Quantum phases and transitions of many-body systems realized using cold atomic gases.

摘要

In recent years, new advances in techniques for trapping and cooling atoms have allowed the production of atomic gases at low-enough temperatures and high-enough densities for collective quantum-mechanical effects to become important. This thesis describes theoretical investigations of certain many-body physics problems motivated by these experimental developments. It consists of two main parts.; In the first, I investigate the array of phases exhibited by degenerate mixtures of bosons and fermions with a Feshbach resonance, a bound molecular state whose energy can be tuned with a magnetic field. These phases are distinguished by the presence or absence of a bosonic condensate and also by the different Luttinger constraints that are shown to apply to the Fermi surface(s).; The second part is concerned with bosons in an optical lattice, in which a periodic potential is produced by counterpropagating lasers. Spinless bosons are known to exhibit a quantum phase transition between a Mott insulator and a superfluid state, while bosons with spin have a much richer phase structure. I consider, in particular, a phase transition with a spinless order parameter, and show that the long-time dynamics of spin-carrying excitations is governed by a nontrivial fixed point. The corresponding anomalous exponents are found using a renormalization-group calculation.