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Ukrainian Journal of Physics

Influence of Photon Subsystem on the Magnetic Properties of Quantum Gases

M. S. Bulakhov, A. S. Peletminskii, Yu. V. Slyusarenko

Published Sep 18, 2024• 2 citations
Publisher

Abstract

The possibility for the photon component to affect the magnetic properties of a system of quantum gases of two-level atoms staying in thermodynamic equilibrium with radiation (photons) has been studied. A corresponding simple model has been proposed, which enabled the general equations describing the thermodynamic equilibrium in this system to be derived. The resulting equations are solved in the temperature interval far from the degeneracy temperatures of all three system components. The analysis of the solutions testified to a non-trivial behavior of the system’s magnetic state as a response to changes in the photon density and the intensity of the external magnetic field. It is shown that the growth of the photon density induced in the system by external sources can increase both system’s magnetization and the density of excited atoms. Such a conclusion is not trivial a priori given the fact that photons in the vacuum have no magnetic moment.

DOI
10.15407/ujpe69.8.600

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The possibility for the photon component to affect the magnetic properties of a system of quantum gases of two-level atoms staying in thermodynamic equilibrium with radiation (photons) has been studied. A corresponding simple model has been proposed, which enabled the general equations describing the thermodynamic equilibrium in this system to be derived. The resulting equations are solved in the temperature interval far from the degeneracy temperatures of all three system components. The analysis of the solutions testified to a non-trivial behavior of the system’s magnetic state as a response to changes in the photon density and the intensity of the external magnetic field. It is shown that the growth of the photon density induced in the system by external sources can increase both system’s magnetization and the density of excited atoms. Such a conclusion is not trivial a priori given the fact that photons in the vacuum have no magnetic moment.
The peculiarities of the influence of photonic component on the magnetic properties of a system of quantum gases in thermodynamic equilibrium with radiation in the presence of an external magnetic field are analyzed. The problem is not trivial, given that photons in a vacuum do not have a magnetic moment. It is assumed that the magnetic moment of photons is zero even in low-temperature gases. To study the announced question, a system of equations was constructed that describe the state of thermodynamic equilibrium of the specified medium. The solutions of these equations in analytical form were obtained in the temperature range far from the degeneracy temperatures of all components of the system. Both analytical and numerical methods were used to study the obtained solutions. The analysis of the solutions indicates a significant influence of photons and the intensity of the external magnetic field on the density distribution of all components of the medium, including the photonic one, and on the magnetic state of the medium. In particular, it is shown that an increase in the photon density in the system due to external sources leads to an increase in the characteristic of the inverse population of atomic levels. However, it was found that the magnetization of the system with an increase in the density of photons from external sources can both significantly increase and significantly decrease, depending on the quantum mechanical characteristics of the atomic states.
The influence of quantum interference between different decay channels of three-level atoms on various characteristics of matter and radiation is considered for the case of thermodynamic equilibrium of atoms in a photon gas. It is shown that for rare gases when collisions between atoms are not important, the direct consequence of such an interference is a spontaneously induced atomic coherence between two upper levels. Therefore, for an accurate description of such atoms and radiation in thermodynamic equilibrium with each other it is not sufficient to specify only Boltzmann exponents, which correspond to the diagonal elements of the density matrix. The reason for this is that the conventional Boltzmann description is applied to infinitely sharp eigenstates of the unperturbed Hamiltonian. As we show, it becomes essential to take into account nonzero width of the levels if the levels are relatively close to each other. This produces nonzero nondiagonal elements of the density matrix that modify the emissivity of the equilibrium medium and lead to a zero point at a certain frequency as well as to an enhanced intensity in the red wing at the corresponding temperature. It is shown that the occupation number of the photons is not changed and obeys the equilibrium Planck distribution.
