Initiated with the investigation of Fermi gases in BEC-BCS crossover, the study of polaron physics has extended to unequal masses fermionic systems and bosonic environments.
[14-15] On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. Experimentally, polaron systems have been realized with a medium composed either of bosonic or fermionic atoms.
[16-19] In a low-temperature fermionic gas medium, results instead in excitations named Fermi polarons, which are a paradigmatic realization of Landau's fundamental concept of a quasi-particle. In this paper the variational approach presents a whole energy spectrum and momentum distribution clearly. In the polaron system with repulsive interactions, there is another complex topic about the itinerant ferromagnetic (IFM) phase argued for a long time.
[20-22] Recent research found that polaron energy can exceed the Fermi energy and the effective mass $m^*$ could be negative in three-dimensional case.
[21] but the IFM phase is still a controversial topic. The repulsive polaron system is stable in 1D, and IFM phase can be rigorously excluded by exact Bethe Ansatz (BA) method.
[23] In whole 1D repulsive regime, it is interesting to see polaron properties calculated by variational method, which can be compared with results by BA method.