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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 Hammer1,3, 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