Two-photon paired solitons supported by medium polarization

Abstract

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. © The Author(s) 2014.