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arXiv:2103.07990 · Physical Review A

Coherently delocalized states in dipole interacting Rydberg ensembles: The role of internal degeneracies

Ghassan Abumwis, Christopher W. Wächtler, Matthew T. Eiles, Alexander Eisfeld

Published Jul 12, 2021• 2 citations
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Abstract

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.

DOI
10.1103/physreva.104.013311

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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.
The long-range dipole-dipole interaction can create delocalized states due to the exchange of excitation between Rydberg atoms. We show that even in a random gas many of the single-exciton eigenstates are surprisingly delocalized, composed of roughly one quarter of the participating atoms. We identify two different types of eigenstates: one which stems from strongly-interacting clusters, resulting in localized states, and one which extends over large delocalized networks of atoms. These two types of states can be excited and distinguished by appropriately tuned microwave pulses, and their relative contributions can be modified by the Rydberg blockade and the choice of microwave parameters.
Abstract As was recently shown in Abumwis et al (2020 Phys. Rev. Lett. 124 193401), many eigenstates of a random Rydberg gas with resonant dipole–dipole interactions are highly delocalized. Although the high degree of delocalization is generic to various types of power-law interactions and to both two and three-dimensional systems, in their detailed aspects the coherence distributions are sensitive to these parameters and vary dramatically between different systems. We calculate the eigenstates of both two and three-dimensional gases and quantify their delocalization throughout the atoms in the gas using a coherence measure. By contrasting the angular dependence of the dipole–dipole interaction with an isotropic interaction we obtain additional information about the generic physical principles underlying random interacting systems. We also investigate the density of states and microwave absorption spectra to obtain information about the types of measurements where these delocalized states play a role, and to check that these delocalized eigenstates are robust against various types of perturbation.
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.
Scientific advance is often driven by identifying conceptually simple models underlying complex phenomena. This process commonly ignores imperfections which, however, might give rise to non-trivial collective behavior. For example, already a small amount of disorder can dramatically change the transport properties of a system compared to the underlying simple model. While systems with disordered potentials were already studied in detail, experimental investigations on systems with disordered hopping are still in its infancy. To this end, we experimentally study a dipole-dipole-interacting three-dimensional Rydberg system and map it onto a simple XY model with random couplings by spectroscopic evidence. We discuss the localization-delocalization crossover emerging in the model and present experimental signatures of it. Our results demonstrate that Rydberg systems are a useful platform to study random hopping models with the ability to access the microscopic degrees of freedom. This will allow to study transport processes and localization phenomena in random hopping models with a high level of control.
We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.