Study of the behavior of impurities in Bose and Fermi systems

An electron moving through a crystal interacts with the atoms of the lattice, creating a quasiparticle called a polaron, composed of the electron surrounded by phonons. The properties of the polaron, such as its effective mass and mobility, can differ significantly from those of the free electron, affecting the electrical and thermal properties of the material. This phenomenon, known for a long time, has recently been linked to the behavior of impurities in ultracold gases.

This Thesis explores the behavior of impurities embedded in Bose and Fermi systems, providing insights into the interplay between impurity dynamics and many-body quantum effects. First, we examine the Bose polaron, i.e., an impurity in a Bose bath, showing that quasiparticle characteristics are lost near the critical temperature, consistent with experimental findings.  Next, we address the thermal properties of repulsive impurities in a harmonically trapped Bose gas. At low temperatures, strong impurity-boson repulsion expels the impurity to the trap edges, but increasing temperature induces a miscibility crossover, with the impurity moving to the center of the trap.  Finally, we analyze a two-dimensional Fermi gas on a lattice with a spin-down impurity interacting attractively with spin-up fermions, where the polaron state remains energetically favorable, maintaining finite quasiparticle residue even at strong interactions.

Together, these studies deepen our understanding of impurity physics in quantum systems, shedding light on thermal effects, miscibility, and quasiparticle properties in diverse scenarios.