  Imaging exoplanetary systems is essential to characterizing exoplanetary
systems and to studying planet-disk interactions to understand planet
formation. Such imaging in the visible and near-infrared is challenging because
these objects are very faint relative to their star and only fractions of an
arcsecond away. Coronagraphic instruments have already allowed the imaging of a
few exoplanets, but their performance is limited by wavefront aberrations.
Adaptive optics systems partly compensate for the Earth's atmosphere
turbulence, but they cannot fully control the wavefront. Some of the starlight
leaks through the coronagraph and forms speckles in the image. Focal plane
wavefront control, used as a second stage after the adaptive optics system, can
minimize the speckle intensity within an area called the dark hole. We
demonstrated the on-sky performance of dark hole techniques, pairwise probing
coupled with electric field conjugation, using the apodized pupil Lyot
coronagraph of the VLT/SPHERE instrument. In this paper, we probe their
performance using the SPHERE four-quadrant phase mask coronagraph. We
demonstrate the interest of combining dark hole techniques and reference
differential imaging (RDI). We create a dark hole on-sky in the narrow band
around~$1.7\,\mu$m observing HR\,4796. We then record broadband images of
HR\,4796 and a reference star at the H band. The dark hole techniques improve
the H-band detection limit by a factor of three. The dark hole is stable from
one star to a nearby star enabling RDI. This stability offers two new
strategies of observation. First, one can quickly create a dark hole observing
a bright star before pointing to a faint target star. Furthermore, one can
couple dark hole techniques and RDI. A very interesting point is that the
performance of these methods does not depend on the astrophysical signal.
