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Physical Review A

Coherent dipole transport in a small grid of Rydberg atoms

Hui Yu, F. Robicheaux

Published Feb 12, 2016• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.023618

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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 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.
Flexible Rydberg aggregates, assemblies of a few Rydberg atoms coherently sharing electronic excitations while undergoing directed atomic motion, show great promise as a quantum simulation platform for nuclear motion in molecules or quantum energy transport. Here we study additional features that are enabled by the presence of more than a single electronic excitation, thus considering multiexciton states. We describe cases where these can be decomposed into underlying single-exciton states and then present dynamical scenarios with atomic motion that illustrate exciton-exciton collisions, exciton routing, and strong nonadiabatic effects in simple one-dimensional settings.
We study the link between atomic motion and exciton transport in flexible Rydberg aggregates, assemblies of highly excited light alkali-metal atoms, for which motion due to dipole-dipole interaction becomes relevant. In two one-dimensional atom chains crossing at a right angle adiabatic exciton transport is affected by a conical intersection of excitonic energy surfaces, which induces controllable nonadiabatic effects. A joint exciton-motion pulse that is initially governed by a single energy surface is coherently split into two modes after crossing the intersection. The modes induce strongly different atomic motion, leading to clear signatures of nonadiabatic effects in atomic density profiles. We have shown how this scenario can be exploited as an exciton switch, controlling direction and coherence properties of the joint pulse on the second of the chains [K. Leonhardt et al., Phys. Rev. Lett. 113, 223001 (2014)]. In this article we discuss the underlying complex dynamics in detail, characterize the switch, and derive our isotropic interaction model from a realistic anisotropic one with the addition of a magnetic bias field.
Strong resonant dipole-dipole interactions in flexible Rydberg aggregates enable the formation of exciton pulses, the interplay of atomic motion and electronic excitation transfer which feature high fidelity entanglement transport. Here, we demonstrate the coherent splitting of such pulses into two modes, which induce strongly different atomic motion, leading to clear signatures of nonadiabatic effects in atomic density profiles. The mechanism exploits local nonadiabatic effects at a conical intersection, turning them from a decoherence source into an asset. The conical intersection is a consequence of the exciton pulses moving along a linear Rydberg chain and approaching an additional linear, perpendicularly aligned Rydberg chain. The intersection provides a sensitive knob controlling the propagation direction and coherence properties of exciton pulses. We demonstrate that this scenario can be exploited as an exciton switch, controlling direction and coherence properties of the joint pulse on the second of the chains. Initially, we demonstrate the pulse splitting on planar aggregates with atomic motion one-dimensionally constrained and employing isotropic interactions. Subsequently, we confirm the splitting mechanism for a fully realistic scenario in which all spatial restrictions are removed and the full anisotropy of the dipole-dipole interactions is taken into account. Our results enable the experimental observation of non-adiabatic electronic dynamics and entanglement transport with Rydberg atoms. The conical intersection crossings are clearly evident, both in atomic mean position information and excited state spectra of the Rydberg system. This suggests flexible Rydberg aggregates as a test-bench for quantum chemical effects in experiments on much-inflated length scales. The fundamental ideas discussed here have general implications for excitons on a dynamic network.
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.