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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 superconductivity1. 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.

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Figure 1: Size comparison in the spatial and energy domains.
Figure 2: Rydberg excitation spectra for different principal quantum numbers and the mechanical effect on the condensate.
Figure 3: Energy shift and lifetime reduction of the Rydberg state in a condensate and Rydberg electron induced loss of BEC atoms.

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We thank K. Rzążewski and J. Hecker Denschlag for discussions and C. Tresp for setting up the Rydberg laser system. This work was funded by the Deutsche Forschungsgemeinschaft (DFG) within SFB/TRR21 and project PF 381/4-2. We also acknowledge support by the ERC under contract number 267100, and A.G. acknowledges support from EU Marie Curie programme ITN-Coherence 265031. S.H. is supported by the DFG through project HO 4787/1-1.

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The experiment was conceived by J.B.B., R.L., S.H. and T.P. and carried out by J.B.B., A.T.K. and A.G.; data analysis was accomplished by J.B.B., A.T.K. and A.G.; perturbation theory was developed by D.P. and H.P.B.; and J.B.B. and D.P. wrote the manuscript with contributions from all authors.

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Correspondence to Tilman Pfau.

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The authors declare no competing financial interests.

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Balewski, J., Krupp, A., Gaj, A. et al. Coupling a single electron to a Bose–Einstein condensate. Nature 502, 664–667 (2013).

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