### 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-H_{2} 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.

Original language | English |
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Article number | 073B02 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2014 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Two-photon paired solitons supported by medium polarization.** / Yoshimura, Motohiko; Sasao, Noboru.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Two-photon paired solitons supported by medium polarization

AU - Yoshimura, Motohiko

AU - Sasao, Noboru

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84905756460&partnerID=8YFLogxK

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U2 - 10.1093/ptep/ptu094

DO - 10.1093/ptep/ptu094

M3 - Article

AN - SCOPUS:84905756460

VL - 2014

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 7

M1 - 073B02

ER -