title: ÐÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð¾Ð³Ð¾ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Quantization of the free electromagnetic field in a waveguide
Creators: name: Ð¡Ð¾ÐºÐ¾Ð»Ð¾Ð², ÐÐ¸ÐºÐ¸ÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ñ Ð¾Ð¿ÑÐ¸ÐºÐ°
Ð°ÑÐ¾Ð¼Ð½ÑÐµ ÑÐ¸ÑÑÐµÐ¼Ñ
Ð´Ð¸Ð¿Ð¾Ð»Ñ-Ð´Ð¸Ð¿Ð¾Ð»ÑÐ½Ð¾Ðµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ
ÐºÐ¾Ð»Ð»ÐµÐºÑÐ¸Ð²Ð½ÑÐµ ÑÑÑÐµÐºÑÑ
Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´
ÑÐ¿Ð¾Ð½ÑÐ°Ð½Ð½ÑÐ¹ ÑÐ°ÑÐ¿Ð°Ð´
Ð°ÑÐ¾Ð¼Ð½Ð°Ñ ÑÐ¿ÐµÐºÑÑÐ¾ÑÐºÐ¾Ð¿Ð¸Ñ
quantum optics
atomic systems
dipole-dipole interaction
collective effects
waveguide
spontaneous decay
atomic spectroscopy

description: ÐÐ±ÑÐµÐºÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ â Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ Ð¿ÑÐ¸Ð¼ÐµÑÐ½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð², Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²ÑÑÑÐ¸Ñ Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐ¼ Ð¿Ð¾Ð»ÐµÐ¼. Ð¦ÐµÐ»Ñ ÑÐ°Ð±Ð¾ÑÑ â ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° ÑÐ°Ð¼Ð¾ÑÐ¾Ð³Ð»Ð°ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð°ÑÐ¾Ð¼Ð¾Ð², Ð½Ð°ÑÐ¾Ð´ÑÑÐ¸ÑÑÑ Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐ¼ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸ÐµÐ¼. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ñ Ð²ÑÐµ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸, Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ: ÑÐµÑÐµÐ½Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ°ÐºÑÐ²ÐµÐ»Ð»Ð° Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ð° Ð²Ð½ÑÑÑÐ¸ Ð¿Ð¾Ð»Ð¾Ð³Ð¾ Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ð° Ð¿ÑÑÐ¼Ð¾ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ñ Ð¸Ð´ÐµÐ°Ð»ÑÐ½Ð¾ Ð¿ÑÐ¾Ð²Ð¾Ð´ÑÑÐ¸Ð¼Ð¸ ÑÑÐµÐ½ÐºÐ°Ð¼Ð¸; Ð¾ÑÐ²Ð¾ÐµÐ½Ð° Ð¿ÑÐ¾ÑÐµÐ´ÑÑÐ° ÐºÐ°Ð½Ð¾Ð½Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð¾Ð¼ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ; Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¾ ÐºÐ°Ð½Ð¾Ð½Ð¸ÑÐµÑÐºÐ¾Ðµ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ðµ; Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¾ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ñ 1-2 Ð°ÑÐ¾Ð¼Ð°Ð¼Ð¸. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ» Ð¾Ð±Ð½Ð°ÑÑÐ¶ÐµÐ½ ÑÑÑÐµÐºÑ Ð½ÐµÐ¿Ð¾Ð»Ð½Ð¾Ð³Ð¾ ÑÐ¿Ð¾Ð½ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÐ¿Ð°Ð´Ð° â ÐºÐ¾Ð³Ð´Ð° Ð·Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð°ÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¸ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶Ð°ÐµÑÑÑ Ðº Ð½ÐµÐ½ÑÐ»ÐµÐ²Ð¾Ð¼Ñ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð² Ð±Ð¾Ð»ÑÑÐ¸Ðµ Ð¼Ð¾Ð¼ÐµÐ½ÑÑ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ, ÐºÐ¾Ð³Ð´Ð° ÑÐ°ÑÑÐ¾ÑÐ° Ð°ÑÐ¾Ð¼Ð½Ð¾Ð³Ð¾ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° Ð±Ð¾Ð»ÑÑÐµ ÑÐ°ÑÑÐ¾ÑÑ ÑÑÐµÐ·Ð° Ð²Ð¾Ð»Ð½Ð¾Ð²Ð¾Ð´Ð° Ð¸ Ð½Ð°ÑÐ¾Ð´Ð¸ÑÑÑ Ð´Ð°Ð»ÐµÐºÐ¾ Ð¾Ñ Ð¾ÐºÑÐµÑÑÐ½Ð¾ÑÑÐµÐ¹ ÑÑÐµÐ·Ð°. ÐÐ±Ð»Ð°ÑÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ²Ð»ÑÐµÑÑÑ ÑÑÐ´ ÐºÐ²Ð°Ð½ÑÐ¾Ð²ÑÑ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸Ð¹, Ð² Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸, ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾-Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½ÑÐµ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸Ð¸
description: The subject of the graduate qualification work is ensemble of impurity atoms interacting with an electromagnetic field. The given work is devoted to development of a self-consistent theory of the interaction of atoms in a waveguide with electromagnetic radiation. As a result of the work, all the tasks were completed, including:Â Maxwell's equations are solved in the region of space inside a hollow rectangular waveguide with perfectly conducting walls;Â the procedure of canonical quantization of the electromagnetic field in free space has been mastered;Â canonical quantization of the electromagnetic field in the waveguide has been performed;Â the interaction of an electromagnetic field with 1-2 atoms is describedIn the course of the work, the effect of incomplete spontaneous decay was discovered â when the population of the excited state asymptotically approaches a non-zero value at large moments of time, in conditions when the frequency of the atomic transition is greater than the frequency of the waveguide cutoff and is far from the vicinity of the cutoff.The field of application of the results is a number of quantum technologies, especially quantum information technologies