Abstract
We present a model that unifies Gaussian wave-packet evolution with the so-called ``time-dependent Thomas-Fermi approximation'' for a Bose-Einstein condensate (BEC) of strongly interacting atoms. The unified simple intuitive formalism describes the stationary or time-dependent properties of single atoms, thermal clouds, or a BEC over a wide range of interaction strengths, including intermediate interaction regimes or scenarios where both interaction regimes coexist. Excellent agreement with precise numerical calculations (Gross-Pitaevskii equations) is obtained. The model is particularly suitable for describing three-dimensional evolution in free space or in time-dependent potentials for trapping, guiding, accelerating, focusing, or splitting matter waves in interferometers. We present a unified theory of spatial coherence in matter-wave interferometers and find good agreement between analytical expressions for the evolution of the coherence length of thermal atoms or a BEC and precise numerical calculations. In addition to the insight provided by the model, it supplies a simple and useful tool for the design and performance analysis of atom interferometers with many operational parameters, where a precise numerical calculation might exhaust unrealistic calculational resources.
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