Functional renormalization group for ultracold atoms

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The condensation and binding phenomena in gases of ultracold fermionic atoms constitute an overwhelmingly rich field of research, the relevance of which extends from atomic and condensed-matter physics to nuclear-matter and astrophysics. This project develops and applies a functional integral description of the relevant strong-coupling many-body physics as well as few-body physics in a unified framework using the functional renormalization group. Three main topics shall be addressed within this project.(1) The phase diagram of a 2-component imbalanced Fermi gas is explored as a function of temperature, average chemical potential and the imbalance parameter, paying special attention to the unitarity limit at resonance. The RG flow of the full effective order-parameter for superfluidity and the fermionic gap are of central interest in order to map out the full phase diagram. The properties of the superfluid phases and the location of 1st-order transition lines as well as of the tri-critical point shall be determined with the aid of a functional RG flow into the symmetry-broken phases.(2) The role of 3-body composites for critical phenomena in fermi systems is little understood and shall be explored in a functional RG study of a 3-component Fermi gas. An expected trionic phase at low temperatures and near the resonance is at the focus of this study. Also, trionic modifications of BCS or BEC pairing and their influence on the phase structure and location of critical regimes will be aimed at, as to perform an unprecedented search for 3-body dominated collective and critical phenomena. In a second step, the influence of explicit symmetry-breaking terms lifting the 3-component degeneracy needs to be studied, in order to be predictive for potential experimental realizations involving dislocated Feshbach resonances.(3) Motivated by recent advances in the preparation of dipolar atoms and dipolar molecules in their rotational and vibrational ground state, we plan to use the functional RG to explore the potentially rich phase structure of dipolar Fermi gases,including nematic, superfluid, magnetic and possibly more exotic phases. While the particle-particle channel was investigated a couple of years back using second order perturbation theory a possible instability in the particle-hole channel was only discussed very recently within mean field theory. The competition between these competing channels seems very appealing to us. Decoupling the long range and anisotropic fermionic interaction by means of bosonic Hubbard-Stratonovich fields we are aiming at describing corrections to mean field theory. In fact, by using the FRG with a cutoff only in the bosonic sector mean field theory serves as an initial condition and by reducing the infrared cutoff we progressively include order parameter fluctuations. In addition to determining the superfluid order parameter and precise shape of the Fermi surface we are also going to study the spectrum of single particle excitations.