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arXiv:2006.15376 · Physical Review A

Tailoring Bose-Einstein-condensate environments for a Rydberg impurity

S. Rammohan, Anil Kumar Chauhan, Rejish Nath, Alexander Eisfeld, Sebastian Wüster

Published Jun 15, 2021• 10 citations
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Abstract

Experiments have demonstrated that the excitation of atoms embedded in a Bose-Einstein condensate to Rydberg states is accompanied by phonon creation. Here we provide the theoretical basis for the description of phonon-induced decoherence of the superposition of two different Rydberg states. To this end, we determine Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities, and reorganization energies. These quantities characterize the influence of the environment and form essential inputs for followup open quantum system approaches. We find that the amplitude of bath correlations scales like the power law ${\ensuremath{\nu}}^{\ensuremath{-}6}$ with the principal quantum number $\ensuremath{\nu}$, while reorganization energies scale exponentially, reflecting the extreme tunability of Rydberg atomic properties.

DOI
10.1103/physreva.103.063307

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Experiments have demonstrated that the excitation of atoms embedded in a Bose-Einstein condensate to Rydberg states is accompanied by phonon creation. Here we provide the theoretical basis for the description of phonon-induced decoherence of the superposition of two different Rydberg states. To this end, we determine Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities, and reorganization energies. These quantities characterize the influence of the environment and form essential inputs for followup open quantum system approaches. We find that the amplitude of bath correlations scales like the power law \ensuremathν\ensuremath−6{\ensuremath{\nu}}^{\ensuremath{-}6}\ensuremathν\ensuremath−6 with the principal quantum number \ensuremathν\ensuremath{\nu}\ensuremathν, while reorganization energies scale exponentially, reflecting the extreme tunability of Rydberg atomic properties.
We show that two major facets of the decoherence paradigm are experimentally accessible for a single impurity atom embedded in a Bose-Einstein condensate, when the impurity is brought into an electronic superposition of two Rydberg states. Not only can the electronic decoherence of the Rydberg atom be read out by microwave interferometry, the platform also provides unique access to the accompanying entangled state of the environment. We theoretically demonstrate signatures of the latter in total atom densities during the transient time in which the impurity is becoming entangled with the medium but the resultant decoherence is not complete yet. The Rydberg impurity thus provides a handle to initiate and read-out mesoscopically entangled superposition states of Bose atom clouds affecting about 500 condensate atoms. We find that the time-scale for its creation and decoherence can be tuned from the order of nanoseconds to microseconds by choice of the excited Rydberg principal quantum number ν\nuν, and that Rydberg decoherence dynamics is typically non- Markovian.
We investigate the absorption spectrum of a Rydberg impurity immersed in and interacting with an ideal Bose-Einstein condensate. Here, the impurity-bath interaction range can greatly exceed the mean interparticle distance; this discrepancy in length scales challenges the assumptions underlying the universal aspects of impurity atoms in dilute bosonic environments. Our analysis finds three distinct parameter regimes, each characterized by a unique spectral response. In the low-density regime, we find that the Rydberg impurity is dressed by the surrounding bath similarly to the known Bose polaron. Transitioning to intermediate densities, the impurity response, given by sharp quasiparticle peaks, fragments into an intricate pattern bearing the hallmarks of a diverse molecular structure. Finally, at high density, a universal Gaussian response emerges as the statistical nature of the bath dominates its quantum dynamics. We complement this analysis with a study of an ionic impurity, which behaves equivalently. Our exploration offers insights into the interplay between interaction range, density, and many-body behavior in impurity systems. Published by the American Physical Society 2024
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.
We report spectroscopic observation of Rydberg polarons in an atomic Bose gas. Polarons are created by excitation of Rydberg atoms as impurities in a strontium Bose-Einstein condensate. They are distinguished from previously studied polarons by macroscopic occupation of bound molecular states that arise from scattering of the weakly bound Rydberg electron from ground-state atoms. The absence of a p-wave resonance in the low-energy electron-atom scattering in Sr introduces a universal behavior in the Rydberg spectral line shape and in scaling of the spectral width (narrowing) with the Rydberg principal quantum number, n. Spectral features are described with a functional determinant approach (FDA) that solves an extended Fröhlich Hamiltonian for a mobile impurity in a Bose gas. Excited states of polyatomic Rydberg molecules (trimers, tetrameters, and pentamers) are experimentally resolved and accurately reproduced with a FDA.
We show how the phase profile of Bose-Einstein condensates can be engineered through its interaction with localized Rydberg excitations. The interaction is made controllable and long range by off-resonantly coupling the condensate to another Rydberg state with laser light. Our technique allows the mapping of entanglement generated in systems of few strongly interacting Rydberg atoms onto much larger atom clouds in hybrid setups. As an example we discuss the creation of a spatial mesoscopic superposition state from a bright soliton. Additionally, the phase imprinted onto the condensate using the Rydberg excitations is a diagnostic tool for the latter. For example, a condensate time-of-flight image would permit reconstructing the pattern of an embedded Rydberg crystal.
We investigate a hybrid system composed of ultracold Rydberg atoms immersed in an atomic Bose-Einstein condensate (BEC). The coupling between Rydberg electrons and BEC atoms leads to excitations of phonons, the exchange of which induces a Yukawa interaction between Rydberg atoms. Because of the small electron mass, the effective charge associated with this quasiparticle-mediated interaction can be large. Its range, equal to the BEC healing length, is tunable using Feshbach resonances to adjust the scattering length between BEC atoms. We find that for small healing lengths, the distortion of the BEC can "image" the Rydberg electron wave function, while for large healing lengths the induced attractive Yukawa potentials between Rydberg atoms are strong enough to bind them.