Quantum Phases of Atom-Molecule Mixtures of Fermionic Atoms

Cold atom experiments have observed atom-molecule mixtures by tuning the interactions between particles.\footnote{M.L. Olsen, J. D. Perreault, T. D. Cumby, and D. S. Jin, Phys. Rev. A 80, 030701(R) (2009)} We study many particle interactions by examaning a simple model that describes the destruction of fermionic atom pairs to form single bosonic molecules and vice versa. A set of functional Renomalization Group equations\footnote{R. Shankar, Rev. Mod. Phys., Vol 66 No. 1, January 1994}$^,$\footnote{S.W. Tsai, A.H. Castro Neto, R. Shankar, D.K. Campbell, Phys. Rev. B 72, 054531 (2005)} describing these processes are set up and solved numerically. The Self Energy of the fermions are attained as a function of frequency and we search for frequency dependent instabilities that could denote a transition from a disordered liquid to a BCS phase. (Financial support from NSF DMR-084781 and UC-Lab Fees Research Program.)