RESUMO

A local excitation in a quantum many-spin system evolves deterministically. A time-reversal procedure, involving the inversion of the signs of every energy and interaction, should produce the excitation revival. This idea, experimentally coined in nuclear magnetic resonance, embodies the concept of the Loschmidt echo (LE). While such an implementation involves a single spin autocorrelation M(1,1), i.e. a local LE, theoretical efforts have focused on the study of the recovery probability of a complete many-body state, referred to here as global or many-body LE MMB Here, we analyse the relation between these magnitudes, with regard to their characteristic time scales and their dependence on the number of spins N We show that the global LE can be understood, to some extent, as the simultaneous occurrence of N independent local LEs, i.e. MMB∼(M(1,1))(N/4) This extensive hypothesis is exact for very short times and confirmed numerically beyond such a regime. Furthermore, we discuss a general picture of the decay of M1,1 as a consequence of the interplay between the time scale that characterizes the reversible interactions (T(2)) and that of the perturbation (τ(Σ)). Our analysis suggests that the short-time decay, characterized by the time scale τ(Σ), is greatly enhanced by the complex processes that occur beyond T(2) This would ultimately lead to the experimentally observed T(3), which was found to be roughly independent of τ(Σ) but closely tied to T(2).

RESUMO

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.

RESUMO

Nuclear spins are promising candidates for quantum information processing because their good isolation from the environment precludes the rapid loss of quantum coherence. Many strategies have been developed to further extend their decoherence times. Some of them make use of decoupling techniques based on the Carr-Purcell and Carr-Purcell-Meiboom-Gill pulse sequences. In many cases, when applied to inhomogeneous samples, they yield a magnetization decay much slower than that of the Hahn echo. However, we have proved that these decays cannot be associated with longer decoherence times, as coherences remain frozen. They result from coherences recovered after their storage as local polarization and thus they can be used as memories. We show here how this freezing of the coherent state, which can subsequently be recovered after times longer than the natural decoherence time of the system, can be generated in a controlled way with the use of field gradients. A similar behaviour of homogeneous samples in inhomogeneous fields is demonstrated. It is emphasized that the effects of inhomogeneities in solid-state nuclear magnetic resonance, independently of their origin, should not be disregarded, as they play a crucial role in multipulse sequences.

RESUMO

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.

RESUMO

A set of new aluminium complexes of norfloxacin (NOR) and ciprofloxacin (CIP) that show an improvement in their pharmaceutical properties were studied using solution and solid-state nuclear magnetic resonance (NMR) and infrared (IR) spectroscopy. The complexes synthesized with two different methods were compared. One of these methods will allow formulation of the compounds at production scale. High-resolution (13)C spectra were obtained with the cross-polarization and magic angle spinning (CP-MAS) experiment. These spectra were assigned by comparing them with the solution data of the pure drug and by using a quaternary carbon edition technique. The carbon relaxation times in the rotating frame, T(1rhoC), were measured for all the complexes. A two-exponential decay evidences that the complexes are nonhomogeneous. The short T(1rhoC) values are in the range 320-1100 micros and the long values in the range 1.8-7 ms. (27)Al MAS NMR spectra revealed an octahedral coordination between the aluminium ion and oxygens of the pure drug, supporting a 3:1 ligand:metal stoichiometry in both CIP and NOR complexes. The stretching and deformation modes of carboxylic acid and carboxylate and keto groups were analyzed by IR. This technique shows that the same modes are present in the aluminium complexes obtained by the two methods and that the coordination of the fluoroquinolone to aluminium occurs through the 4-keto and 3-carboxylic groups.

Assuntos

RESUMO

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 |(up arrow, down arrow)> and |(down arrow, up arrow)>. In NMR, this is achieved turning on and off the spin-spin interaction b=DeltaE that splits the energy levels and induces an oscillation with a natural frequency DeltaE/Planck's. Interaction of strength Planck's/tau(SE), with an environment of neighboring spins, degrades this oscillation within a decoherence time scale tau(phi). While the experimental frequency omega and decoherence time tau(phi) were expected to be roughly proportional to b/Planck's and tau(SE), respectively, we present here experiments that show drastic deviations in both omega and tau(phi). By solving the many spin dynamics, we prove that the swapping regime is restricted to DeltaEtau(SE) similar or greater than Planck's. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/tau(phi) proportional to (b/Planck's)2tau(SE). The transition between quantum dynamical phases occurs when omega proportional to sqrt (b/Planck's)2-(k/tau(SE)2 becomes imaginary, resembling an overdamped classical oscillator. Here, 0< or =k2< or =1 depends only on the anisotropy of the system-environment 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.

RESUMO

We study the variation of 13C spectra as function of off-resonances in protons during decoupling, for continuous wave (cw) and small phase incremental alternation with 64-step (SPINAL-64) schemes in the liquid crystals 4-n-octyl-4'-cyanobiphenyl (8CB) and 4-n-pentyl-4'-cyanobiphenyl (5CB). The self-decoupling mechanism induced by the strong homonuclear dipolar interactions provides a method to study the dynamics of the proton system through the 13C spectra. In the n-cyanobiphenyl (nCB) liquid crystals each nonquaternary carbon is coupled through dipolar interactions to more than one proton constituting a SI(N) group (with N> or =2). We extend the analytical treatment of the variation of the 13C spectrum with the off-resonance, described for SI groups, to SI(N) under cw decoupling. The dependence of the maxima of the 13C spectra as a function of proton off-resonance follows a Lorentzian line that depends on the rate of exchange among proton spin states. From the fitting parameters of this curve and the heteronuclear interaction measured in cross-polarization experiments, we extract dynamical information of the intramolecular 1H-1H interactions. In the case of SPINAL-64 we experimentally observe the same behavior. Under both kinds of decouplings, we characterize the chemical shift of the protons through the NMR spectra of carbons. The resulting values are in very good agreement with those obtained by other methods.

RESUMO

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.