title: ÐÐ»Ð¸ÑÐ½Ð¸Ðµ Ð¼ÐµÐ¶Ð°ÑÐ¾Ð¼Ð½Ð¾Ð³Ð¾ Ð´Ð¸Ð¿Ð¾Ð»Ñ-Ð´Ð¸Ð¿Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð½Ð° Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ ÑÐ¿Ð¾Ð½ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÐ¿Ð°Ð´Ð° Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð°ÑÐ¾Ð¼Ð°
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: The effect of the interatomic dipoleâdipole interaction on the dynamics of spontaneous decay of the excited state of an atom
Creators: name: ÐÐ¾Ð½Ð´Ð°ÑÐµÐ², ÐÐ»Ð°Ð´Ð¸ÑÐ»Ð°Ð²
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: 2024
Subjects: Ñ Ð¾Ð»Ð¾Ð´Ð½ÑÐ¹ Ð°ÑÐ¾Ð¼Ð½ÑÐ¹ Ð³Ð°Ð·
ÑÐ²ÐµÑÐ´Ð¾ÑÐµÐ»ÑÐ½ÑÐ¹ Ð´Ð¸ÑÐ»ÐµÐºÑÑÐ¸Ðº
Ð´Ð¸Ð¿Ð¾Ð»Ñ-Ð´Ð¸Ð¿Ð¾Ð»ÑÐ½Ð¾Ðµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ
Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ñ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¹
Ð¼Ð°ÑÑÐ¸ÑÐ° Ð¿ÐµÑÐµÐ¸Ð·Ð»ÑÑÐµÐ½Ð¸Ð¹
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹
cold atomic gas
solid-state dielectric
dipole-dipole interaction
state amplitudes
re-emission matrix
population dynamics

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description: The object of the study is an ensemble of cold atoms under conditions of strong dipole-dipole interaction. The purpose of the work is to review the literature on collective effects in nonâdegenerate cold atomic gases and ensembles of impurity atoms in a solid-state dielectric, calculate the quantum mechanical amplitudes of once excited states of atoms in a dense disordered ensemble of arbitrary spatial configuration, as well as calculate the dynamics of populations of excited states of atoms. Open educational resources and information search and analysis programs were used. Automation (automated) development tools such as MATLAB was/were used. The MATLAB software has been applied (tested). In the course of this work, we introduce the amplitude of the states. Next, we use the dipole approximation in the nonstationary Schrodinger equation for the wave function of a closed unified system, where we consider systems of free atoms and free electromagnetic fields. After that, we apply the Fourier transform to this system to obtain a finite system of equations of the amplitudes of the states of the atom. During the calculation of the integral and the use of the pole approximation, we obtain an expression for the re-emission matrix, which we use in a system of equations to find the amplitudes of states. To calculate population dynamics, we take the square of the modulus of the obtained state amplitudes, having previously performed the inverse Fourier transform. As a result of this work, we calculated the amplitudes of the states for a certain frequency range, thereby obtaining the transition spectrum, and obtained the dynamics of the populations of the excited state of the atom for large and small distances between them (in comparison with the wavelength of the radiation of the resonant transition). Based on the result obtained, we can say that the obtained population dynamics for the excited state of the atom has the following character: for time intervals much smaller than Î³0 (the rate of spontaneous decay), the dependence is decreasing, and it decreases very sharply, which can be explained by single photon superradiance. For time intervals of the order of Î³0, we were able to see a complex nonmonotonic dependence. This dependence can be explained by the transfer of energy from one atom to another, which is why we can observe quasiâperiodic oscillations. At time intervals, the order of which is much greater than Î³0, we were able to observe a decrease in dependence, which can be explained by the natural attenuation of collective excitation. We were also able to detect a collective Lamb shift on the absorbing and dispersive circuits. These results can be used, for example, in the design of atomic clocks.