EXACT BCS SOLUTION IN THE BCS-BEC CROSSOVER

Ayan Khan

Gerardo Ortíz, J. Dukelsky

Jean-Noël Fuchs, RECATI A, W. Zwerger

Andrea Spuntarelli, P. Pieri, Giancarlo Calvanese Strinati

J. Dukelsky, Gerardo Ortíz, S. Rombouts

The exact Richardson solution of the reduced BCS Hamiltonian is used to study the BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media. Based on the exact eigenstate we will discuss the Cooper-pair concept proposing a scenario for the BCS-to-BEC crossover in which a mixture of quasifree fermions and pair resonances (BCS) evolves to a system of weakly bound molecules (BEC). In this single unified scenario the Cooper-pair wavefunction has a unique functional form. We propose a new definition of the condensate fraction which, within the limits of the BCS model, gives a qualitative description of recent experiments in ultracold atomic Fermi gases. Finally, we will introduce a new integrable model for asymmetric superfluid systems able to describe different homogeneous and inhomogeneous competing phases such as, breached superconductivity, deformed Fermi superfluidity, and the elusive Larkin-Ovchinnikov-Flde-Ferrell (LOFF) state.

J. Dukelsky, Gerardo Ortíz

The exact Richardson solution of the reduced BCS Hamiltonian is reviewed with special emphasis on the structure of the many-body wavefunction. A clear definition of the Cooper pairs in the superconducting or Fermi superfluid medium emerges. The structure of the Cooper pair wavefunction is general enough to describe large overlapping pair resonances in the weak coupling limit (BCS) as well as a Bose-Einstein condensate (BEC) of quasi-bound molecules in the strong coupling limit.