Rydberg Composites

We introduce the Rydberg composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms. The properties of the composite depend on both the Rydberg excitation, which provides the gross energetic and spatial scales, and the distribution of ground state atoms within the volume of the Rydberg wave function, which sculpt the electronic states. The latter range from the “trilobites,” for small numbers of scatterers, to delocalized and chaotic eigenstates, for disordered scatterer arrays, culminating in the dense scatterer limit in symmetry-dominated wave functions which promise good control in future experiments. We discuss one-, two-, and three- dimensional arrangements of scatterers using different theoretical methods, enabling us to obtain scaling behavior for the regular spectrum and measures of chaos and delocalization in the disordered regime. We also show that analogous quantum dot composites can elucidate in particular the dense scatterer limit. Thus, we obtain a systematic description of the composite states. The two-dimensional monolayer composite possesses the richest spectrum with an intricate band structure in the limit of homogeneous scatterers, experimentally accessible with pancake-shaped condensates.

Ultralong-range molecules composed of a Rydberg atom and a ground state atom, colloquially known as trilobites, were proposed in 2000. Soon thereafter theoretical explorations regarding the possibility of polyatomic molecules involving several ground state atoms followed. The experimental verification of ultralong-range Rydberg dimers in 2009 also confirmed accidentally the existence of trimers. Since then, interest in Rydberg excitations beyond isolated atoms has rapidly branched out into quite diverse scenarios. These include the replacement of the ground state atom in the original trilobite dimer by larger and more complex systems, e.g., one or more polar molecules, the (re)discovery of Rydberg excitations in solid-state systems, and a large variety of excitonic Rydberg dynamics in the gas phase, just to name a few. For the increasingly dense gases now achievable in experiments, one can elegantly describe this system as a Rydberg excitation dressed by ground state atoms from the gas. In fact, recent experiments exhibit spectral features corresponding to polyatomic molecules containing up to five ground state atoms, and mean-field shifts in the spectrum reveal this polaronic behavior involving the coupling of many hundreds of atoms to the Rydberg electron. One may wonder how many ground state “scatterer” atoms within the volume occupied by the Rydberg wave function can a trilobite molecule tolerate. A recent study found that trilobites thrive in dense gas, which is counterintuitive at first glance.

What we lack is a systematic approach which connects the trilobite regime with a few scatterers to the regime of very dense scatterers, although the phenomena just described suggest that Rydberg excitations immersed in dense and structured media might have very interesting properties. The present investigation opens a new venue for Rydberg composite systems along this way, which involve many thousands of atoms in a structured environment coupled to a single Rydberg atom. These composites can be formed by exciting a Rydberg atom within a one-, two-, or three- dimensional optical lattice such that the electronic wave function envelops many atoms on the surrounding sites but can also be created in other settings involving randomly positioned scatterers within a geometrically confined volume. We present a systematic and detailed investigation of this Rydberg composite and provide its properties as a function of principal quantum number ν, lattice constant d, and fill factor F of lattice sites.

With the Rydberg composite we change the perspective from the molecular one—using chemical approaches to characterize polyatomic trilobites via Born-Oppenheimer potential surfaces, rovibrational couplings, etc.,—to a condensed matter one, emphasizing generic scaling principles, gross structure, and properties associated with the high density of states obtained here. This allows us to approach systematically dense atomic environments.

Indeed, we will see that toward the limit of homogeneous filling a bandlike structure in the spectrum emerges. Moreover, the unique property of a Rydberg electron bound to an isolated atom with a singular point of infinite density of states (DOS) at the ionization threshold limν→∞ Eν ≡ −1=ð2ν2Þ ¼ 0 and full degeneracy makes such a Rydberg composite an interesting object to study, as the distribution of scatterers can break the degeneracy in a controlled, yet flexible, way. We identify nontrivial scaling properties as a function of ν. They allow us to connect the situation at finite ν with threshold ν → ∞.

Finally, the composite’s key properties are derived analytically in the homogeneous limit, while random matrix theory is used for the irregular part of the spectrum. We also explain how a planar environment breaks the symmetry of the Rydberg composite and leads to much richer spectral structures as compared to a wirelike (one- dimensional) or crystal-like (three-dimensional) atomic environment. Hence, we put emphasis on a planar sheet of atoms arranged in a lattice containing a Rydberg excitation as an exemplary Rydberg composite whose experimental realization is facilitated by the routine creation of two-dimensional optical lattices and, increasingly, the rapid progress in optical tweezer arrays. Several of the Rydberg composite properties we study are observable in a 2D system without a regular lattice arrangement and could be studied in sufficiently dense pancake-shaped condensates. Moreover, we briefly discuss how quantum dots can give rise to similar composite structures. They further elucidate the dense scatterer limit, offer additional possibilities to create a composite experimentally, and underline the generality of the excitation composite idea beyond Rydberg composites.

More generally, excitation composites as introduced here describe how the high degeneracy of an underlying excitation (zeroth-order Hamiltonian) can be lifted in a controlled way. The “generic” situation of sufficiently many scatterers to remove all degeneracies exhibits chaotic level dynamics. It can be smoothly tuned to the few- scatterer limit where less degenerate polyatomic electronic symmetries replace the highly degenerate and symmetric underlying excitation spectrum. In the opposite limit of very many scatterers, the latter lose their individual role. Rather, the symmetry of their geometric support becomes dominant. If it is planar, it turns the degenerate spectrum of the Rydberg excitation into well-structured energy bands, which is a manifestation of novel correlation effects.

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