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A Composite Fermion Approach to the Ultracold Dilute Fermi Gas

It is argued that the recently observed Fermi liquids in strongly interacting ultracold Fermi gases are adiabatically connected to a projected Fermi gas. This conclusion is reached by constructing a set of Jastrow wavefunctions, following Tan's observations on the structure of the physical Hilbert space [Annals of Physics 323, 2952 (2008)]. The Jastrow projection merely implements the Bethe-Peierls condition on the BCS and Fermi gas wavefunctions. This procedure provides a simple picture of the emergence of Fermi polarons as composite fermions in the normal state of the highly polarized gas. It is also shown that the projected BCS wavefunction can be written as a condensate of pairs of composite fermions (or Fermi polarons). A Hamiltonian for the composite fermions is derived. Within a mean-field theory, it is shown that the ground state and excitations of this Hamiltonian are those of a non-interacting Fermi gas although they are described by Jastrow-Slater wavefunctions.