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arXiv:1305.2526 · Annalen der Physik

Quantum simulations of localization effects with dipolar interactions

Gonzalo A. Álvarez, Robin Kaiser, Dieter Suter

Published Oct 8, 2013• 22 citations
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Abstract

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.

DOI
10.1002/andp.201300096

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•Jan 1, 2013•0 citations
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.
The loss of coherence in quantum mechanical superposition states limits the time for which quantum information remains useful. Similarly, it limits the distance over which quantum information can be transmitted. Here, we investigate in a nuclear spin-based quantum simulator, the localization of the size of spin clusters that are generated by a Hamiltonian driving the transmission of information, while a variable-strength perturbation counteracts the spreading. We find that the system reaches a dynamic equilibrium size, which decreases with the square of the perturbation strength.
The spurious interaction of quantum systems with their environment known as decoherence leads, as a function of time, to a decay of coherence of superposition states. Since the interactions between system and environment are local, they can also cause a loss of spatial coherence: correlations between spatially distant parts of the system are lost and the equilibrium states can become localized. This effect limits the distance over which quantum information can be transmitted, e.g., along a spin chain. We investigate this issue in a nuclear magnetic resonance quantum simulator, where it is possible to monitor the spreading of quantum information in a three-dimensional network: states that are initially localized on individual spins (qubits) spread under the influence of a suitable Hamiltonian apparently without limits. If we add a perturbation to this Hamiltonian, the spreading stops and the system reaches a limiting size, which becomes smaller as the strength of the perturbation increases. This limiting size appears to represent a dynamical equilibrium. We present a phenomenological model to describe these results.
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.
We theoretically investigate the localization of an expanding Bose–Einstein condensate (BEC) with repulsive atom–atom interactions in a disordered potential. We focus on the regime where the initial inter-atomic interactions dominate over the kinetic energy and the disorder. At equilibrium in a trapping potential and for the considered small disorder, the condensate shows a Thomas–Fermi shape modified by the disorder. When the condensate is released from the trap, a strong suppression of the expansion is obtained in contrast to the situation in a periodic potential with similar characteristics. This effect crucially depends on both the momentum distribution of the expanding BEC and the strength of the disorder. For strong disorder as in the experiments reported by Clément et al 2005 Phys. Rev. Lett. 95 170409 and Fort et al 2005 Phys. Rev. Lett. 95 170410, the suppression of the expansion results from the fragmentation of the core of the condensate and from classical reflections from large modulations of the disordered potential in the tails of the condensate. We identify the corresponding disorder-induced trapping scenario for which large atom–atom interactions and strong reflections from single modulations of the disordered potential play central roles. For weak disorder, the suppression of the expansion signals the onset of Anderson localization, which is due to multiple scattering from the modulations of the disordered potential. We compute analytically the localized density profile of the condensate and show that the localization crucially depends on the correlation function of the disorder. In particular, for speckle potentials the long-range correlations induce an effective mobility edge in 1D finite systems. Numerical calculations performed in the mean-field approximation support our analysis for both strong and weak disorder.
Spin squeezed entanglement enables metrological precision beyond the classical limit. Understood through the lens of continuous symmetry breaking, dipolar spin systems exhibit the remarkable ability to generate spin squeezing via their intrinsic quench dynamics. To date, this understanding has primarily focused on lattice spin systems; in practice however, dipolar spin systems$\unicode{x2014}$ranging from ultracold molecules to nuclear spin ensembles and solid-state color centers$\unicode{x2014}$often exhibit significant amounts of positional disorder. Here, we develop a theory for scalable spin squeezing in a two-dimensional randomly diluted lattice of quantum dipoles, which naturally realize a dipolar XXZ model. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order, and by extension scalable spin squeezing, as a function of both disorder and Ising anisotropy. As the disorder increases, we find that scalable spin squeezing survives only near the Heisenberg point. We show that this behavior is due to the presence of rare tightly-coupled dimers, which effectively heat the system post-quench. In the case of strongly-interacting nitrogen-vacancy centers in diamond, we demonstrate that an experimentally feasible strategy to decouple the problematic dimers from the dynamics is sufficient to enable scalable spin squeezing.
In this thesis we address relevant problems of the physics of quantum disordered systems from a numerical and theoretical point of view, with specific attention to the connection of our findings with ultracold atomic gases experiments. We concentrate on two main issues: the interplay between localization and interaction in disordered systems and the problem of localization in correlated random potentials. The first problem is investigated considering the expansion of a weakly interacting Bose gas in a bichromtic optical lattice. We observe that interaction has a destructive effect on the disorder-induced localization and leads to a subdiffusive expansion of the atomic gas. By comparing three characteristic energy scales of the system one can identify three different spreading regimes: weak chaos, strong chaos and self-trapping. The spreading behaviour in these regimes is predicted theoretically and verified numerically. We also interpreted existing experimental data on the basis of our findings and showed that there is a qualitative agreement between our numerical simulations and experiments. The second problem is investigated proposing a new model of correlated disorder that can be implemented experimentally using ultracold dipolar gases. We show that this model is characterized by the presence of both short and long range correlations. We study the localization properties of the model and highlight the role played by short and long range correlations in the determination of those properties. In particular we show that when short-range correlations are dominant, extended states can appear in the spectrum. The effect of long-range correlations is instead to restore localization over the whole spectrum and lead to counterintuitive behaviours of the localization length. More precisely, depending on the localization regime they can enhance or reduce the localization length at the centre of the band.