  We establish that for PSR B0031-07 the orthogonal polarization modes switch
at a single pulse level synchronously with the periodic drifting subpulses seen
in total intensity. There are only four other pulsars known for which this
phenomenon is observed. PSR B0031-07 is unique as it is the only source in this
group which has multiple stable drift modes. For both drift modes visible at
our observing frequency centered at 1369 MHz, the modulation of polarization
modes is synchronous with the drifting subpulses. In one of the drift modes, a
discontinuity in the modulation pattern of polarization properties occurs
halfway through the pulse, coinciding with a slight change in the slope of the
intensity drift band. In contrast to what has been suggested for this pulsar in
the past, this, plus other differences in the polarization of the modulated
emission observed for the two drift modes, suggests that a drift mode change is
more than a change in the underlying carousel radius and that magnetospheric
propagation effects play an important role. The ellipticity evolves
asymmetrically in time during the modulation cycle, which in the framework of a
carousel model implies that the polarized sub-beams are asymmetric with respect
to the sense of circulation, something which is not observed for other pulsars.
Birefringence in the magnetosphere, resulting in the orthogonal polarization
modes to spatially separate, is not enough to explain these results. It is
argued that more complex magnetospheric processes, which possibly allow
conversion between orthogonal polarization modes, play a role.
