  We simulate the time-dependent coherent dynamics of a spatially indirect
exciton (an electron-hole pair with the two particles confined in different
layers) in a GaAs coupled quantum well system. We use a unitary wave-packet
propagation method taking into account in full the four degrees of freedom of
the two particles in a two-dimensional system, including both the long-range
Coulomb attraction and arbitrary two-dimensional electrostatic potentials
affecting the electron and/or the hole separately. The method has been
implemented for massively parallel architectures to cope with the huge
numerical problem, showing good scaling properties and allowing evolution for
tens of picoseconds. We have investigated both transient time phenomena and
asymptotic time transmission and reflection coefficients for potential profiles
consisting of i) extended barriers and wells and ii) a single-slit geometry. We
found clear signatures of the internal two-body dynamics, with transient
phenomena in the picosecond time-scale which might be revealed by optical
spectroscopy. Exact results have been compared with mean-field approaches
which, neglecting dynamical correlations by construction, turn out to be
inadequate to describe the electron-hole pair evolution in realistic
experimental conditions.
