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10 Ultra-cold Polarized Fermi Gases

Christophe Mora

Published Aug 26, 2015• 97 citations
OpenAlex

Abstract

Abstract. Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half-century old open problem in condensed matter physics, and raised new interrogations of their own. 1.

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In recent years, ultracold bosonic and fermionic atom gases in optical lattices have allowed us to realize experimentally phenomena originally predicted or observed in condensed matter physics with unprecedented control and purity. Among others, proposals have been made to demonstrate a key feature of one dimensional (1D) quantum systems, the so-called spin-charge separation, which has been quite elusive in condensed matter systems. However, as we want to discuss in this paper using the time-dependent density-matrix renormalization group (DMRG), beyond a mere demonstration of spin-charge separation cold atom gases will also shed light on previously inaccessible aspects of this phenomenon. Moreover, the previous proposals for experimental realizations will be revisited taking into account the modelling of an external magnetic field.
The search for novel phases of quantum coherent matter has been one of the main driving forces in condensed matter physics for many years. The unprecedented experimental sophistication reached recently in ultracold atomic gases has opened new and exciting perspectives in this search. The ability to externally manipulate the interatomic interaction, the capacity to embed atomic clouds in optical lattices or confine them in low dimensions, as well as the possibility to prepare mixtures of atoms with different statistics and/or populations, is presenting an opportunity to realise and explore novel correlated phases of matter. During the lectures I will focus mainly on aspects of condensation and superfluidity phenomena in fermionic systems. Theoretical elements will be discussed together with recent experimental realisations.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words: