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arXiv:2303.12266

Dynamic Stark shift of Hydrogen-like atoms in the presence of circularly polarized laser light

Behnam Nikoobakht

Published Mar 22, 2023• 0 citations
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Abstract

The analytic derivation of the dynamic Stark shift of hydrogenic energy levels in the presence of the circularly polarized laser light is presented. We use the classical framework with considering an adiabatically damped laser+atom interaction and an approach relies on time-independent perturbation theory with a second-quantized laser+atom dipole interaction Hamiltonian. We thus investigate the excitation process in atomic hydrogen or in a hydrogen like ion with low nuclear charge number in the presence of the circularly polarized laser light. The derived formula for the dynamic AC Stark shift of hydrogenic energy levels using these two methods are shown to be same in the limit of large photon numbers.

DOI
10.48550/arxiv.2303.12266

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The analytic derivation of the dynamic Stark shift of hydrogenic energy levels in the presence of the circularly polarized laser light is presented. We use the classical framework with considering an adiabatically damped laser+atom interaction and an approach relies on time-independent perturbation theory with a second-quantized laser+atom dipole interaction Hamiltonian. We thus investigate the excitation process in atomic hydrogen or in a hydrogen like ion with low nuclear charge number in the presence of the circularly polarized laser light. The derived formula for the dynamic AC Stark shift of hydrogenic energy levels using these two methods are shown to be same in the limit of large photon numbers.
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We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.
The stimulated radiative corrections (or ac-Stark shift, or light shift...) of the energy levels of a hydrogenic atom irradiated by an intense, nonresonant, monomode laser field, are evaluated within the framework of the time-dependent perturbation theory, up to and including fourth order. The calculation is performed by using a Sturmian representation of the Coulomb Green's function. Whenever it is possible, comparison is made with other results, and several limiting cases are considered. If the laser frequency $\ensuremath{\omega}\ensuremath{\rightarrow}0$, one recovers the results of the dc-Stark effect. If $2\ensuremath{\omega}$ becomes larger than the ionization energy of the atomic state considered, the fourth-order level shift acquires an imaginary part which may be connected, via an extension of the optical theorem, to the two-photon ionization cross section. We point out also the difficulties encountered, when trying to get sensible estimates from partial summation of the infinite sums entering the perturbative expression of the fourth-order amplitudes. Finally, the order of magnitude of these various corrections is discussed.
The energy shift of an atom due to its interaction with the oscillating electric field of an electromagnetic wave, or a laser light, is called the ac Stark shift. It has been studied both in the field of precision spectroscopy and atom optics. When the laser intensity is not constant spatially, its gradient gives rise to a dipole force. The force was used either to trap atoms in an optical trap or to reflect or guide atoms. We studied the ac Stark effect taking into account the fine structure of an alkali atom. We found that when the laser light is circularly polarized and properly detuned between the D1 and D2 transitions, the ac Stark shift can take the form of a pure Zeeman shift, hence the name analogous Zeeman shift.
This paper presents a theoretical study of the light-induced shift of the coherent population trapping resonance. An analytical model is proposed that describes the interaction of two radiation components with an atomic system using a ΛΛΛ scheme and takes into account an additional level of excited state. Both weak and strong coupling regimes with off-resonant transitions are considered. It is shown that, in addition to the conventional dynamic Stark shift, an extra shift arises due to the distortion of the resonance line shape when bichromatic laser radiation interacts with off-resonant atomic transitions. An analytical expression for this additional shift is derived in the weak-coupling limit, and its significant impact on the resonance shape and sensitivity to the intensities of the laser field components is demonstrated. It is found that under strong coupling conditions, the additional shift can deviate substantially from a linear dependence on light intensity, suggesting new opportunities for controlling light shifts in precision atomic devices such as quantum frequency standards.
This paper systematically studies the energy level shift (Stark effect) of the highly excited Rydberg state of cesium (Cs) atoms under the action of an electrostatic field. In view of the limitations of the traditional hydrogen atom Stark perturbation theory in describing alkali metal atoms, we propose a complete set of parametric approximation methods, which fully consider the correction of energy level structure by quantum number deficiency. By introducing the effective principal quantum number n* and the correction coefficient 𝛽l, we extend the fourth-order Stark perturbation formula for hydrogen atoms to the Cs atomic system. The study first reviewed the analytical theory of the Stark effect of hydrogen atoms and derived the fourth-order energy shift expression based on parabolic quantum numbers. Then, the quantum number depletion characteristics of Cs atoms and their influence on Stark matrix elements were analyzed; On this basis, the parametric correction rules of the system were established, including the replacement of the effective quantum number, the determination of the polarizability correction coefficient, and the conditional use of the linear term. We have developed corresponding computing programs that can quickly estimate the energy shift of different quantum states under any electric field. By comparing with the existing experimental data and precise numerical calculation results, the reliability and application scope of this method were verified. Research shows that for the high-Rydberg state with n>20, the relative error of this parametric method under moderate electric field intensity (10-100 V/cm) is very small, making it particularly suitable for rapid estimation in large-scale parameter scanning and experimental design. The work of this paper provides practical tools and theoretical basis for the theoretical research and experimental analysis of the Stark effect of alkali metal atoms.