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Nature Communications

Experimental realization of a 3D random hopping model

Carsten Lippe, Tanita Klas, Jana Bender, Patrick Mischke, Thomas Niederprüm, Herwig Ott

Published Nov 30, 2021• 9 citations
Publisher

Abstract

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.

DOI
10.1038/s41467-021-27243-2

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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.
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 study excitation transport in a two-dimensional system of randomly assembled spins with power-law hopping in two dimensions. This model can be realized in cold atom quantum simulators with Rydberg atoms. In these experiments, due to the Rydberg blockade effect, the degree of disorder in the system is effectively tunable by varying the spin density. We study dynamics and eigenstate properties of the model as a function of disorder strength and system size and discuss potential limitations for experiments. At strong disorder we predominantly observe localized eigenstates with power-law tails. In this regime the spectral and eigenstate properties can be understood in a perturbative picture of states localized on small clusters of spins. As the disorder strength is weakened eigenstates become increasingly delocalized and a set of seemingly multifractal states appears in the low-energy tail of the spectrum. A detailed study of the system-size scaling of the eigenstate properties indicates that in the infinite-size limit all states eventually become localized. We discuss the feasibility of observing localization effects experimentally in the spatial spreading of an initially localized excitation and identify limited system sizes and finite decoherence rates as major challenges. Our study paves the way towards an experimental observation of localization effects in Rydberg spin systems with tunable disorder.
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.
Programmable arrays of neutral Rydberg atoms are one of the leading platforms today for scalable quantum simulation and computation. In these systems, the dipole-dipole interactions between the individual atoms, or qubits, typically result in binary -- i.e., two-body -- couplings. In this work, we develop an experimentally accessible scheme for engineering three-body interactions in Rydberg lattices. Such strong three-body couplings can fundamentally modify the underlying physics compared to systems with only two-body interactions: we demonstrate this, in particular, by systematically investigating the effective many-body Hamiltonian and its emergent quantum phases. This capability paves the way for the quantum simulation of a broader class of correlated models of condensed matter and high-energy physics.
Strongly interacting quantum systems subject to quenched disorder exhibit intriguing phenomena such as glassiness and many-body localization. Theoretical studies have mainly focused on disorder in the form of random potentials, while many experimental realizations naturally feature disorder in the interparticle interactions. Inspired by cold Rydberg gases, where such disorder can be engineered using the dipole blockade effect, we study a Heisenberg XXZ spin model where the disorder is exclusively due to random spin-spin couplings, arising from power-law interactions between randomly positioned spins. Using established spectral and eigenstate properties and entanglement entropy, we show that this system exhibits a localization crossover and identify strongly interacting pairs as emergent local conserved quantities in the system, leading to an intuitive physical picture consistent with our numerical results.
The exploration of large-scale many-body phenomena in quantum materials has produced many important experimental discoveries, including novel states of entanglement, topology and quantum order as found for example in quantum spin ices, topological insulators and semimetals, complex magnets, and high-T c superconductors.Yet, the sheer scale of solid-state systems and the difficulty of exercising exacting control of their quantum mechanical degrees of freedom limit the pace of rational progress in advancing the properties of these and other materials.With extraordinary effort to counteract natural processes of dissipation, precisely engineered ultracold quantum simulators could point the way to exotic new materials.Here, we look instead to the quantum mechanical character of the arrested state formed by a quenched ultracold molecular plasma.This novel class of system arises spontaneously, without a deliberate engineering of interactions, and evolves naturally from statespecified initial conditions, to a long-lived final state of canonical density, in a process that conflicts with classical notions of plasma dissipation and neutral dissociation.We take information from experimental observations to develop a conceptual argument that attempts to explain this state of arrested relaxation in terms of a minimal phenomenological model of randomly interacting dipoles of random energies.This model of the plasma forms a starting point to describe its observed absence of relaxation in terms of many-body localization (MBL).The large number of accessible Rydberg and excitonic states gives rise to an unconventional web of many-body interactions that vastly exceeds the complexity of MBL in a conventional few-level scheme.This experimental platform thus opens an avenue for the coupling of dipoles in disordered environments that will demand the development of new theoretical tools.