Bose–Einstein Condensation of Collective Electron Pairs

Sebastian Hofferberth, Jonathan Balewski, Alexander Krupp +5 more

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.

Johannes Hecker Denschlag

Akio Tokumitu, Kazumasa Miyake, Kazuo Yamada

The problem on crossover between the Cooper-pair condensation and the Bose-Einstein condensation of “di-electronic molecules” in two-dimensional superconductors is discussed. a result based on the Nozières and Schmitt-Rink formalism is reviewed and a preliminary result beyond their formalism is presented. In the latter, effect of repulsion between electron pairs due to the exchange effect among constituent electrons plays a crucial role.

M. F. M. Osborne

The condensation and accumulation phenomena of charged Bose-Einstein particles in a magnetic field are examined, neglecting electrostatic interactions. For weak fields a single condensation occurs at the same temperature as that for uncharged particles; for strong fields there is a separate lower accumulation temperature, indicating the accumulation of particles in the lowest translational state. The total energy, free energy, and polarization are calculated, and applied to the properties of a gas of electron pairs, and a solution of deuterons in a metal, these being systems whose low temperature behavior might show a Bose-Einstein condensation. It is shown that the Bose-Einstein condensation of free electron pairs cannot provide a theory of superconductivity.

William J. Mullin, Asaad R. Sakhel