A new integro-differential operator equation which describes the propagation of a quantized radiation field in a resonant medium is obtained. We have investigated a system of atoms on the basis of the interaction of H-like atoms through the field of virtual photons, taking into account electronic and positronic intermediate states in the atomic spectrum. This interaction is treated as a third-order effect in quantum electrodynamics. We suggest a new method to solve boundary-value problems in quantum optics which employs the joint system of material and field equations.
A new integro-differential operator equation which describes the propagation of a quantized radiation field in a resonant medium is obtained. We have investigated a system of atoms on the basis of the interaction of H-like atoms through the field of virtual photons, taking into account electronic and positronic intermediate states in the atomic spectrum. This interaction is treated as a third-order effect in quantum electrodynamics. We suggest a new method to solve boundary-value problems in quantum optics which employs the joint system of material and field equations.
The interaction of an atomic system with an unquantized electromagnetic field is studied by means of the Heisenberg-operator equations of motion. The electromagnetic fields created by the atom are taken into account by assuming that the charge and probability current densities are the actual charge and current source terms in Maxwell's equation. When Ehrenfest's theorem is written to order (1/c)2, the equations of motion are found to have a constant of motion that can be interpreted as stating that the sum of the atomic energy, energy of interaction, and energy stored in the electromagnetic field is constant. This constant of integration can be expressed as an expectation of a new semiclassical Hamiltonian that now includes the effects of the atomic self-fields to order 1/c2. This Hamiltonian is related to the classical Darwin Lagrangian. Since the new approximate Hamiltonian is the sum of an atomic and a field Hamiltonian, it provides a formulation of semiclassical radiation theory that is formally close to the usual formulation of quantum electrodynamics. A Schr\"odinger equation can be derived by applying the variational principle to the expectation of the new Hamiltonian. The result is a nonlinear integro-differential equation, in \ensuremath{\Psi}, which is somewhat similar to Hartree's self-consistent equation for a multielectron atom.When the Heisenberg equations are written to include the next-higher-order terms, 1/c3, it is found that the total energy of the atom and the electromagnetic field in the vicinity of the atom decreases at a rate that is given by the Larmor power formula (2e2/3c3)(d〈v〉/dt)2, where 〈v〉 is the quantum-mechanical expectation of the electron's velocity operator. This approximate formulation of semiclassical radiation theory is applied to semiclassical calculations of atomic radiative shifts. It is then shown that, if some retardation effects are included to all orders of 1/c in the vector potential, the semiclassical analysis provides a formula for radiative energy-level shifts that are time dependent and that contain coefficients similar to the starting point of the Bethe calculation of the Lamb shift. The incorporation of mass renormalization in semiclassical theory is then discussed.
Background. At present, researchers are paying considerable attention to the search for new magnetic metamaterials. In this regard, this article solves the urgent problem of deriving nonlocal equations for the propagation of electromagnetic waves in magnetic media, where spin transitions are carried out under the action of radio frequency, microwave and terahertz fields. Based on these equations, it is proposed to solve various problems similar to those already being solved in optics. Materials and methods. The solution to the problem posed is based on the effects of the 2nd and 3rd orders of quantum electrodynamics, highlighting the spinspin interactions of spatially separated electrons of two hydrogen atoms. In this case, the expansion of the retarded potentials takes into account two smallness parameters (v/c) and (Δξ/R12), where v is the speed of motion of electrons, c is the speed of light in vacuum, Δξ is the displacement of electrons relative to immobile nuclei, R12 is the distance between the nuclei of atoms. Сonclusions. It is shown that the operator of the spin-spin interaction of two spatially separated electrons belonging to two hydrogen-like atoms contains terms proportional to 1 / R12 3, 1 / R12 2, 1 / R12, in contrast to the Breit operator, where the interaction of two electrons is determined only by the terms 1 / R12 3. On the basis of the obtained operator of spin-spin interaction of two spatially separated electrons, passing to the effects of the third order of quantum electrodynamics, an equation for the propagation of electromagnetic waves in a system of electron spins is obtained.
A method of integro-differential equation associated with the optical loch equations is proposed to consider the problem of nonlinear transient reflection (refraction) of two laser noncomplanar pulses. It is a 3D boundary-value problem of a semiclassical nonlinear resonant transient optics for the phase memory effects exhibited by surface atoms in response to pulses of fields resolved in space and time. A generalized Lorentz- Lorenz formula and a theorem of extinction of nonlinear transient optics are used to investigate generalized reflection and refraction laws.
The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.
Theory of the interaction between atom and radiation field: three pictures in quantum mechanics description two-level atom and the optical Bloch equation quantized description of the radiation field Dicke Hamiltonian and Jaynes - Cummings model quantum theory of a small system coupling to a reservoir. The quantum properties of light: coherence of light squeezed states of light resonance fluorescence superfluorescence optical bistability effects of virtual photon processes. Quantum properties of the atomic behaviour under the interaction of the radiation field: collapses and revivals of the atomic populations squeezing effects of the atomic operators coherent trapping of the atomic population quantum characteristics of a two-atom system under the interaction of radiation field autoionization of the atom in a laser field motion of the atom in a laser field laser cooling.
Based on the separability with respect to position variables of the susceptibility for a finite system, we have developed a formulation which solves Schri:idinger and Maxwell equations selfconsistently. The case of linear response is' described in detail. As a manifes tation of the selfconsistency between the two equations, the appearance of radiative damping rate with correct magnitude has been demonstrated for a two-level atom in vacuum. The interaction of electromagnetic (EM) radiation with matter has been studied in various aspects for quite a long time. The relevant phenomena range, in the scale of wavelength, from rf wave (NMR, for example) to gamma ray (Mossbauer effect): They are related with the absorption, reflection, transmission, propagation, refrac tion, scattering, diffraction, emission, etc. of EM wave in linear and nonlinear manner. For the theoretical treatment of these phenomena, we need Schrodinger equation for the description of matter and Maxwell equations in classical or quantized form for radiation field. When the Maxwell equations are treated in classical form, this is called semiclassical treatment of radiation-matter interaction. Though it has a certain limitation, the semiclassical treatment can be appliedto most of the phenom ena mentioned above. For the treatment of the interaction of EM radiation with solids, it is usual to employ a susceptibility function to describe the solid, and solve the Maxwell equa tions containing that susceptibility as an integral kernel. In doing so, we must consider the boundary conditions (BC) arising from the shape of the sample in question. However, we do not consider BC's in treating microscopic systems such as an atom or small molecule. This would mean that the use of BC(s is in general not compulsory, although we are so much accustomed to it. In this respect, there has been a long debated problem of additional boundary condition (ABC) in relation with exciton polaritons in semiconductors or insulators, where the nonlocal nature of the medium allows the existence of two or more eigenmodes of the coupled exciton-EM radiation. After the long history of the ABC problem,r>- 4 > we now have a recipe to derive the appropriate form(s) of ABC(s) from a microscopic model of the medium including the details of the surface. 5 >-s> Another form of the microscopic solution of the ABC problem has been given as an ABC-free formulation, 9 >-n> where one needs