Regime of Validity of the Pairing Hamiltonian in the Study of Fermi Gases.pdfVIP

Regime of Validity of the Pairing Hamiltonian in the Study of Fermi Gases 6 S. Y. Chang and V. R. Pandharipande 0 0 Department of Physics, University of Illinois at Urbana-Champaign, 2 r 1110 W. Green St., Urbana, IL 61801, U.S.A. a M (Dated: February 2, 2008) 2 1 Abstract ] The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio h p - stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing m o Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction t a. strength. In the weakly interacting (1/akF 0) regime the BCS Hamiltonian should describe s c Landau quasi-particle energies and interactions, on the other hand in the strongly pairing regime, i s y that is 1/akF 0, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian ∼ h p is not adequate for describing atomic gases in the regime of weak to moderate interaction strength [ 1 −∞ 1/akF 0 such as akF ∼ −1. v 3 PACS: 05.30.Fk, 03.75.Ss, 21.65.+f 9 0 3 0 6 0 / s c i s y h p : v i X r a 1 The superfluid state of alkali fermion gases such as 6 Li, 40 K is analogous to the super- conducting state found in the electronic systems [1] and it has been studied theoretically [2] and experimentally [3]. Recent experimental progress includes the detection of the Bose Einstein Condensate (BEC) state of the bound Fermi pairs [4, 5, 6, 7] as an evidence of the predicted BCS-BEC crossover. The interaction among 6Li atoms can be attractive and requires