Matter wave detection and phase fluctuations in Bose-Einstein condensates
Accepted analogies between matter waves and electromagnetic waves are extended in order to show that matter waves should have mechanical properties. A semiclassical description of the continuity equations describing these mechanical properties is presented and a general expression for their flux density is obtained. A semiclassical detection theory for matter waves is developed, drawing upon the theory of photoelectron detection and the conservation equations from fluid mechanics. It is the intrinsically dispersive nature of matter waves which is important in deriving such a theory. It is shown that the detection rate can be related to the flux of particles through the detector surface. A fully quantum matter wave detection theory is also presented, beginning from a microscopic description of detection. Both the short-time approximation to the detection rate and its long-time correction are developed. Again it is shown that the detection rate can be related to the flux through the detector surface. The relative phase fluctuations of two one-dimensional condensates coupled along their whole length with a local single-atom interaction is examined. The thermal equilibrium is defined by the competition between independent longitudinal thermally excited phase fluctuations and the coupling between the condensates which locally favours identical phase. The relative phase fluctuations and their correlation length are computed as a function of the temperature and the strength of the coupling. Finally, the future potential of the work contained herein is examined.