Applications I: Fermions, Bosons, Condensation Phenomena

Ofir E. Alon, Lorenz S. Cederbaum

For small scattering lengths, cold bosonic atoms form a condensate the density profile of which is smooth. With increasing scattering length, the density gradually acquires more and more oscillations. Finally, the number of oscillations equals the number of bosons and the system becomes fermionized. On this pathway from condensation to fermionization intriguing phenomena occur, depending on the shape of the trap. These include macroscopic fragmentation and coexistence of condensed and fermionized parts that are separated in space.

M. Ya. Amusia, Konstantin G. Popov, Vasily R. Shaginyan +1 more

O. S�rensen, D. V. Fedorov, A. S. Jensen

Hagen M. Kleinert, She-Sheng Xue

Our goal is to understand the phenomena arising in optical lattice fermions at low temperature in an external magnetic field. Varying the field, the attraction between any two fermions can be made arbitrarily strong, where composite bosons form via so-called Feshbach resonances. By setting up strong-coupling equations for fermions, we find that in spatial dimension d>2 they couple to bosons which dress up fermions and lead to new massive composite fermions. At low enough temperature, we obtain the critical temperature at which composite bosons undergo the Bose–Einstein condensate (BEC), leading to BEC-dressing massive fermions. These form tightly bound pair states which are new bosonic quasi-particles producing a BEC-type condensate. A quantum critical point is found and the formation of condensates of complex quasi-particles is speculated over.

Oleg Tchernyshyov, J.-B. Fouet, Frédéric Mila +1 more

Igor V. Lerner

Advances in cooling and trapping of atoms have enabled unprecedented experimental control of many-body quantum systems.This led to the observation of numerous quantum phenomena, important for fundamental science, indispensable for high-precision simulations of condensed-matter systems and promising for technological applications.However, transport measurements in neutral quantum gases are still in their infancy in contrast to the central role they play in electronics.In these lectures, after reviewing nascent experiments on quantum fermionic transport, I will focus on our theoretical prediction and the possibility of experimental observations of qualitatively new phenomena in transport of ultracold bosons which do not have a direct counterpart in quantum electronic transport in condensed matter systems.The description of this transport is based on the Luttinger liquid theory.So in the first part of the lectures I will introduce main concepts of the Luttinger liquid based on the functional bosonisation approach.