We derive for the first time fundamental equations that describe soliton spatial profiles consisting of two-photon mode fields and macroscopic polarization of a medium. Numerical solutions of this basic equation are presented to suggest both single soliton and multiple soliton chains in infinitely long targets, using the example of para-H2 ν = 0 → 1 (E1 forbidden) vibrational parameters. Although the effects of dissipative relaxation are included in the general form for the two-level system, the existence of a static soliton condensate is established. For finite-size targets, we can precisely formulate the profile equation in the framework of a nonlinear eigenvalue problem. Its first iteration provides approximate semi-analytic results under a potential well in the linearized equation; these results have qualitatively similar profiles to the case of an infinitely long target, an important difference being the exponentially decreasing profile near target ends. A large number of weakly interacting solitons correspond to localized portions between adjacent nodes of highly excited bound-state wave functions in a 1D potential well of large size. These soliton condensates are expected to be important in enhancing the signal to the background ratio in the proposed neutrino mass spectroscopy using atoms.
ASJC Scopus subject areas
- General Physics and Astronomy