Alexander T. Krupp

Coupling a single electron to a Bose-Einstein condensate

The coupling of electrons to matter lies at the heart of our understanding of material properties such as electrical conductivity. Electron–phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, which forms the basis for Bardeen–Cooper–Schrieffer superconductivity. Here we study the interaction of a single localized electron with a Bose–Einstein condensate and show that the electron can excite phonons and eventually trigger a collective oscillation of the whole condensate. We find that the coupling is surprisingly strong compared to that of ionic impurities, owing to the more favourable mass ratio. The electron is held in place by a single charged ionic core, forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size of up to eight micrometres, comparable to the dimensions of the condensate. In such a state, corresponding to a principal quantum number of n = 202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects caused by the electron exploring the outer regions of the condensate. We anticipate future experiments on electron orbital imaging, the investigation of phonon-mediated coupling of single electrons, and applications in quantum optics.

From molecular spectra to a density shift in dense Rydberg gases

The transition from a few-body system to a many-body system can result in new length scales, novel collective phenomena or even in a phase transition. Such a threshold behavior was shown for example in He droplets, where He turns into a superfluid for a specific number of particles [1]. A particularly interesting question in this context is at which point a few-body theory can be substituted by a mean field model, i. e. where the discrete number of particles can be treated as a continuous quantity. Such a transition from two non-interacting fermionic particles to a Fermi sea was demonstrated recently [2]. In this letter, we study a similar crossover to a many-body regime based on ultralong-range Rydberg molecules [3] forming a model system with binary interactions. This class of exotic molecules shows very weak binding energies, similar to magneto-associated Feshbach molecules [4, 5], and thus requires ultracold temperatures. A wide range of fascinating phenomena, starting from the coherent creation and breaking of chemical bonds [6] to a permanent electric dipole moment in a homonuclear molecule [7], has been studied. Dimers, consisting of a single atom in the Rydberg state and one atom in the ground state, have been observed in an ultracold gas of Rb in the Rydberg S -state [8], D -state [9, 10] and P -state [11], and of Cs [12] in the Rydberg S -state. The manybody regime, where the Rydberg electron experiences a mean shift by thousands of atoms within its orbit, has been studied at very high densities in a BEC, leading to electron-phonon coupling [13], and in a hot vapor [14]. Here, we trace the transition between the two regimes in an ultracold cloud with a constant density by tuning only one parameter: the principal quantum number n of the excited Rydberg state. We probe the border of the mean field limit, where the energy and length scales of these molecules become extreme. While the binding energies are the smallest ever observed for this type of molecules, the size reaches the dimensions of macroscopic biological objects like viruses or bacteria. The bond in ultralong-range Rydberg molecules results from the scattering of a slow Rydberg electron from a neutral atom with a negative scattering length a [3]. The theoretical approach is based on Fermi’s original concept of the pseudopotential [15]In Rydberg atoms, at least one electron is excited to a state with a high principal quantum number. In an ultracold environment, this low-energy electron can scatter off a ground state atom allowing for the formation of a Rydberg molecule consisting of one Rydberg atom and several ground state atoms. Here we investigate those Rydberg molecules created by photoassociation for the spherically symmetric S-states. A step by step increase of the principal quantum number up to n=111 enables us to go beyond the previously observed dimer and trimer states up to a molecule, where four ground state atoms are bound by one Rydberg atom. The increase of bound atoms and the decreasing binding potential per atom with principal quantum number results finally in an overlap of spectral lines. The associated density-dependent line broadening sets a fundamental limit, for example, for the optical thickness per blockade volume in Rydberg quantum optics experiments.

Rydberg dressing: understanding of collective many-body effects and implications for experiments

The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose–Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure two-body interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas–Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results and point out possible solutions for future approaches. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.

Hybridization of Rydberg Electron Orbitals by Molecule Formation.

The formation of ultralong-range Rydberg molecules is a result of the attractive interaction between a Rydberg electron and a polarizable ground-state atom in an ultracold gas. In the nondegenerate case, the backaction of the polarizable atom on the electronic orbital is minimal. Here we demonstrate how controlled degeneracy of the respective electronic orbitals maximizes this backaction and leads to stronger binding energies and lower symmetry of the bound dimers. Consequently, the Rydberg orbitals hybridize due to the molecular bond.

Imaging single Rydberg electrons in a Bose–Einstein condensate

The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron-phonon coupling in a Bose-Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experimental data. Our scheme requires only well-established experimental techniques that are readily available and allows for the direct capture of textbook-like spatial images of single electronic orbitals in a single shot experiment.

Condensate losses and oscillations induced by Rydberg atoms

We numerically analyze the impact of a single Rydberg electron onto a Bose–Einstein condensate. Both S- and D-Rydberg states are studied. The radial size of S- and D-states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investigate the mechanical effect in which the Rydberg atoms force the condensate to oscillate. Our numerical analysis is based on the classical fields approximation. Finally, we compare numerical results to experimental data.

Coupling a Single Electron to a Bose-Einstein Condensate

We present results of our study of the interaction of a single electron with a Bose-Einstein condensate.