Two-photon paired solitons supported by medium polarization

We derive for the first time fundamental equations that describe soliton spatial profiles consisting of two-photon mode fields and macroscopic polarization of medium. Numerical solutions of this basic equation are presented to give single and multiple soliton chains taking an example of para-H$_2$ $v=0 \leftrightarrow 1$ vibrational system. Although effects of dissipative relaxation are included in the general form for two-level system, the existence of static soliton-condensate is established. Stability analysis of soliton solutions is given. Arguments given here support that soliton-condensates thus derived are final remnants of time evolution of macro-coherent two-photon process. These soliton-condensates are expected to be important in the proposed neutrino mass spectroscopy using atoms.