  Over the past five years, radial-velocity and transit techniques have
revealed a new population of Earth-like planets with masses of a few Earth
masses. Their very close orbit around their host star requires an exquisite
inner working angle to be detected in direct imaging and sets a challenge for
direct imagers that work in the visible range, like SPHERE / ZIMPOL. Among all
known exoplanets with less than twenty-five Earth-masses we first predict the
best candidate for direct imaging. Our primary objective is then to provide the
best instrument setup and observing strategy for detecting such a peculiar
object with ZIMPOL. As a second step, we aim at predicting its detectivity.
Using exoplanet properties constrained by radial velocity measurements,
polarimetric models and the diffraction propagation code CAOS, we estimate the
detection sensitivity of ZIMPOL for such a planet in different observing modes
of the instrument. We show how observing strategies can be optimized to yield
the best detection performance on a specific target. In our current knowledge
of exoplanetary systems, alpha Centauri B b is the most promising target with
less than twenty-five Earth-masses for ZIMPOL. With a gaseous
Rayleigh-scattering atmosphere and favorable inclinations, the planet could be
detected in about four hours of observing time, using the four-quadrant
phase-mask coronograph in the I band. However, if alpha Centauri B b should
display unfavorable polarimetric and reflective properties similar to that of
our Moon, it is around 50 times fainter than the best sensitivity of ZIMPOL.
Alpha Centauri B is a primary target for SPHERE. Dedicated deep observations
specifically targeting the radial velocity-detected planet can lead to a
detection if the polarimetric properties of the planet are favorable.
