use a model of the irreversible adiabatic decoherence of spin pairs coupled with a phonon bath which allows evaluating an upper bound for the decoherence times. This model accounts for both the observed dependence of the decoherence times on the eigenvalues of the spin-environment Hamiltonian, and the independence from the sample temperature. This result, then, supports the adiabatic decoherence induced by the dipole-phonon coupling as the explanation for the observed irreversible decay of reverted NMR signals in solids.
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.
An experimental study of NMR spin decoherence in nematic liquid crystals is presented. Decoherence dynamics can be put in evidence by means of refocusing experiments of the dipolar interactions. The experimental technique used in this work is based on the MREV8 pulse sequence. The aim of the work is to detect the main features of the irreversible quantum decoherence in liquid crystals, on the basis of the theory presented by the authors recently. The focus is laid on experimentally probing the eigen-selection process in the intermediate time scale, between quantum interference of a closed system and thermalization, as a signature of the quantum spin decoherence of the open quantum system, as well as on quantifying the effects of non-idealities as possible sources of signal decays which could mask the intrinsic decoherence. In order to contrast experiment and theory, the theory was adapted to obtain the decoherence function corresponding to the MREV8 reversion experiments. Non-idealities of the experimental setting, like external field inhomogeneity, pulse misadjustments, and the presence of non-reverted spin interaction terms are analysed in detail within this framework, and their effects on the observed signal decay are numerically estimated. It is found that though all these non-idealities could in principle affect the evolution of the spin dynamics, their influence can be mitigated and they do not present the characteristic behaviour of the irreversible spin decoherence. As unique characteristic of decoherence, the experimental results clearly show the occurrence of eigen-selectivity in the intermediate timescale, in complete agreement with the theoretical predictions. We conclude that the eigen-selection effect is the fingerprint of decoherence associated with a quantum open spin system in liquid crystals. Besides, these features of the results account for the quasi-equilibrium states of the spin system, which were observed previously in these mesophases, and lead to conclude that the quasi-equilibrium is a definite stage of the spin dynamics during its evolution towards equilibrium.
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.
We study the quantum adiabatic decoherence of a multispin array, coupled with an environment of harmonic phonons, in the framework of the theory of open quantum systems. We follow the basic formal guidelines of the well-known spin-boson model, since in this framework it is possible to derive the time dependence of the reduced density matrix in the adiabatic time scale, without resorting to coarse-graining procedures. However, instead of considering a set of uncoupled spins interacting individually with the boson field, the observed system in our model is a network of weakly interacting spin pairs; the bath corresponds to lattice phonons, and the system-environment interaction is generated by the variation of the dipole-dipole energy due to correlated shifts of the spin positions, produced by the phonons. We discuss the conditions that the model must meet in order to fit within the adiabatic regime. By identifying the coupling of the dipole-dipole spin interaction with the low-frequency acoustic modes as the source of decoherence, we calculate the decoherence function of the reduced spin density matrix in closed way, and estimate the decoherence rate of a typical element of the reduced density matrix in one- and three-dimensional models of the spin array. Using realistic values for the various parameters of the model we conclude that the dipole-phonon mechanism can be particularly efficient to degrade multispin coherences, when the number of active spins involved in a given coherence is high. The model provides insight into the microscopic irreversible spin dynamics involved in the buildup of quasiequilibrium states and in the coherence leakage during refocusing experiments in nuclear magnetic resonance of crystalline solids.
We present a Nuclear Magnetic Resonance experiment aimed to scan the evolution of a spin system, in liquid crystals, during the transient to a quasi-equilibrium state. New evidence is presented in favor of irreversible decoherence as the mechanism which leads an initial out-of-equilibrium state to quasi-equilibrium. The experiment combines the Jeener-Broekaert sequence with reversal of the dipolar evolution, and decoding of multiple quantum coherences, to allow visualizing the evolution of the spectra of the different coherences during the formation of the quasi-equilibrium states. We vary the reversion strategies and the preparation of initial states, and observe that the amplitude of the spectra attenuate with the reversion time, and notably, that the decay is frequency selective in all the samples. We interpret this effect as an evidence of 'eigen-selection', a signature of the occurrence of irreversible decoherence, which indicates that the spin system in liquid crystal NMR experiments conforms an actual open quantum system, where quasi-equilibrium can be rigorously described as a stage of the dynamics which develops in a time-scale far earlier than thermal equilibrium. This explanation is supported by a derivation of the observed signals and spectra in terms of the coherences of the spin-system of a single molecule, within the theoretical framework of open quantum systems.
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.