The paper explores the numerical stability and the computational efficiency of a direct method for unfolding the resolution function from the measurements of the neutron induced reactions. A detailed resolution function formalism is laid out, followe
d by an overview of challenges present in a practical implementation of the method. A special matrix storage scheme is developed in order to facilitate both the memory management of the resolution function matrix, and to increase the computational efficiency of the matrix multiplication and decomposition procedures. Due to its admirable computational properties, a Cholesky decomposition is at the heart of the unfolding procedure. With the smallest but necessary modification of the matrix to be decomposed, the method is successfully applied to system of $10^5times10^5$. However, the amplification of the uncertainties during the direct inversion procedures limits the applicability of the method to high-precision measurements of neutron induced reactions.
We studied quantum reflection of Bose-Einstein condensates at normal incidence on a square array of silicon pillars. For incident velocities of 2.5-26 mm/s observations agreed with theoretical predictions that the Casimir-Polder potential of a reduce
d density surface would reflect slow atoms with much higher probability. At low velocities (0.5-2.5 mm/s), we observed that the reflection probability saturated around 60% rather than increasing towards unity. We present a simple model which explains this reduced reflectivity as resulting from the combined effects of the Casimir-Polder plus mean field potential and predicts the observed saturation. Furthermore, at low incident velocities, the reflected condensates show collective excitations.
Two spatially separate Bose-Einstein condensates were prepared in an optical double-well potential. A bidirectional coupling between the two condensates was established by two pairs of Bragg beams which continuously outcoupled atoms in opposite direc
tions. The atomic currents induced by the optical coupling depend on the relative phase of the two condensates and on an additional controllable coupling phase. This was observed through symmetric and antisymmetric correlations between the two outcoupled atom fluxes. A Josephson optical coupling of two condensates in a ring geometry is proposed. The continuous outcoupling method was used to monitor slow relative motions of two elongated condensates and characterize the trapping potential.
Doubly quantized vortices were topologically imprinted in $|F=1>$ $^{23}$Na condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dyn
amical instability. The time scale of the splitting process was found to be longer at higher atom density.
Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the t
wo wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.
A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the
spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 $mu$m for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.
