This article is written as a Lecture given in the 2006 Varenna Summer School on "Ultracold Fermi Gases". Here we present a review of BCS--Bose Einstein condensation (BEC) crossover theory with emphasis on finite temperature effects. We discuss the role of temperature
T as it enters a theoretical formalism which is based on the standard BCS-Leggett ground state. We also discuss the role of temperature in the context of experiments ranging from thermometric issues to signatures of superfluidity. Particularly important to this discussion is the novel normal state associated with the crossover regime, intermediate between BCS and BEC. The experimental evidence for this unusual normal state (associated with pre-formed pairs) and its counterpart below
Tc (associated with non-condensed pairs) is presented in the context of different experiments. We end with a discussion of finite temperature effects in spin polarized superfluids, where
T is found to play a crucial role in both theory and experiment.
The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.
Abstract The properties of ultracold quantum gases of bosons with dipole–dipole interaction are investigated at finite temperature in the frame of representative ensembles theory. Self-consistent coupled equations of motion are derived for the condensate and the non-condensate components. Corrections due to the dipolar interaction to condensate depletion, the anomalous density and thermodynamic quantities such as the ground state energy, the equation of state, the compressibility and the presure are calculated in the homogeneous case at both zero and finite temperatures. Effects of interaction and temperature on the structure factor are also discussed. Within the realm of the local density approximation, we generalize our results to the case of a trapped dipolar gas.