Theory of ultracold atomic Fermi gases

Abstract

The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, of the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to non-perturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare the theoretical predictions with the available experimental results.

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

“…When the densities are fine-tuned to the definite commensurability (7), then all other cosine operators in the sum are oscillating, in which case they do not contribute in the continuum limit (or they are less relevant for multiples of p and q). The remaining important operator in the sum (6) is thus the sine-Gordon term…”

“…The recent years have witnessed a growing availability of experimental studies of mixtures of unlike particles. This includes loading ultracold atoms to spin-dependent optical lattices [5] and trapping atoms of different masses [6] or even different statistics [7]. While most of experimental progress so far is in the domain of ultracold atoms, we stress that the relevance of such asymmetric mixtures is not confined to the realm of cold gases: Dealing with more traditional solid-state systems, one faces an asymmetric mixture situation as soon as the Fermi level spans several bands (which a priori need not be equivalent).…”

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

“…The cuprates are quasi-two-dimensional materials which experimentally are found to exhibit d-wave superconductivity and nonuniform magnetic order [2], both of which have been proposed to exist in the phase diagram of the repulsive Hubbard model for some parameters. Experimental methods for realizing the Hubbard Hamiltonian have also been developed in the ultracold gas community [3][4][5]. Especially, the recent development of the fermionic quantum gas microscopes provides an interesting platform for observing magnetic order [6][7][8][9][10][11][12][13][14][15], although further advances are needed to reach the possible superconducting phases.…”

Anomalous density of states in multiband superconductors near the Lifshitz transition

“…8,12 the superconducting gap was observed on the side of the Lifshitz transition where the band would have been empty in the normal state. These observations were interpreted as a manifestation of the Bose-Einstein condensation of electron pairs formed as a result of strong electron-electron attraction 13 .…”