Mixtures of charged-neutral superfluids

Motivated by the developments of artificial magnetic fields (AMFs) enabling cou- pling to the neutral particles of ultracold quantum gases, we have theoretically studied charged-neutral mixtures in various settings. The techniques that have been used to manufacture these AMFs are highly sensitive to the internal de- grees of freedom of the atoms, resulting in unequal coupling to the components of a mixture. We demonstrate the possible consequences of this unequal coupling by considering two different systems. First, we examine an impurity problem in a fermion background under an AMF coupling selectively to the impurity in a ring trap. We calculate the response of the system exactly by using Bethe Ansatz and argue that the AMF can be employed as a probe to analyze polaron formation. Secondly, we explore Bardeen-Cooper-Schrieffer theory of supercon- ductivity in the presence of a charge imbalance under an AMF. We analytically calculate the gap equation for any degree of asymmetry between the Landau level spectra of up and down spin particles, and show that the system displays reentrant superconductivity both in magnetic field and temperature. Apart from mixtures, we also investigate the non-equilibrium Hall response of a topological system. The strength of an AMF applied on a optical lattice can be suddenly changed without creating Eddy currents, allowing us to quench the system across a topological phase boundary. We report a fractional Hall response for the result- ing non-equilibrium system and discuss possible implementations for cold atom experiments.