Quantum Phases of Fermionic Cold Atoms Through Pairing and Dissociation

Cold atom experiments have realized molecule creation consisting of paired fermions and dissociation of weakly bound molecules into correlated fermions by tuning of the interactions with external fields [1,2]. We study many-body correlations in such system where molecules are weakly bound and therefore pairs of fermionic atoms convert into and dissociate from the bound molecule state. This exchange mediates a long-range interaction between the fermions. We consider a simple many-body Hamiltonian that includes the destruction of fermionic atom pairs to form single bosonic molecules and vice versa [3]. We employ a functional renormalization-group approach to search for instabilities from the disordered quantum liquid phase that may arise from a boson mediated fermion-fermion interaction. We calculate the renormalized frequency-dependent fermion interactions vertices and renormalized molecular binding energy. \\[4pt] [1] M. Greiner, C. A. Regal, and D. S. Jin, Nature {\bf 426}, 537 (2003).\\[0pt] [2] M. Greiner, C. A. Regal, J. T. Stewart, and D. S. Jin, Phys. Rev. Lett. {\bf 94}, 110401 (2005).\\[0pt] [3] E. Timmermans, K. Furuya, P. W. Milonni, and A. K. Kerman, Phys. Lett. A {\bf 285}, 228 (2001).