The theory of interaction of intense bichromatic field of laser radiation with multilevel atomic system in the external magnetic field is considered. The magnitudes of interaction are much larger than the width of atomic levels. The vector-potential of radiation field consisting of two monochromatic components with the frequencies resonant to adjacent transitions is taken in electric dipole approximation. The eigenvalues and eigenstates of the Hamiltonian, including spin-orbit interaction and interactions with laser radiation and external magnetic fields, are found without perturbation theory using resonant approximation. When the effects of resonantly excited radiation are considered the Hamiltonian of interaction with the weak field of scattered radiation is included also. Its eigenfunctions are found with the help of perturbation theory. We consider tow types of effects: polarization effects and effects of resonantly excited radiation. As the atomic system is multilevel we use the numerical methods. The influence of the magnetic field on coherent population trapping effect for multilevel systems is considered. Some of our theoretical results coincide with known experimental ones.
A rather complete discussion of the electrodynamic behavior of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is presented. The method presented here is based on the general principles of elementary nonrelativistic quantum theory and takes account of the Doppler-broadening effects arising from the random thermal motion of the particles and the Compton recoil effects arising from the emission (spontaneous plus the induced or the stimulated emission) and absorption of photons by the spin-\textonehalf{} particles. In the first half of the paper a method is presented for calculating the spin permeability tensor which determines the propagation of transverse electromagnetic radiation through a gas of spin-\textonehalf{} particles in a uniform external magnetic field. It is shown that the spin permeability tensor thus obtained yields the familiar results of solid-state physics, such as the nuclear and electronic-spin radiofrequency susceptibility and the spin paramagnetism. In the second half of this paper the subject of spin-radiative equilibrium of a gas of spin-\textonehalf{} particles in a uniform external magnetic field is discussed in some detail. Simple closed-form expressions for the steady-state photon number density and the spin-radiative relaxation time of the system under study are thus derived. It is shown that the steady-state photon number density is the familiar distribution function corresponding to Bose---Einstein statistics for "complete thermodynamic equilibrium." The conditions under which the system of spin-\textonehalf{} particles in a uniform magnetic field can become unstable for transverse electromagnetic radiations are also discussed.
The features of Bose condensation in an equilibrium ideal gas consisting of two types of charged fermions and their bound states—hydrogenlike atoms—in the presence of equilibrium between the photons and matter are investigated. It is shown that under such conditions the main influence on the Bose–Einstein condensation comes from the existence of levels concerned with the hyperfine splitting of the ground state of the hydrogenlike atom. The critical temperature and condensate density as functions of magnetic field are determined by considering effects due to the additional splitting of the levels of the hyperfine structure of the ground state in an external uniform static magnetic field (the Zeeman and Paschen–Back effects). It is found that under conditions of total statistical equilibrium in the system, a condensate is formed only by atoms found in the lowest energy state. It is shown that in the absence of equilibrium between radiation and matter, in the region of ultralow temperatures and low densities, the system can be treated as a multicomponent ideal gas of hydrogenlike atoms. The existence of a hierarchy of individual transition temperatures of each of the samples to the state with Bose–Einstein condensation is established. Expressions are found for the critical temperatures and number densities of particles in the condensate for each of the system components.
In the present work, the role of temperature in the occurrence of optical phases in a system of a large number of atoms interacting with photons is reported. To this end, it is assumed that the cavity inside which the constituents interact is in equilibrium with a heat reservoir, held at a fixed temperature. To achieve this goal, we start with the conventional density operator to calculate the mean values of electromagnetic quadratures. To make the realization of three distinct optical phases, trivial, electric, and magnetic superradiance, possible, the medium inside the cavity is assumed to be a second-order nonlinear one. The nonlinearity of the medium is further assumed to be activated by an externally applied classical pump field. As a consequence, now there are two external controlling agents, the temperature and nonlinearity strength. We then proceed to calculate the quadrature mean values in the thermodynamical limit and for a large number of atoms as a function of temperature. An analysis of the calculated mean values, along with relevant figures, reveals temperature-dependent conditions for realizing trivial, electric, and magnetic optical phases. Moreover, we shall demonstrate that the atom-field coupling strength gives rise to two distinct regimes where the optical phases behave quite differently. In one of the two regimes it is possible for the phases to coexist, while in the other it is not. As a profound result, it is demonstrated that for such a system there can exist a unique temperature (triple point) at which the three optical phases coexist.