title: ÐÐ·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð±Ð¸Ñ ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð»Ð°Ð·ÐµÑÐ½Ð¾Ð³Ð¾ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ñ Ñ ÑÐµÐ»Ð¾ÑÐ½ÑÐ¼Ð¸ Ð°ÑÐ¾Ð¼Ð°Ð¼Ð¸ Ð² ÑÑÐµÐ¹ÐºÐ°Ñ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð³Ð¾ ÑÐ°Ð·Ð¼ÐµÑÐ° Ð² Ð¾Ð¿ÑÐ¸ÑÐµÑÐºÐ¸ Ð¿Ð»Ð¾ÑÐ½Ð¾Ð¹ ÑÑÐµÐ´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: alkaline atoms in cells of finite size with anti-relaxation wall coating
Creators: name: ÐÐ¼Ð¼Ð¾ÑÐ¾Ð², ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
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: 2023
Subjects: ÑÐµÐ»Ð¾ÑÐ½ÑÐµ Ð°ÑÐ¾Ð¼Ñ
Ð³Ð°Ð·Ð¾Ð²Ð°Ñ ÑÑÐµÐ¹ÐºÐ°
Ð´Ð²Ð¸Ð¶ÑÑÐ¸ÐµÑÑ Ð°ÑÐ¾Ð¼Ñ
Ð¾ÑÑÑÑÐ¾Ð¹ÐºÐ°
ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾Ðµ Ð¿Ð»ÐµÐ½ÐµÐ½Ð¸Ðµ Ð½Ð°ÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹
ÑÑÐµÑ ÑÑÐ¾Ð²Ð½ÐµÐ²Ð°Ñ ÑÑ ÐµÐ¼Ð°
Ð±Ð¸Ñ ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ðµ
alkaline atoms
gas cell
moving atoms
detuning
coherent population trapping
three-level scheme
bichromatic radiation

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½ ÑÑÑÐµÐºÑ ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»ÐµÐ½ÐµÐ½Ð¸Ñ Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ (ÐÐÐ) Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÑÐµÑÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ Î â ÑÑÐµÐ¼Ñ Ð¿ÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ¸Ð¸ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð¸ Ñ ÑÑÐµÑÐ¾Ð¼ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð¼ÐµÑÐ¾Ð² ÑÑÐµÐ´Ñ. ÐÑ ÑÐ´ÐµÐ»Ð°Ð»Ð¸ ÑÑÐ´ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ð¹ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ñ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ ÑÐ°Ð·Ð½Ð¾ÑÑÐ¸ Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ Ð¼ÐµÐ¶Ð´Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐ¼Ð¸ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸ÑÐ¼Ð¸. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð² Î â ÑÑÐµÐ¼Ðµ Ð¿ÑÐ¸ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð¸Ð¸ Ð² ÑÐµÐ»Ð¾ÑÐ½ÑÑ Ð°ÑÐ¾Ð¼Ð°Ñ Ð´Ð²ÑÑÑÐ°ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð¸Ñ Ð² ÑÑÐµÐ¹ÐºÐ°Ñ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð³Ð¾ ÑÐ°Ð·Ð¼ÐµÑÐ° Ð¸Ð¼ÐµÐµÑÑÑ Ð¸Ð½Ð²ÐµÑÑÐ¸Ñ Ð½Ð°ÑÐµÐ»ÑÐ½Ð½Ð¾ÑÑÐµÐ¹ Ð¼ÐµÐ¶Ð´Ñ ÑÐ²ÐµÑÑÑÐ¾Ð½ÐºÐ¸Ð¼Ð¸ Ð¿Ð¾Ð´ÑÑÐ¾Ð²Ð½ÑÐ¼Ð¸ Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ ÑÐµÐ»Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð°ÑÐ¾Ð¼Ð°. ÐÐµÑÐ¼Ð¾ÑÑÑ Ð½Ð° ÑÐ´ÐµÐ»Ð°Ð½Ð½ÑÐµ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ðµ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ðµ ÑÑÐ¸ÑÑÐ²Ð°ÐµÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÑÑÐµÐºÑÐ¾Ð², ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ðµ Ð°ÑÐ¾Ð¼Ð¾Ð², ÑÐ¾ÑÐ´Ð°ÑÐµÐ½Ð¸Ðµ ÑÐ¾ ÑÑÐµÐ½ÐºÐ°Ð¼Ð¸ ÑÑÐµÐ¹ÐºÐ¸, Ð²ÑÐ·ÑÐ²Ð°ÑÑÐµÐµ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð½ÐµÐ²ÑÑÐ¾Ð¶Ð´ÐµÐ½Ð½Ð¾ÑÑÑ Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ. ÐÐ¾ÑÑÐ¾Ð¼Ñ Ð¼Ñ ÑÑÐ¸ÑÐ°ÐµÐ¼, ÑÑÐ¾ Ð²Ð¾ Ð²ÑÐµÑ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ Ð¿ÑÐ¸Ð»Ð¾Ð¶ÐµÐ½Ð¸ÑÑ ÑÑÑÐµÐºÑÐ° ÐÐÐ, Ð² ÐºÐ¾ÑÐ¾ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ Ð³Ð°Ð·Ð¾Ð²ÑÐµ ÑÑÐµÐ¹ÐºÐ¸ Ñ Ð°Ð½ÑÐ¸ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐ¼ ÑÑÐµÐ½Ð¾ÑÐ½ÑÐ¼ Ð¿Ð¾ÐºÑÑÑÐ¸ÐµÐ¼ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ ÑÑÐ¸ÑÑÐ²Ð°ÑÑ Ð²ÐºÐ»Ð°Ð´ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð½ÑÑ Ð² Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÑÑÐµÐºÑÐ¾Ð². Ð¢Ð°ÐºÐ¶Ðµ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· Ð±ÐµÐ·Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð¹ ÑÑÐµÐ´Ñ Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ñ Ð´Ð»Ñ ÑÐ°Ðº Ð½Ð°Ð·ÑÐ²Ð°ÐµÐ¼Ð¾Ð³Ð¾ ÑÐ´Ð²Ð¸Ð³Ð° Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ Ð¸ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½ Ð½ÐµÐ°Ð´Ð´Ð¸ÑÐ¸Ð²Ð½ÑÐ¹ Ð²ÐºÐ»Ð°Ð´ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐºÐ¾ÑÐ¾ÑÑÐ½ÑÑ Ð³ÑÑÐ¿Ð¿ Ð½Ð° Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ñ ÑÐ´Ð²Ð¸Ð³Ð°. ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ðµ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ðµ: Wolfram Mathematica.
description: In this paper, the effect of coherent population trapping (CPT) is analyzed for a model of a threeâlevel Î-scheme in the presence of atomic motion and considering the finite dimensions of the medium. We have made several approximations that allow us to obtain an analytical expression for the population difference between the main states. It is shown that in the Îâscheme, when two-frequency excitation is excited in alkaline atoms in cells of finite size, there is an inversion of populations between hyperfine sublevels of the ground state of an alkaline atom. Despite the approximations made, the resulting expression considers the effects of effects such as the movement of atoms, collision with the walls of the cell, causing a change in the direction of movement, as well as the non-degeneracy of the ground state. Therefore, we believe that in all potential applications of the CPN effect, in which gas cells with an anti-relaxation wall coating are used, it is necessary to consider the contribution of the effects considered in this paper. The paper also analyzes the boundless environment and obtains analytical expressions for the so-called population shift and shows the non-additive contribution of various velocity groups to the magnitude of the shift. Software applied: Wolfram Mathematica.