Atoms and molecules in intense laser fields: gauge invariance of theory and models

Abstract

Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature, stating that different forms of these potentials yield the same physical description: they describe the same electromagnetic field as long as they are related to each other by gauge transformations. Gauge invariance can also be included into the quantum description of matter interacting with an electromagnetic field by assuming that the wave function transforms under a given local unitary transformation. The result of this procedure is a quantum theory describing the coupling of electrons, nuclei and photons. Therefore, it is a very important concept: it is used in almost every fields of physics and it has been generalized to describe electroweak and strong interactions in the standard model of particles. A review of quantum mechanical gauge invariance and general unitary transformations is presented for atoms and molecules in interaction with intense short laser pulses, spanning the perturbative to highly nonlinear nonperturbative interaction regimes. Various unitary transformations for single spinless particle Time Dependent Schrödinger Equations, TDSE, are shown to correspond to different time-dependent Hamiltonians and wave functions. Accuracy of approximation methods involved in solutions of TDSE's such as perturbation theory and popular numerical methods depend on gauge or representation choices which can be more convenient due to faster convergence criteria. We focus on three main representations: length and velocity gauges, in addition to the acceleration form which is not a gauge, to describe perturbative and nonperturbative radiative interactions. Numerical schemes for solving TDSE's in different representations are also discussed. A final brief discussion is presented of these issues for the relativistic Time Dependent Dirac Equation, TDDE, for future super-intense laser field problems.

Ionization dynamics of orbitals and high-harmonic generation of N 2 and CO molecules at the various XC potentials by TD-DFT

“…2 denotes the external potential due to the interaction with the laser field in the velocity gauge [23]. It is given by…”

“…According to the Ehrenfest's theorem, the expectation value of the dipole-velocity can be written [23] ఙ ௭ ఙ…”

“…The power spectrum for the MHOHG, , can be computed from the absolute square of the Fourier transform of the time-dependent dipole velocity , which is given by [23]:…”

“…In this calculation, a numerical grid in three dimensional (3D) real space is utilized as and using an appropriate absorber at the edge of the grid. The radius of the spherical simulation box is 23 . Four types of the XC potential with A-LDA of Perdew and Zunger, B 3 LYP, LB94 and LBα is characterized to investigate the ionization rates and harmonic spectra with high accuracy.…”

Enhancing high-order-harmonic generation by time delays between two-color, few-cycle pulses

“…In order to avoid any static field component of a short pulse [44,45], we derive the electric field F (t) via the vector potential A(t): F (t) = −∂ t A(t)/c, where A(t) is either A TD (t) or A NTD (t). In both our numerical and analytical calculations we employ pulse envelopes defined as follows:…”