najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2026-17-4-482-490najo-1910Research ArticlePHYSICSФИЗИКАAdiabatic conditions for non-stationary optical phase modulation: a non-degenerate caseАдиабатические условия для нестационарной оптической фазовой модуляции: невырожденный случайhttps://orcid.org/0000-0001-9870-9285ГайдашА. А.GaidashA. A.

Andrei A. Gaidash

199178, 59-1-B 6th line of Vasilievsky island, Saint Petersburg; 3b Kadetskaya Line, 199034 Saint Petersburg

andrewdgk@gmail.comМемехЭ. Е.MemekhE. E.

Evelina E. Memekh

195251, Polytechnicheskaya 29, Saint Petersburg

 

memekh.evi@gmail.comhttps://orcid.org/0000-0002-4265-8818МирошниченкоГ. П.MiroshnichenkoG. P.

George P. Miroshnichenko

3b Kadetskaya Line, 199034 Saint Petersburg

gpmirosh@gmail.comhttps://orcid.org/0000-0002-4468-5406КозубовА. В.KozubovA. V.

Anton V. Kozubov 

199178, 59-1-B 6th line of Vasilievsky island, Saint Petersburg; 3b Kadetskaya Line, 199034 Saint Petersburg

avkozubov@itmo.ruSMARTS-Quanttelecom LLC; ITMO UniversityRussian FederationPeter the Great St. Petersburg Polytechnic UniversityRussian FederationITMO UniversityRussian Federation202631082026174482490Copyright © Gaidash A.A., Memekh E.E., Miroshnichenko G.P., Kozubov A.V., 20262026Гайдаш А.А., Мемех Э.Е., Мирошниченко Г.П., Козубов А.В.Gaidash A.A., Memekh E.E., Miroshnichenko G.P., Kozubov A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1910

This work examines a non-stationary phase-modulation process characterized by a time-dependent interaction coefficient, confined to the non-degenerate case. We derive an exact non-adiabatic solution to the time-dependent Schro¨ dinger equation. We then establish the criterion under which adiabatic considerations become valid-specifically, the condition permitting a stationary-state solution to approximate the non-stationary problem. Our results hold for an arbitrary number of interacting modes and an arbitrary photon number.

В данной работе исследуется нестационарный процесс фазовой модуляции, характеризующийся зависящим от времени коэффициентом взаимодействия, ограниченный невырожденным случаем. Мы выводим точное неадиабатическое решение зависящего от времени уравнения Шрёдингера. Затем мы устанавливаем критерий, при котором адиабатические соображения становятся справедливыми, а именно, условие, позволяющее стационарному решению аппроксимировать нестационарную задачу. Наши результаты справедливы для произвольного числа взаимодействующих мод и произвольного числа фотонов.

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The authors declare that there are no conflicts of interest present.