Universal long-time behavior of nuclear spin decays in a solid

Signatures of chaos in time series generated by many-spin systems at high temperatures

Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time series. In this paper, we explore a method of discriminating chaotic from multi-periodic integrable motion in many-particle systems. The applicability of this method is supported by our numerical simulations of the dynamics of classical spin lattices at high temperatures. We compared chaotic and nonchaotic regimes of these lattices and investigated the transition between the two. The method is based on analyzing higher-order time derivatives of the time series of a macroscopic observable-the total magnetization of the spin lattice. We exploit the fact that power spectra of the magnetization time series generated by chaotic spin lattices exhibit exponential high-frequency tails, while, for the integrable spin lattices, the power spectra are terminated in a non-exponential way. We have also demonstrated the applicability limits of the above method by investigating the high-frequency tails of the power spectra generated by quantum spin lattices and by the classical Toda lattice.

Multidimensional mapping of spin-exchange optical pumping in clinical-scale batch-mode 129Xe hyperpolarizers

We present a systematic, multiparameter study of Rb/¹²⁹Xe spin-exchange optical pumping (SEOP) in the regimes of high xenon pressure and photon flux using a 3D-printed, clinical-scale stopped-flow hyperpolarizer. In situ NMR detection was used to study the dynamics of ¹²⁹Xe polarization as a function of SEOP-cell operating temperature, photon flux, and xenon partial pressure to maximize ¹²⁹Xe polarization (P_Xe). P_Xe values of 95 ± 9%, 73 ± 4%, 60 ± 2%, 41 ± 1%, and 31 ± 1% at 275, 515, 1000, 1500, and 2000 Torr Xe partial pressure were achieved. These P_Xe polarization values were separately validated by ejecting the hyperpolarized ¹²⁹Xe gas and performing low-field MRI at 47.5 mT. It is shown that P_Xe in this high-pressure regime can be increased beyond already record levels with higher photon flux and better SEOP thermal management, as well as optimization of the polarization dynamics, pointing the way to further improvements in hyperpolarized ¹²⁹Xe production efficiency.

Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2

We show that macroscopic nonintegrable lattices of spins 1/2, which are often considered to be chaotic, do not exhibit the basic property of classical chaotic systems, namely, exponential sensitivity to small perturbations. We compare chaotic lattices of classical spins and nonintegrable lattices of spins 1/2 in terms of their magnetization responses to an imperfect reversal of spin dynamics known as Loschmidt echo. In the classical case, magnetization is exponentially sensitive to small perturbations with a characteristic exponent equal to twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2, magnetization is only power-law sensitive to small perturbations.

Multispin correlations and pseudo-thermalization of the transient density matrix in solid-state NMR: free induction decay and magic echo

Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately "rewind" the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analysis based on mean magnetization we use a phase encoding technique to measure the growth of spin correlations in the density matrix at different points in time following magic echoes of varied durations and compare the results to those obtained during a free induction decay (FID). While considerable differences are documented at short times, the long-time behavior of the density matrix appears to be remarkably universal among the types of initial states considered - simple low order multispin correlations are observed to decay exponentially at the same rate, seeding the onset of increasingly complex high order correlations. This manifestly athermal process is constrained by conservation of the second moment of the spectrum of the density matrix and proceeds indefinitely, assuming unitary dynamics.

Largest Lyapunov exponents for lattices of interacting classical spins

We investigate how generic the onset of chaos in interacting many-body classical systems is in the context of lattices of classical spins with nearest-neighbor anisotropic couplings. Seven large lattices in different spatial dimensions were considered. For each lattice, more than 2000 largest Lyapunov exponents for randomly sampled Hamiltonians were numerically computed. Our results strongly suggest the absence of integrable nearest-neighbor Hamiltonians for the infinite lattices except for the trivial Ising case. In the vicinity of the Ising case, the largest Lyapunov exponents exhibit a power-law growth, while further away they become rather weakly sensitive to the Hamiltonian anisotropy. We also provide an analytical derivation of these results.

Revisiting the mean-field picture of dipolar effects in solution NMR

For more than three decades, the classical or mean-field picture describing the distant dipolar field has been almost always simplified to an effective field proportional to the local longitudinal magnetization, differing only by a scale factor of 1.5 for homomolecular (identical resonance frequency) and heteromolecular interactions. We re-examine the underlying assumptions, and show both theoretically and experimentally that the mathematical framework needs to be modified for modern applications such as imaging. We demonstrate new pulse sequences which produce unexpected effects; for example, modulating an arbitrarily small fraction of the magnetization can substantially alter the frequency evolution. Thus, matched gradient pulse pairs (a seemingly innocuous module in thousands of existing pulse sequences) can alter the time evolution in highly unexpected ways, particularly with small flip angle pulses such as those used in hyperpolarized experiments. We also show that specific gradient pulse combinations can retain only dipolar interactions between unlike spins, and the dipolar field can generate a secular Hamiltonian proportional to I(x).

Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance

The many-body quantum dynamics of dipolar coupled nuclear spins I=1/2 on an otherwise isolated cubic lattice are studied with nuclear magnetic resonance. By increasing the signal-to-noise ratio by 2 orders of magnitude compared with previous reports for the free induction decay (FID) of (19)F in CaF(2) we obtain new insight into its long-time behavior. We confirm that the tail of the FID is an exponentially decaying cosine, but our measurements reveal a second decay mode with comparable frequency but twice the decay constant. This result is in agreement with a recent theoretical prediction for the FID in terms of eigenvalues for the time evolution of chaotic many-body quantum systems.

Collisional 3He and 129Xe frequency shifts in Rb-noble-gas mixtures

The Fermi-contact interaction that characterizes collisional spin exchange of a noble gas with an alkali-metal vapor also gives rise to NMR and EPR frequency shifts of the noble-gas nucleus and the alkali-metal atom, respectively. We have measured the enhancement factor κ0 that characterizes these shifts for Rb-129Xe to be 493±31, making use of the previously measured value of κ0 for Rb-3He. This result allows accurate 129Xe polarimetry with no need to reference a thermal-equilibrium NMR signal.

Breakdown of angular momentum selection rules in high pressure optical pumping experiments

We present measurements, by using two complementary methods, of the breakdown of atomic angular momentum selection rules in He-broadened Rb vapor. Atomic dark states are rendered weakly absorbing due to fine-structure mixing during Rb-He collisions. The effect substantially increases the photon demand for optical pumping of dense vapors.

Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates

This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed provided all these superpositions have the same fixed energy. Such a condition is not equivalent to the conventional microcanonical condition because the latter limits the participating eigenstates to a very narrow energy window. The statistics is obtained analytically for both the entire system and its small subsystem. In a significant departure from the Boltzmann-Gibbs statistics, the average occupation numbers of quantum states exhibit in the present case weak algebraic dependence on energy. In the macroscopic limit, this dependence is routinely accompanied by the condensation into the lowest-energy quantum state. This work contains initial numerical tests of the above statistics for finite systems and also reports the following numerical finding: when the basis states of large but finite random matrix Hamiltonians are expanded in terms of eigenstates, the participation of eigenstates in such an expansion obeys the newly obtained statistics. The above statistics might be observable in small quantum systems, but for the macroscopic systems, it rather re-enforces doubts about self-sufficiency of nonrelativistic quantum mechanics for justifying the Boltzmann-Gibbs equilibrium.