Freiburg 2024 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 58: Ultra-cold Atoms, Ions and BEC IV (joint session A/Q)

Q 58.7: Talk

Friday, March 15, 2024, 12:30–12:45, HS 1098

Effective Theory for the Gaudin-Yang model — •Timothy George Backert¹, Hans-Werner Hammer^1,3, Artem Volosniev², Fabian Brauneis¹, Joachim Brand⁴, and Matija Čufar⁴ — ¹Technische Universität Darmstadt, Department of Physics — ²Institute of Science and Technology Austria (ISTA) — ³ExtreMe Matter Institute EMMIand Helmholtz Forschungsakademie Hessen für FAIR (HFHF) — ⁴New Zealand Institute for Advanced Study, Massey University, New Zealand

We investigate the crossover from a Bardeen-Cooper-Schrieffer superfluid with loosely bound Cooper pairs to a Bose-Einstein condensate of tightly bound dimers (molecules) for a one-dimensional spin-1/2 Fermi gas (Gaudin-Yang model [GY]) on a ring. We obtain exact Bethe-Ansatz solutions which describe the BCS-BEC crossover in the form of a transition from a (BCS-like) gas of loosely bound fermion pairs to a Tonks-Girardeau gas of tightly bound dimers. For the experimentally relevant case of an external potential only numerical solutions can be obtained. In order to obtain analytical insights into the case with an external potential, we set up an effective theory with fermions and dimers as degrees of freedom and determine the coupling constants by matching to the Bethe-Ansatz results. We find good agreement with the numerical results for small particle numbers. This paves the way for the exploration of many-body systems using this effective theory. Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) * Project-ID 279384907 * SFB 1245.

Keywords: Gaudin-Yang; Bethe ansatz; Effective Field Theory; BCS-BEC crossover