Relativistic and radiative corrections to the dynamic Stark shift: Gauge invariance and transition currents in the velocity gauge

Abstract

We investigate the gauge invariance of the dynamic (ac) Stark shift under "hybrid" gauge transformations from the "length" ( E · r) to the "velocity" ( A· p) gauge. By a "hybrid" gauge transformation, we understand a transformation in which the scalar and vector potentials are modified, but the wave function remains unaltered. The gauge invariance of the leading term is well known, while we here show that gauge invariance under perturbations holds only if one takes into account an additional correction to the transition current, which persists only in the velocity gauge. We find a general expression for this current, and apply the formalism to radiative and relativistic corrections to the dynamic Stark effect, which is described by the sum of two polarizability matrix elements.

Natural line profile asymmetry

“…Alongside this, the former initially arises in the QED theory, while the latter is the result of the approximation. Recently, the gauge invariance was analyzed in [30], see also [11][12][13] for details and further extensions. This immediately leads to (by inserting Γ(ω)) a modification of the Lorentz profile, L(ω), which becomes asymmetric.…”

Helium tune-out wavelength: Gauge invariance and retardation corrections

“…Recent high-precision measurements in helium [1] are sensitive to relativistic and quantum electrodynamic corrections. The effect has traditionally been formulated as a zero in the ac Stark shift for an atom trapped in an optical lattice formed by counter-propagating laser beams [2,3], and detailed relativistic configuration-interaction (CI) calculations have been carried out [4]. However, an optical lattice corresponds to an electric potential that is fixed in space and oscillates in time such that the interaction with an atom depends on its location relative to the nodes of the potential.…”