  Context. The temperate Earth-mass planet Proxima b is the closest exoplanet
to Earth and represents what may be our best ever opportunity to search for
life outside the Solar System. Aims. We aim at directly detecting Proxima b and
characterizing its atmosphere by spatially resolving the planet and obtaining
high-resolution reflected-light spectra. Methods. We propose to develop a
coupling interface between the SPHERE high-contrast imager and the new ESPRESSO
spectrograph, both installed at ESO VLT. The angular separation of 37 mas
between Proxima b and its host star requires the use of visible wavelengths to
spatially resolve the planet on a 8.2-m telescope. At an estimated
planet-to-star contrast of ~10^-7 in reflected light, Proxima b is extremely
challenging to detect with SPHERE alone. However, the combination of a
~10^3-10^4 contrast enhancement from SPHERE to the high spectral resolution of
ESPRESSO can reveal the planetary spectral features and disentangle them from
the stellar ones. Results. We find that significant but realistic upgrades to
SPHERE and ESPRESSO would enable a 5-sigma detection of the planet and yield a
measurement of its true mass and albedo in 20-40 nights of telescope time,
assuming an Earth-like atmospheric composition. Moreover, it will be possible
to probe the O2 bands at 627, 686 and 760 nm, the water vapour band at 717 nm,
and the methane band at 715 nm. In particular, a 3.6-sigma detection of O2
could be made in about 60 nights of telescope time. Those would need to be
spread over 3 years considering optimal observability conditions for the
planet. Conclusions. The very existence of Proxima b and the SPHERE-ESPRESSO
synergy represent a unique opportunity to detect biosignatures on an exoplanet
in the near future. It is also a crucial pathfinder experiment for the
development of Extremely Large Telescopes and their instruments (abridged).
