Abstract. The use is suggested of a laser-accelerated dense electron sheet with an energy of (E =γmc 2 ) as a relativistic mirror to reflect coherently a second laser with photon energy ω, generating by the Doppler boost high-energy γ photons with ω = 4γ2 ω and short duration [A. Einstein, Annalen der Physik 17, 891 (1905); D. Habs et al., Appl. Phys. B 93, 349 (2008)]. Two of these counter-propagating γ beams are focused by the parabolically shaped electron sheets into the interaction region with small, close to diffraction-limited, spot size. Comparing the new nγ−mγ collider with former proposed γγ collider schemes we achieve the conversion of many photon-pairs in a small space-time volume to matter-antimatter particles, while in the other discussed setups only two isolated, much more high-energetic photons will be converted, reaching in the new approach much higher energy densities and temperatures. With a γ-field strength somewhat below the Schwinger limit we can reach this complete conversion of the γ bunch energy into e + e − or quark-antiquark qq-plasmas. , 2006)] the strong induced transition into this coherent state is of special interest for single-cycle γ pulses. Due to annihilation these cold coherent states are very short-lived. For γ beams with photon energies of 1-10 keV the rather cold e + e − -plasma or e + e − -BEC expands to a cold dense aggregate of positronium (Ps) atoms, where the production of Ps molecules is discussed. For photon energies of 1-10 MeV we discuss the production of a cold induced π 0 -BEC followed by the formation of molecules. For the direct population of higher qq densities we can study condensates of color-neutral mesons with enhanced population. For a γγ collider with several-cycle laser pulses the following cycles heat up the fermion-antifermion ff system to a certain temperature. Thus we can reach high energy densities and temperatures of an e + e − γ plasma, where the production of hadrons in general or the quark-gluon phase transition can be observed. Within the long-term goal of very high photon energies of about 1 GeV in the nγ−mγ-collider, even the electro-weak phase transition or SUSY phase transition could be reached.PACS. 42.55.Vc X-and gamma-ray lasers -29.27.-a Beams in particle accelerators -41.75.Jv Laser-driven acceleration -41.75.Ht Relativistic electron and positron beams