Dynamics of Bose - Einstein condensates and the atom laser
Authors: Buchmann Lukas 
Published: January 2014

We studied the creation of coherent atomic ensembles by various means, allof which are either already demonstrated experimentally or within reach ofcurrent experiments. We investigated the dynamics of the outcoupling of acoherent beam from an atomic Bose-Einstein condensate. Since this problemis well treated in present literature, we focused on another aspect of proposedatom-laser schemes, the pumping. To this end, we investigated the merging ofindependent condensates and paid particular attention to the role of the relativephase. We found that it emerges as a key parameter during the merging process,almost solely defining the resulting dynamics. More concretely, the phasedifference determines the depth of an adiabatically formed soliton as well as thedynamics of a dipole oscillation of the atomic cloud, which builds up during themerging process. Under the assumption of a coherent cooling, such as evaporationof higher energy atoms from the ensemble, we were able to empiricallyfind an analytic formula for the phase of the final condensate. We studied themerging as an independent process, not necessarily linked to the atom laseritself. Our results might shed light onto new, non-destructive ways of readingout phase-differences between condensates as it is necessary in matter-wavespectroscopy. Although not related to our work, it is worth mentioning thatin the mean-time, a different pumping mechanism was demonstrated. It relieson two electronic transitions, with a reservoir condensate and a separate lasingcondensate [74]. We turned towards a different way of producing matter wavepulses altogether, namely superradiance from condensates, which shows otherpromising aspects, such as well defined populations and momenta of the createdpulses. We constructed a quantum treatment for the early stages of the process,which, as we have shown, is not well described within the available mean-fieldmodels. This semi-classical model can, however, produce quantum expectationvalues by means of averaging over randomly seeded trajectories. We used thisrelations to investigate the statistics of delay– and passage-times of superradiantpulses. Beyond the mean-field treatment of the problem, the quantum modelpredicts long range order as well as atomic bunching in the side-modes and enhancedcross-correlations between forward and backwards scattered atoms. Inthe strong pulse regime, the two counter-propagating clouds become entangledand the number difference between them is squeezed.4.6.2 OutlookThe experimental verification of our results is within reach of current experiments,and the tools available to probe Bose-Einstein condensates are advancingat a fast rate. As far as our studies are concerned, there are still open questions.We found that, in general, the merging of condensates is related to the formationof a soliton. The decay of such a structure is a topic of current debate, but theconsensus that this depends highly on the geometry of the trapping potentialsused seems reached.We investigated the early stage of superradiance from condensates and it isnatural to ask what is to expect for later stages, or in other situations wheredepletion of the primary condensate, population of higher order side-modes or120interaction between end-fire modes become relevant. Our results suggest thatthe exotic correlations we found decay with time, but this is not conclusive