Quantitative analysis of cross-talk in partly deuterated samples of nuclear spins hyperpolarized by dynamic nuclear polarization (DNP) in the thermal mixing regime.

Dynamical nuclear polarization (DNP) is a powerful method that allows one to polarize virtually any spin-bearing nucleus by transferring electron polarization by microwave irradiation of the electron Zeeman transitions. Under certain conditions, the DNP process can be described in thermodynamical terms using the thermal mixing (TM) model. Different nuclear species can exchange energy indirectly through their interactions with the electron spins and reach a common spin temperature. Such "cross-talk" effects can occur between proton (H) and deuterium (D) nuclei in de- and re-polarization experiments. In this work, we investigate such effects experimentally, using either protonated or deuterated TEMPOL radicals as polarizing agents. An analysis of these experiments based on Provotorov's equations allows one to extract the relevant kinetic parameters, such as the rates of energy transfer between the different reservoirs, and the heat capacity of the non-Zeeman (NZ) electron reservoir, while the heat capacities of the proton and deuterium reservoirs can be estimated based on their usual expressions. These parameters allow one to make predictions of the behaviour of heteronuclei such as carbon-13 or phosphorous-31, provided that their heat capacities are negligible. Finally, we present an experimental study of the dependence of Provotorov's kinetic parameters on the TEMPOL concentration and on the H/D ratio, thus providing insight into the nature of "hidden" spins that are not observable directly because of their proximity to the radicals.

Spin relaxation: is there anything new under the Sun?

Spin relaxation has been at the core of many studies since the early days of nuclear magnetic resonance (NMR) and the underlying theory worked out by its founding fathers. This Bloch-Redfield-Abraham relaxation theory has been recently reinvestigated () in the perspective of Lindblad theory of quantum Markovian master equations in order to account for situations where the widely used semi-classical relaxation theory breaks down. In this article, we review the conventional approach of quantum mechanical theory of NMR relaxation and show that, under the usual assumptions, it is equivalent to the Lindblad formulation. We also comment on the debate on semi-classical versus quantum versions of spectral density functions involved in relaxation.

Constant-adiabaticity pulse schemes for manipulating singlet order in 3-spin systems with weak magnetic non-equivalence.

Parahydrogen-induced polarization (PHIP) is a source of nuclear spin hyperpolarization, and this technique allows for the preparation of biomolecules for in vivo metabolic imaging. PHIP delivers hyperpolarization in the form of proton singlet order to a molecule, but most applications require that a heteronuclear (e.g. 13C or 15N) spin in the molecule is hyperpolarized. Here we present high field pulse methods to manipulate proton singlet order in the [1-13C]fumarate, and in particular to transfer the proton singlet order into 13C magnetization. We exploit adiabatic pulses, i.e., pulses with slowly ramped amplitude, and use constant-adiabaticity variants: the spin Hamiltonian is varied in such a way that the generalized adiabaticity parameter is time-independent. This allows for faster polarization transfer, and we achieve 96.2% transfer efficiency in thermal equilibrium experiments. We demonstrate this in experiments using hyperpolarization, and obtain 6.8% 13C polarization. This work paves the way for efficient hyperpolarization of nuclear spins in a variety of biomolecules, since the high-field pulse sequences allow individual spins to be addressed.

Constant-adiabaticity ultralow magnetic field manipulations of parahydrogen-induced polarization: application to an AA'X spin system.

The field of magnetic resonance imaging with hyperpolarized contrast agents is rapidly expanding, and parahydrogen-induced polarization (PHIP) is emerging as an inexpensive and easy-to-implement method for generating the required hyperpolarized biomolecules. Hydrogenative PHIP delivers hyperpolarized proton spin order to a substrate via chemical addition of H2 in the spin-singlet state, but it is typically necessary to transfer the proton polarization to a heteronucleus (usually 13C) which has a longer spin lifetime. Adiabatic ultralow magnetic field manipulations can be used to induce the polarization transfer, but this is necessarily a slow process, which is undesirable since the spins continually relax back to thermal equilibrium. Here we demonstrate two constant-adiabaticity field sweep methods, one in which the field passes through zero, and one in which the field is swept from zero, for optimal polarization transfer on a model AA'X spin system, [1-13C]fumarate. We introduce a method for calculating the constant-adiabaticity magnetic field sweeps, and demonstrate that they enable approximately one order of magnitude faster spin-order conversion compared to linear sweeps. The present method can thus be utilized to manipulate nonthermal order in heteronuclear spin systems.

Algorithmic cooling of nuclear spins using long-lived singlet order.

