  We report a proposal to observe the two-photon Breit-Wheeler process in
plasma driven by compact lasers. A high charge electron bunch can be generated
from laser plasma wakefield acceleration when a tightly focused laser pulse
transports in a sub-critical density plasma. The electron bunch scatters with
the laser pulse coming from the opposite direction and results the emitting of
high brilliance X-ray pulses. In a three-dimensional particle-in-cell
simulation with a laser pulse of $\sim$10 J, one could produce a X-ray pulse
with photon number higher than $3\times10^{11}$ and brilliance above $1.6\times
10^{23}$ photons/s/mm$^2$/mrad$^2$/0.1$\%$BW at 1 MeV. The X-ray pulses collide
in the plasma and create more than $1.1\times 10^5$ electron-positron pairs per
shot. It is also found that the positrons can be accelerated transversely by a
transverse electric field generated in the plasma, which enables the safe
detection in the direction away from the laser pulses. This proposal which has
solved key challenges in laser driven photon-photon collision could demonstrate
the two-photon Breit-Wheeler process on a much more compact device in a single
shot.
