Rostock 2019 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 35: Quantum Gases (Fermions) I

Q 35.5: Talk

Wednesday, March 13, 2019, 15:15–15:30, S HS 037 Informatik

Diverging exchange force for ultracold fermionic atoms — •Christian Schilling¹ and Rolf Schilling² — ¹Clarendon Laboratory, University of Oxford — ²Institut für Physik, Johannes Gutenberg-Universität Mainz

The Pauli exclusion principle 0 ≤ n_k≤ 1 is a kinematical constraint on fermionic occupation numbers which strongly shapes the behavior and the properties of fermionic quantum systems on all length scales. We demonstrate that this fundamental restriction can also be interpreted dynamically: the fermionic exchange symmetry manifests itself in the one-fermion picture in the form of an “exchange force” which repulsively diverges on the boundary of the allowed region, preventing fermionic occupation numbers n_k from leaving their domain 0 ≤ n_k≤ 1. Moreover, for translationally invariant one-band lattice models (e.g. ultracold atoms in an optical lattice), we exploit the ab initio knowledge of the natural orbitals (momentum states) and discover the exact one-matrix functional F(n^→) for smaller cluster systems (such as the Hubbard square). Remarkably, F(n^→) turns out to be strongly shaped by Pauli’s exclusion principle and its recently found generalization.