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arXiv:1610.03686 · Journal of Physics B Atomic Molecular and Optical Physics

Condensate losses and oscillations induced by Rydberg atoms

Tomasz Karpiuk, Mirosław Brewczyk, Kazimierz Rza̧żewski, Anita Gaj, Alexander T Krupp, Robert Löw, Sebastian Hofferberth, Tilman Pfau

Published Feb 10, 2017• 1 citation
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Abstract

Abstract 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.

DOI
10.1088/1361-6455/aa5245

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Abstract 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.
Abstract Recent experiments with Bose–Einstein condensates have entered a regime in which thousands of ground-state condensate atoms fill the Rydberg-electron orbit. After the excitation of a single atom into a highly excited Rydberg state, scattering off the Rydberg electron sets ground-state atoms into motion, such that one can study the quantum-many-body dynamics of atoms moving within the Rydberg atom. Here we study this many-body dynamics using Gross–Pitaevskii and truncated Wigner theory. Our simulations focus in particular on the scenario of multiple sequential Rydberg excitations on the same rubidium condensate which has become the standard tool to observe quantum impurity dynamics in Rydberg experiments. We investigate to what extent such experiments can be sensitive to details in the electron–atom interaction potential, such as the rapid radial modulation of the Rydberg molecular potential, or p-wave shape resonance. We demonstrate that both effects are crucial for the initial condensate response within the Rydberg orbit, but become less relevant for the density waves emerging outside the Rydberg excitation region at later times. Finally we explore the local dynamics of condensate heating. We find that it provides only minor corrections to the mean-field dynamics. Combining all these insights, our results suggest Bose–Einstein condensates as a viable platform for the in situ and real time interrogation of ultra-cold chemistry dynamics involving Rydberg states.
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.
This thesis was established in the field of ultracold atoms where the interaction of highly excited D-state electrons with rubidium atoms was examined. This work is divided into two main parts: In the first part we study D-state Rydberg molecules resulting from the binding of a D-state Rydberg electron to a ground state rubidium atom. We show that we can address specific rovibrational molecular states by changing our laser detuning and thus create perfectly aligned axial or antialigned toroidal molecules, in good agreement with our theoretical calculations. Furthermore the influence of the electric field on the Rydberg molecules was investigated, creating novel states which show a different angular dependence and alignment. In the second part of this thesis we excite single D-state Rydberg electrons in a Bose-Einstein condensate. We study the lifetime of these Rydberg electrons, the change of the shape of our condensate and the atom losses in the condensate due to this process. Moreover, we observe quadrupolar shape oscillations of the whole condensate created by the consecutive excitation of Rydberg atoms and compare all results to previous S-state measurements. In the outlook we propose a wide range of further experiments including the proposal of imaging a single electron wavefunction by the imprint of its orbit into the Bose-Einstein condensate.
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 present our investigations of a single electron embedded in a Bose–Einstein condensate. We 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 favorable 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. The Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We discuss experiments on in-situ electron orbital imaging, the investigation of phonon- mediated coupling of single electrons, and applications in quantum optics.
Measurements of the loss rates for strontium n3S1n^{3}S_{1}n3S1​ Rydberg atoms excited in a dense Bose-Einstein condensate are presented for values of principal quantum number nnn in the range $49\ensuremath{\lesssim}n\ensuremath{\lesssim}150$ and local atom densities of $\ensuremath{\sim}1$ to $3\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. Two main processes contribute to loss, associative ionization, and state changing. The relative importance of these two loss channels is investigated, and their nnn and density dependences are discussed using a model in which the Rydberg atom loss is presumed to involve a close collision between the Rydberg core ion and ground-state atoms. The present measurements are compared to earlier results obtained using rubidium Rydberg atoms. For both species the observed loss rates are sizable, $\ensuremath{\sim}{10}^{5}\ensuremath{-}{10}^{6}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, and limit the timescales over which measurements involving Rydberg atoms immersed in quantum degenerate gases can be conducted.
The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein condensate is investigated. The Heisenberg equations of motions for the condensate and the Rydberg atom are derived. Neglecting the back action of the Rydberg atom onto the condensate decouples the equations describing the condensate and Rydberg atom. In this case the spectral structure of the Rydberg atom is completely determined by an effective potential which depends on the density distribution of the condensate. We study the spectral properties for the situation of an isotropic harmonic and anharmonic as well as axially symmetric confinement. In the latter case an intriguing analogy with Rydberg atoms in magnetic fields is encountered.