najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-65-2-176-182najo-13Research ArticlePHYSICSФИЗИКАQuantum coupling between radio modes in a single-atom maser with two resonatorsКвантовая связь между двумя радио-модами в одноатомном мазере с двумя резонаторамиhttps://orcid.org/0000-0003-0223-097XПоповЕ. Н.PopovE. N.

Евгений Николаевич Попов

Eugeniy N. Popov – Laboratory of Quantum Processes and Measurements, Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101

enp-tion@yandex.ruhttps://orcid.org/0000-0002-5109-2086ТрифановА. И.TrifanovA. I.

Александр Игоревич Трифанов

Alexander I. Trifanov – Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101

alextrifanov@gmail.comМоскаленкоМ. А.MoskalenkoM. A.

Мария Александровна Москаленко

Maria A. Moskalenko – Center of Mathematics

Kroverkskiy, 49, St. Petersburg, 197101

moskalenko.mary@gmail.comhttps://orcid.org/0009-0000-6418-6121РешетовВ. А.ReshetovV. A.

Владимир Александрович Решетов

Vladimir A. Reshetov

Belorusskaya str., 14, Togliatti, 445667

vareshetov@tltsu.ruITMO UniversityRussian FederationTogliatti State UniversityRussian Federation202519052025162176182Copyright © Popov E.N., Trifanov A.I., Moskalenko M.A., Reshetov V.A., 20252025Попов Е.Н., Трифанов А.И., Москаленко М.А., Решетов В.А.Popov E.N., Trifanov A.I., Moskalenko M.A., Reshetov V.A.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/13

In this work, we investigate the effect of quantum coupling between radio fields in a single-atom maser with two spatially separated resonators. Each atom in a beam, depending on its state, can emit one photon into the first resonator and absorb another from the second, thereby entangling the quantum states of two independent modes. Resulting from entanglement, we obtain a coherence between states of two-mode field with the same total number of photons in the both modes. To study the arising coupling, an analytical solution of the stationary master equation is found under conditions of a trapped field state and the dependence of the von Neumann entanglement entropy on the quality factor of the resonators. Numerical analysis reveals that the best conditions for the appearance of quantum coupling are the low quality factor of the first resonator and the high quality factor of the second one.

В данной работе описан эффект возникновения квантовой связи между радио-полями в одноатомном мазере с двумя разнесёнными в пространстве резонаторами. Один и тот же атом пучка в зависимости от состояния может излучить фотон в один резонатор и поглотить из второго, перепутывая тем самым квантовые состояния двух независимых мод. Следствием перепутанности является когерентность между состояниями двухмодового поля с одинаковым суммарным количеством фотонов в обеих модах. Для изучения возникающей связи найдено аналитическое решение стационарного управляющего уравнения в условиях запертого состояния поля, а также построена зависимость энтропии запутанности фон Неймана от добротности резонаторов. Численный анализ показал, что наилучшими условиями для появления квантовой связи является низкая добротность первого резонатора и высокая добротность второго.

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