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Collective behaviours in interacting spin systems

Inés Rodríguez-Arias

Published Sep 27, 2018• 0 citations
Publisher

Abstract

Dynamic nuclear polarization (DNP) is one of the most promising techniques towards a new generation of Magnetic Resonance Imaging (MRI). The idea is to use the Nuclear Magnetic Resonance (NMR) in other nuclei rather than the traditional hydrogen, such as carbon. For the carbon signal to be detected, one needs to enhance its spin polarization. In thermal equilibrium — at low temperature and high magnetic field — electron spins are far more polarized than any system of nuclear spins, which is due to their smaller mass. With the DNP technique we bring the system out-of-equilibrium irradiating it with microwaves. This triggers polarization transfer from the electron spins to the nuclear ones. During my Ph.D, I have studied both analytically and numerically the competition between the dipolar interactions among electron spins (which can be tuned experimentally) and the disorder naturally present in the sample. I proposed two models to study DNP: a Heisenberg spin-chain and a system free-fermions in the Anderson model. Two different regimes were found : For strongly interacting electron spins, the out-of-equilibrium steady state displays an effective thermodynamic behavior characterised by a very low spin temperature. In the weakly interacting regime, it is not possible to define a spin temperature, and it is associated to a many-body localized phase (or an Anderson-localized phase). My research was focused on the properties of the two phases with respect to the performance of DNP, and I found it to be optimal at the transition between the two. This is a very important result that has been verified by recent experiments carried in École Normale Supérieure de Paris.

