Properties of strongly correlated Fermi systems: from cold atoms to nuclear matter
IDPASC Portugal - PHD Programme 2016
2016 / 2017
Theoretical Particle Physics | Astrophysics
Universidade de Coimbra
The study of strongly correlated Fermi systems is of wide interest for very different areas of physics, ranging from condensed matter to nuclear physics and astrophysics. Developing a quantitative understanding of these systems is important since they offer a unique tool for quantum many-body physics. Cold Fermi atoms and neutron-rich nuclear systems, such as exotic nuclei or neutron stars, are particularly interesting examples of strongly correlated Fermi systems. These systems exhibit a richness of phenomena and phases and, despite the different nature of their constituents, interactions and scales, they present many common features: superfluidity, exotic phases, BEC-BCS crossover, universal behavior in the unitary limit. The most fascinating property of cold Fermi (and Bose) atoms is their high experimental tunnability: the geometry, dimensionality and even the interaction strength (handled magnetically via Feshbach resonances) of these systems can be varied, almost at will. This property makes them an unprecedented tool to test many-body theories. Another fascinating and powerful way to take advantage of this incredible flexibility is to use them to constrain the properties of other physical systems. In particular, multicomponent cold Fermi atoms can be used to mimic low-density neutron-rich matter, whose study is fundamental to understand, among others, the properties of neutron-star crusts or the liquid-gas phase transition of nuclear matter. In this Ph.D. project we will address several open questions whose answers are relevant for a better understanding of the physics of both cold Fermi atoms and neutron-rich nuclear systems. Some of these questions are: Q1: What are the properties of a single impurity, the so-called polaron, in a degenerate Fermi gas? Q2 What are the properties of a superfluid Fermi gas in the unitary limit ? Q3: To which extent is low density neutron matter a unitary gas? or Q4: What is the phase diagram of a multicomponent Fermi system and particularly that of neutron-rich matter ? To such end several many-boy techniques will be employed and developed by the Ph.D. candidate. Keywords: Polaron problem, Unitary Fermi gas, superfluidity References:  C. Pethick and H. Scmith, Bose-Einstein condensation in Dilute Gases, 2nd Ed. Cambridge University Press, 2008  S. Giorgini, L. P. Pitaevski and S. Stringari, Theory of ultracold atomic Fermi gases, Rev. Mod. Phys. 80, 1215 (2008).  W. Zweger Ed., The BCS-BEC crossover and the unitary Fermi gas Lecture Notes in Physics 836 (2012).  M. W. Zwierlein, J. R. Abo-Shaeer, S. Schirotzek, C. H. Schunk and W. Ketterle, Vortices and superfluid in a strongly interacting Fermi gas, Nature, 435, 1047 (2005).