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.

Author Correction: Generating and sustaining long-lived spin states in 15N,15N'-azobenzene.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Representation of population exchange at level anti-crossings.

A theoretical framework is proposed to describe the spin dynamics driven by coherent spin mixing at level anti-crossings (LACs). We briefly introduce the LAC concept and propose to describe the spin dynamics using a vector of populations of the diabatic eigenstates. In this description, each LAC gives rise to a pairwise redistribution of eigenstate populations, allowing one to construct the total evolution operator of the spin system. Additionally, we take into account that in the course of spin evolution a "rotation" of the eigenstate basis case take place. The approach is illustrated by a number of examples, dealing with magnetic field inversion, cross-polarization, singlet-state nuclear magnetic resonance and parahydrogen-induced polarization.

Fast destruction of singlet order in NMR experiments.

Some nuclear spin systems support long-lived states, which display greatly extended relaxation times relative to the relaxation time of nuclear spin magnetization. In spin-1/2 pairs, such a long-lived state is given by singlet order, representing the difference of the population of the nuclear singlet state and the mean population of the three triplets. In many cases, the experiments with long-lived singlet order are very time-consuming because of the need to wait for singlet order decay before the experiment can be repeated; otherwise, spin order remaining from a previous measurement may lead to experimental artifacts. Here, we propose techniques for fast and efficient singlet order destruction. These methods exploit coherent singlet-triplet conversion; in some cases, multiple conversion steps are introduced. We demonstrate that singlet order destruction enables a dramatic reduction of the waiting time between consecutive experiments and suggest to use this approach in singlet-state Nuclear Magnetic Resonance (NMR) experiments with nearly equivalent spins.

Generating and sustaining long-lived spin states in 15N,15N'-azobenzene.

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-15N,15N'-azobenzene. The singlet state of the 15N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the 15N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of 15N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization.

Transport of hyperpolarized samples in dissolution-DNP experiments.

Dissolution dynamic nuclear polarization (D-DNP) experiments rely on the transfer of a sample between two high-field magnets. During this transfer, samples might experience passage through regions where the stray fields of the magnets are very weak, can approach zero, and even change their sign. This can lead to unexpected spectral features in spin systems that undergo transitions from weak- to strong-coupling regimes and vice versa, much like in field cycling nuclear magnetic resonance experiments. We herein demonstrate that the spectral features observed in D-DNP experiments can be rationalized, provided the time-dependence of the spin Hamiltonian upon field cycling is sufficiently adiabatic. Under such conditions, a passage through a weak static field can lead to the emergence of a long-lived state (LLS) based on an imbalance between the populations of singlet and triplet states in pairs of nuclei that are strongly coupled during the passage through low field. The LLS entails the appearance of anti-phase multiplet components upon transfer to a high-field magnet for observation of NMR signals.

Constant-adiabaticity radiofrequency pulses for generating long-lived singlet spin states in NMR.

A method is implemented to perform "fast" adiabatic variation of the spin Hamiltonian by imposing the constant adiabaticity condition. The method is applied to improve the performance of singlet-state Nuclear Magnetic Resonance (NMR) experiments, specifically, for efficient generation and readout of the singlet spin order in coupled spin pairs by applying adiabatically ramped RF-fields. Test experiments have been performed on a specially designed molecule having two strongly coupled 13C spins and on selectively isotopically labelled glycerol having two pairs of coupled protons. Optimized RF-ramps show improved performance in comparison, for example, to linear ramps. We expect that the methods described here are useful not only for singlet-state NMR experiments but also for other experiments in magnetic resonance, which utilize adiabatic variation of the spin Hamiltonian.

Using optimal control methods with constraints to generate singlet states in NMR.

A method is proposed for optimizing the performance of the APSOC (Adiabatic-Passage Spin Order Conversion) technique, which can be exploited in NMR experiments with singlet spin states. In this technique magnetization-to-singlet conversion (and singlet-to-magnetization conversion) is performed by using adiabatically ramped RF-fields. Optimization utilizes the GRAPE (Gradient Ascent Pulse Engineering) approach, in which for a fixed search area we assume monotonicity to the envelope of the RF-field. Such an approach allows one to achieve much better performance for APSOC; consequently, the efficiency of magnetization-to-singlet conversion is greatly improved as compared to simple model RF-ramps, e.g., linear ramps. We also demonstrate that the optimization method is reasonably robust to possible inaccuracies in determining NMR parameters of the spin system under study and also in setting the RF-field parameters. The present approach can be exploited in other NMR and EPR applications using adiabatic switching of spin Hamiltonians.