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arXiv:1401.4776 · Physical Review A

Effect of random positions for coherent dipole transport

F. Robicheaux, N. M. Gill

Published May 30, 2014• 18 citations
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Abstract

We calculate the effect of two kinds of randomness on the coherent motion of an exciton whose transport is governed by the dipole-dipole interaction. As our example, we use the idealized case of stationary Rydberg atoms on a lattice. We present calculations for how fast the excitation can move away from its starting position for different dimensional lattices and for different levels of randomness. We also examine the asymptotic in time final position of the excitation to determine whether or not the excitation can be localized. The one-dimensional system is an example of Anderson localization where the randomness is in the off-diagonal elements although the long-range nature of the interaction leads to nonexponential decay with distance. The two-dimensional square lattice shows a mixture of extended and localized states for large randomness, while there is no visible sign of localized states for weak randomness. The three-dimensional cubic lattice has few localized states even for strong randomness.

DOI
10.1103/physreva.89.053429

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We calculate the effect of two kinds of randomness on the coherent motion of an exciton whose transport is governed by the dipole-dipole interaction. As our example, we use the idealized case of stationary Rydberg atoms on a lattice. We present calculations for how fast the excitation can move away from its starting position for different dimensional lattices and for different levels of randomness. We also examine the asymptotic in time final position of the excitation to determine whether or not the excitation can be localized. The one-dimensional system is an example of Anderson localization where the randomness is in the off-diagonal elements although the long-range nature of the interaction leads to nonexponential decay with distance. The two-dimensional square lattice shows a mixture of extended and localized states for large randomness, while there is no visible sign of localized states for weak randomness. The three-dimensional cubic lattice has few localized states even for strong randomness.
We calculate the effect of two kinds of randomness on the coherent motion of an exciton whose transport is governed by the dipole-dipole interaction. As our example, we use the idealized case of stationary Rydberg atoms on a lattice. We present calculations for how fast the excitation can move away from its starting position for different dimensional lattices and for different levels of randomness. We also examine the asymptotic in time final position of the excitation to determine whether or not the excitation can be localized. The one-dimensional system is an example of Anderson localization where the randomness is in the off-diagonal elements although the long-range nature of the interaction leads to nonexponential decay with distance. The two-dimensional square lattice shows a mixture of extended and localized states for large randomness, while there is no visible sign of localized states for weak randomness. The three-dimensional cubic lattice has few localized states even for strong randomness.
Randomness and disorder have strong impact on transport processes in quantum systems and give rise to phenomena such as Anderson localization [1-3], many-body localization [4] or glassy dynamics [5]. Their characteristics thereby depend on the strength and type of disorder. An important class are hopping models, where particles or excitations move through a system which has randomized couplings. This includes, e.g., spin glasses [5], coupled optical waveguides [6], or NV center arrays [7]. They are also key to understand excitation transport in molecular and biological systems, such as light harvesting complexes [8]. In many of those systems, the microscopic coupling mechanism is provided by the dipole-dipole interaction. Rydberg systems [9] are therefore a natural candidate to study random hopping models. Here, we experimentally study a three-dimensional many-body Rydberg system with random dipole-dipole couplings. We measure the spectrum of the many-body system and find good agreement with an effective spin model. We also find spectroscopic signatures of a localization-delocalization transition. Our results pave the way to study transport processes and localization phenomena in random hopping models in detail. The inclusion of strong correlations is experimentally straightforward and will allow to study the interplay between random hopping and localization in strongly interacting systems.
We calculated the motion of one or two excitons through a small grid of Rydberg atoms. Both one- and two-dimensional grids were studied with the number of sites in a direction between 4 and 10. To mimic the possibility of nonperfect filling, calculations were performed with atoms randomly missing from sites. Results are presented for four qualitatively different situations. (1) The corners and edges, with the randomness of nonperfect filling, strongly affects the exciton motion and can pin the exciton. (2) For the case where a single exciton is simultaneously generated at two sites, the direction in which the exciton moves can be controlled by imprinting a phase difference on the two adjacent sites. (3) For the case where two excitons are generated at adjacent sites, calculations where a pair of excitons move through the grid are compared to the one exciton case to see whether exciton-exciton correlations are measurable. (4) The grid version of an exciton current can be defined by analogy to a continuity equation in one dimension and by using the analogy to a velocity operator in one, two, or three dimensions; for one dimension, the two definitions give similar results which means the direct measurement of the current in one dimension is possible.
We investigate the effect of degenerate atomic states on the exciton delocalization of dipole-dipole interacting Rydberg assemblies. Using a frozen gas and regular one-, two-, and three-dimensional lattice arrangements as examples, we see that degeneracies can enhance the delocalization compared to the situation when there is no degeneracy. This enhancement is particularly large in the case of the three-dimensional (3D) random gas, but is absent for 1D arrangements. Using the Zeeman splitting provided by a magnetic field, we controllably lift the degeneracy to study in detail the transition between degenerate and nondegenerate regimes. These observations, although specific to the experimentally clean Rydberg gas, have generic implications for various dipole-interacting systems.
We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t ∼ 1 s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.