  We propose a phase space method to propagate a quantum wavepacket driven by a
strong external field. The method employs the so-called biorthogonal von
Neumann basis recently introduced for the calculation of the energy eigenstates
of time-independent quantum systems [A. Shimshovitz and D.J. Tannor,
arXiv:1201.2299v1]. While the individual elements in this basis set are
time-independent, a small subset is chosen in a time-dependent manner to adapt
to the evolution of the wavepacket in phase space. We demonstrate the accuracy
and efficiency of the present propagation method by calculating the electronic
wavepacket in a one-dimensional soft-core atom interacting with a superposition
of an intense, few-cycle, near-infrared laser pulse and an attosecond
extreme-ultraviolet laser pulse.
