Elementary Excitations in BECs

Abstract

We now discuss the elementary waves and oscillations that can take place in a Bose Einstein condensate. We first deal with the elementary excitations as described by the quantum fluid equations. This allows us to study the sound waves in the condensate, sometimes also called Bogoliubov waves, as well as the global modes of the condensed cloud. We then approach the study of kinetic effects, based on the use of the wave kinetic equation. This will allow us to understand the microscopical wave-atom interactions taking place inside the condensate, as well as more refined processes such as the atomic Landau damping, fluid and kinetic instabilities such as beam and modulational instabilities. We show that the sound waves can become unstable, and determine the instability growth rates in both the quantum and the quasi-classical regime. Two specific examples of unstable oscillations are considered in detail. First, the two-stream instability, associated with two counter-propagating condensate beams. Then, the wakefield excitation by a moving condensate in a background thermal gas. Such instabilities can eventually be the seed for the excitation of a broadband turbulent spectrum.