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We study the unitary propagation of a two-particle one-dimensionalSchr\"odinger equation by means of the Split-Step Fourier method, to study thecoherent evolution of a spatially indirect exciton (IX) in semiconductorheterostructures. The mutual Coulomb interaction of the electron-hole pair andthe electrostatic potentials generated by external gates and acting on the twoparticles separately are taken into account exactly in the two-particledynamics. As relevant examples, step/downhill and barrier/well potentialprofiles are considered. The space- and time-dependent evolution during thescattering event as well as the asymptotic time behavior are analyzed. Fortypical parameters of GaAs-based devices the transmission or reflection of thepair turns out to be a complex two-particle process, due to comparable andcompeting Coulomb, electrostatic and kinetic energy scales. Depending on theintensity and anisotropy of the scattering potentials, the quantum evolutionmay result in excitation of the IX internal degrees of freedom, dissociation ofthe pair, or transmission in small periodic IX wavepackets due to dwelling ofone particle in the barrier region. We discuss the occurrence of each processin the full parameter space of the scattering potentials and the relevance ofour results for current excitronic technologies.

Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures