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arXiv:1503.08181 · Physical Review Letters

Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization

Andrea De Luca, Alberto Rosso

Published Aug 20, 2015• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.115.080401

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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.
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.
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.
Understanding how closed quantum systems dynamically approach thermal equilibrium presents a major unresolved problem in statistical physics. Generically, non-integrable quantum systems are expected to thermalize as they comply with the Eigenstate Thermalization Hypothesis. However, in the presence of strong disorder, the dynamics can possibly slow down to a degree that systems fail to thermalize on experimentally accessible timescales, as in spin glasses or many-body localized systems. In general, particularly in long-range interacting quantum systems, the specific nature of the disorder necessary for the emergence of a prethermal, metastable state--distinctly separating the timescales of initial relaxation and subsequent slow thermalization--remains an open question. We study an ensemble of Heisenberg spins with a tunable distribution of random coupling strengths realized by a Rydberg quantum simulator. We observe a drastic change in the late-time magnetization when increasing disorder strength. The data is well described by models based on pairs of strongly interacting spins, which are treated as thermal for weak disorder and isolated for strong disorder. Our results indicate a crossover into a pair-localized prethermal regime in a closed quantum system of thousands of spins in the critical case where the exponent of the power law interaction matches the spatial dimension.
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.
We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of vibrational modes, uncorrelated for different spins, serving as a model for dynamic nuclear polarization protocols. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4-5 K in these protocols.
Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.