Vision of a fully laser-driven ${\sf n\gamma}{-}{\sf m\gamma}$ collider.

The use is suggested of a laser-accelerated dense electron sheet with an energy of ( $E=\tilde{\gamma} mc^2$) as a relativistic mirror to reflect coherently a second laser with photon energy ħω, generating by the Doppler boost high-energy γ photons with $$ \hbar \omega ' = 4\tilde \gamma ^2 \hbar \omega $$ 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 $q\bar{q}$-plasmas. For a Bose-Einstein condensate (BEC) [A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 261 (1924); A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 3 (1925); A. Griffin, D.W. Snoke, S. Stringari, Bose-Einstein Condensation (Cambridge University Press, 1995)] final state or for the Cooper pair ground state at higher densities [A.J. Leggett, Quantum Liquids, Oxford Graduate Texts (Oxford University Press, 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 π⁰-BEC followed by the formation of molecules. For the direct population of higher $q\bar{q}$ 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 $f\bar{f}$ 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. [ABSTRACT FROM AUTHOR]