Fermionic Mediated Effective Interaction for the Two-Dimensional Bose-Fermi Mixtures under Artificial Magnetic Field

The strongly interacting bosonic and non-interacting fermionic mixtures of diluted gases are studied. An artificial magnetic field is introduced in theory by imposing a Peierls phase shift on the wave functions of the constituents. A highly nontrivial limit of the quantum-Hall limit is achieved which provides oscillations effects of the fermion mediated interaction between bosons. In consequence the effective interaction between bosons can change the magnitude and sign. This provides possible explanations of the bosonic coherence loss observed experimentally in the "time of flight" and "peak width" experiments.