DOI
10.70675/592e6e27z4483z41bcz8f51zd96f637766b3

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Dynamic nuclear polarization (DNP) is one of the most promising techniques towards a new generation of Magnetic Resonance Imaging (MRI). The idea is to use the Nuclear Magnetic Resonance (NMR) in other nuclei rather than the traditional hydrogen, such as carbon. For the carbon signal to be detected, one needs to enhance its spin polarization. In thermal equilibrium — at low temperature and high magnetic field — electron spins are far more polarized than any system of nuclear spins, which is due to their smaller mass. With the DNP technique we bring the system out-of-equilibrium irradiating it with microwaves. This triggers polarization transfer from the electron spins to the nuclear ones. During my Ph.D, I have studied both analytically and numerically the competition between the dipolar interactions among electron spins (which can be tuned experimentally) and the disorder naturally present in the sample. I proposed two models to study DNP: a Heisenberg spin-chain and a system free-fermions in the Anderson model. Two different regimes were found : For strongly interacting electron spins, the out-of-equilibrium steady state displays an effective thermodynamic behavior characterised by a very low spin temperature. In the weakly interacting regime, it is not possible to define a spin temperature, and it is associated to a many-body localized phase (or an Anderson-localized phase). My research was focused on the properties of the two phases with respect to the performance of DNP, and I found it to be optimal at the transition between the two. This is a very important result that has been verified by recent experiments carried in École Normale Supérieure de Paris.
Dynamic nuclear polarization (DNP) is to date the most effective technique to increase the nuclear polarization opening disruptive perspectives for medical applications. In a DNP setting, the interacting spin system is quasi-isolated and brought out of equilibrium by microwave irradiation. Here we show that the resulting stationary state strongly depends on the ergodicity properties of the spin many-body eigenstates. In particular, the dipolar interactions compete with the disorder induced by local magnetic fields resulting in two distinct dynamical phases: while for weak interaction, only a small enhancement of polarization is observed, for strong interactions the spins collectively equilibrate to an extremely low effective temperature that boosts DNP efficiency. We argue that these two phases are intimately related to the problem of thermalization in closed quantum systems where a many-body localization transition can occur varying the strength of the interactions.
Comportements collectifs dans des systèmes de spins en interaction La polarisation dynamique nucléaire (DNP pour son acronyme en anglais) est une des techniques les plus prometteuses d’amélioration de l’IRM. En pratique, on voudrait utiliser la résonance magnétique nucléaire (RMN) sur d’autres noyaux que ceux d’hydrogène, par exemple le carbone. Pour pouvoir détecter le carbone, sa polarisation de spin doit être augmentée. À l’équilibre thermodynamique — à basse température et forts champs magnétiques — les électrons sont bien plus polarisés que tout système de spin nucléaires, ce qui est dû à leur plus petite masse. La technique de DNP consiste à amener le système hors d’équilibre avec une irradiation par des microondes. Cette irradiation va induire le transfer de polarisation des spins électroniques vers les spins nucléaires. Pendant ma thèse, j’ai étudié, par des méthodes analytiques et numériques, la compétition entre les interactions dipolaires présentes entre les spins électroniques (qui peuvent se régler expérimentalement) et le désordre naturellement présent dans l’échantillon. Pour ce faire, j’ai proposé deux modèles : une chaîne de spins d’Heisenberg et un système de fermions libres dans le modèle d’Anderson. J’ai trouvé l’existence de deux régimes : Pour le régime de fortes interactions, l’état stationnaire a des traces d’un comportement thermodynamique, étant caractérisé par une température effective. Dans le régime de faibles interactions, il n’est pas possible de définir une température effective, et l'on peut le relier à une phase de many-body localization (ou localisation d'Anderson). Mes recherches portent sur l’étude des propriétés deux phases en relation avec la performance de la DNP et j’ai trouvé qu’elle est optimale à la transition entre les deux phases. Ce résultat intéressant a récemment été confirmé par des expériences menées à l’École Normale Supérieure de Paris.
We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclear polarization (DNP). We point out that a critical strength of interactions is required to obtain significant nuclear hyperpolarization. Otherwise, the electron spins do not thermalize among each other, due to the incipient many-body localization transition in the electron spin system. Only when the interactions are sufficiently strong, in the so-called spin-temperature regime, they establish an effective thermodynamic behavior in the out-of-equilibrium stationary state. The highest polarization is reached at a point where the spin temperature is just not able to establish itself anymore. We provide numerical predictions for the level of nuclear hyperpolarization and present an analytical technique to estimate the spin temperature as a function of interaction strength and quenched disorder. We show that, at sufficiently strong coupling, nuclear spins perfectly equilibrate to the spin temperature that establishes among the spins of radicals.
Dynamic nuclear polarization (DNP) is a promising strategy for generating a significantly increased nonthermal spin polarization in nuclear magnetic resonance (NMR) and its applications that range from medicine diagnostics to material science. Being a genuine nonequilibrium effect, DNP circumvents the need for strong magnetic fields. However, despite intense research, a detailed theoretical understanding of the precise mechanism behind DNP is currently lacking. We address this issue by focusing on a simple instance of DNP-so-called solid effect DNP-which is formulated in terms of a quantum central spin model where a single electron is coupled to an ensemble of interacting nuclei. We show analytically that the nonequilibrium buildup of polarization heavily relies on a mechanism which can be interpreted as kinetically constrained diffusion. Beyond revealing this insight, our approach furthermore permits numerical studies of ensembles containing thousands of spins that are typically intractable when formulated in terms of a quantum master equation. We believe that this represents an important step forward in the quest of harnessing nonequilibrium many-body quantum physics for technological applications.
Dynamic nuclear polarisation transfers polarisation from electron to nuclear spins by relying on a dissipative channel. Here we introduce a cavity-based DNP mechanism which uses the radiative relaxation of the electronic spin through the Purcell effect to bring about the nuclear spin polarisation. We implement this protocol on an ensemble of bismuth donor spins (I=9/2, S=1/2) in isotopically purified silicon coupled to a superconducting resonator. A single cycle, combining adiabatic microwave and radio-frequency pulses with Purcell relaxation, increases a target ground state's population by a factor of 1.79±0.041.79\pm0.041.79±0.04; a cumulative enhancement of 4.6±0.24.6\pm0.24.6±0.2 is reached with additional cycles, to be compared with the theoretical limit of ninefold set by the degeneracy of the ground manifold. We explain this difference by the competition between Purcell and intrinsic relaxation on the one hand and a collective effect that slows down the electronic spin radiative decay as the nuclear spin population grows on the other hand. Our results place radiative DNP as an available mechanism at millikelvin temperatures where phonon-mediated relaxation is frozen.
The goal of this project was to improve our control over nuclear spins in the solid state, and to extend this control to coupled electron-nuclear spins. Our key results are summarized below. 1. We extended the control techniques developed in liquid state NMR quantum information processing to the control of a three-qubit solid state NMR quantum information processor. 2. To explore multi-body spin dynamics and their sensitivity to decoherence, we have measured the decay of NMR multiple quantum coherence intensities in the presence and absence of the dipolar Hamiltonian, in a cubic and a one-dimensional spin system. 3. We also studied the transport of polarization in the one-dimensional fluoroapatite system, both experimentally and theoretically, and created special states in which the polarization is localized to the ends of the chain. This enables both universal Quantum Computing and Quantum Simulation in 1-D systems. 4. We devised a novel scheme for electron-nuclear quantum information processing that exploits the anisotropic hyperfine coupling. This scheme enables universal control over a 1-electron, N-nuclear spin system, addressing only a single electron spin transition. Not having to address the nuclear spins directly significantly speeds up the control. We designed and fabricated a pulsed electron spin resonance spectrometer, along with a cryogenic probe which we used to experimentally implement this scheme on a single crystal sample of irradiated malonic acid. 5. We demonstrated the role of nuclear spin dipolar diffusion in dynamic nuclear polarization (DNP) experiments, in dielectric samples with abundant nuclear spins. We achieved a 29Si polarization of 8.3% at 66 GHz and 1.1 K in single crystal P-doped, the highest ever reported, using DNP.