We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode, while the second one describes the interaction with field fluctuations. The first part is usually associated with the resonant cavity mode. This division enables us to determine the applicability condition of the single-mode approximation. In addition we identify simple approximate relations for the description of the eigenstates, eigenfunctions and the time evolution of the quantum Rabi model beyond the rotating wave approximation.
The relativistic quantum dynamics of an electron in an intense single-mode quantized electromagnetic field is investigated with special emphasis on the spin degree of freedom. In addition to fast spin oscillations at the laser frequency, a second time scale is identified due to the intensity dependent emissions and absorptions of field quanta. In analogy to the well-known phenomenon in atoms at moderate laser intensity, we put forward the conditions of collapses and revivals for the spin evolution in laser-driven electrons starting at feasible 10 18 W/cm 2 .PACS number(s): 12.20.-m, 13.88.+e
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach. However, despite the great efficiency of modern numerical algorithms [9,10], simple analytical approximations [11][12][13][14] still play an important role for many applications, where there is no need for extremely high accuracy, but a simple algorithm of repeated calculations of atomic characteristics is required. For example, the models based on, e.g., the or multiparametric screening hydrogen [16] approximations are widely used in computational plasma [17][18][19][20][21] and X-ray physics [16,22], crystallography [22][23][24] or semiconductors physics [25][26][27]. In addition, the simplest possible inclusion of screening corrections in various cross sections like bremsstrahlung [28] or pair production [29,30] is required for later usage in particle-in-cell computer codes for simulation of strong laser-matter interaction [31], where computational efficiency is crucial.In the present work we suggest a new basis set of fully analytical SEWF, which on the one hand provides a suf- * olegskor@gmail.com † Corresponding author: ilya.feranchuk@tdt.edu.vn ficiently accurate analytical zeroth-order approximation and on the other hand allows one to construct regular perturbation theory (RPT) for the inclusion of higherorder corrections. Our basis set includes the hydrogenlike wave functions with a single-variational parameter, namely the effective charge Z * , which is identical for all SEWF of a given atom. The fact that the effective charge is identical for all SEWF is the principal difference of our approach in comparison with the inclusion of the multiparametric screening corrections [23,32,33] or the quantum defect method [34]. The identical effective charge for all wave functions automatically provides the complete and orthonormal basis and, consequently, renders the transition into the secondary-quantiz...
The interaction Hamiltonian of an electron and a quasi-monochromatic pulse of a strong quantized electromagnetic field is examined. Canonical transformations of the field variables are found that allow the division of the system's Hamiltonian in two parts. The first one describes the interaction between an electron and a single collective mode of the field. The properties of this mode are defined by the superposition of the modes corresponding to the pulse wave packet. The second part describes the field fluctuations relatively to the collective mode. The field intensity, pulse duration and transversal spread are estimated for which a single-mode approximation can be used for the system's description.PACS 34.80.Nz
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