Low temperature theory for Bose-Einstein condensates

Summary form only given. The dilute gas experiments on the Bose-Einstein condensation of magnetically confined alkali vapors have already generated widespread interest across a broad spectrum of traditional fields of physics. They have provided an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems with the single particle microscopic physics described in quantum optics and laser physics. The approach I discuss is based on a derivation of the quantum kinetic theory from first principles. Based on a microscopic picture of the weakly interacting bosonic gas, a generalized kinetic theory for a Markovian many-body density operator is derived. The density operator is functionally dependent on a few key variables, which must be carefully chosen. These quantities serve as master variables and determine the system´s evolution on a coarse-grained time scale. The weak interactions allow a perturbative expansion of the evolution, from which kinetic equations that describe the dynamics of the expectation value of any single-time observable are obtained. The final structure of the theory has many analogies with the quantum theory of the laser, such as amplitude and phase noise for the macroscopic field, squeezing dynamics, and a nonlinear master equation describing the underlying evolution.