localization effects

Science: Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins

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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.


Gonzalo A. Álvarez (1), Dieter Suter (2), Robin Kaiser (3)

(1) Department of Chemical Physics, Weizmann Institute of Science, 76100, Rehovot, Israel.
(2) Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany.
(3) Institut Non-Linéaire de Nice, CNRS, Université de Nice Sophia Antipolis, 06560, Valbonne, France.

Science 349, 846 (2015)

DOI: 10.1126/science.1261160


Time evolution of the cluster size of correlated spins K for different quench strengths (1-p) and finite-time scaling procedure. (A) Cluster-size K as a function of the time t after the quench. The unperturbed quenched evolution (black squares) shows a cluster-size K that grows as ∼t^(4.3) at long times (dashed line is a guide to the eye). The solid symbols show the points used for a finite-time scaling analysis, while the empty symbols do not belong to the long time regime (t < 0.3 ms). For the largest perturbation strengths p to the quench, localization effects are clearly visible by the saturation of the cluster size. (B and C) In these two panels, we present the finite-time scaling procedure. In (B), the rescaled and squared correlation length l^2= K^(2/3) as a function of the evolution time 1=t^(k_2) is plotted. In (C), the curves of (B) are rescaled horizontally by the scaling factor ξ(p) to obtain a universal scaling law.


Scaling factor and critical exponents. Normalized scaling factor ξ(p) as a function of p (blue triangles). The red solid line is a fit to the blue triangles with a expression ξ(p) proportional to|p − p_c|^nu, the critical exponent is then nu= 0,42. The two insets show the distribution of coherence orders of the density matrix as a function of the evolution time t for two perturbation strengths, which correspond to a delocalized and localized regime, respectively. The corresponding scaling factors are indicated by the arrows.

via Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.

Quantum simulations of localization effects with dipolar interactions | Annalen der Physik – 2013

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Quantum simulations of localization effects with dipolar interactions

Gonzalo A. Álvarez, Robin Kaiser, Dieter Suter

Quantum information processing often uses systems with dipolar interactions. Here a nuclear spin-based quantum simulator is used to study the spreading of information in such a dipolar-coupled system. While the information spreads with no apparent limits in the case of ideal dipolar couplings, additional perturbations limit the spreading, leading to localization. In previous work [Phys. Rev. Lett. 104, 230403 (2010)], it was found that the system size reaches a dynamic equilibrium that decreases with the square of the perturbation strength. This work examines the impact of a disordered Hamiltonian with dipolar interactions. It shows that the expansion of the cluster of spins freezes in the presence of large disorder, reminiscent of Anderson localization of non-interacting waves in a disordered potential.

Keywords: spin dynamics;dipolar interaction;decoherence;localization;disorder;NMR;long range interactions;quantum information processing

Annalen der Physik
Special Issue on “Quantum Simulations“, featuring review papers written by last year’s Nobel Prize winners describing their foundational work (Wineland and Haroche). Issue edited by: Rainer Blatt, Immanuel Bloch, Ignacio Cirac, Peter Zoller.
Ann. Phys. 525, 833 (2013).
DOI: 10.1002/andp.201300096

© 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

via Quantum simulations of localization effects with dipolar interactions – Álvarez – 2013 – Annalen der Physik – Wiley Online Library.

Quantum simulations of localization effects with dipolar interactions - Álvarez - 2013 - Annalen der Physik - Wiley Online Library
Time evolution of the cluster-size of correlated spins starting from different initial sates. The experimental data is shown for two different perturbation strengths given in the legend. The solid black squares, red triangles and green rhombuses are evolutions from an uncorrelated initial state. Empty symbols start from an initial state with K0 correlated spins. The insets show the Multiple Quantum Coherence spectrum starting from K0 = 141 as a functions of time for a perturbation strength.