Procedures for the evaluation of atomic transition matrix elements in the interaction with laser light

• Published in: Computer physics communications 1999-08, Vol.120 (2), p.231-237
• Main Authors: Madsen, L.B., Hansen, J.P., Nilsen, H.M.
• Format: Article
• Language: English
• Subjects: 32.80.Bx; 32.80.Rm; 42.50.Hz; Atomic and molecular physics; Atomic properties and interactions with photons; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Laser—atom interactions; Level crossing and optical pumping; Multiphoton ionization and excitation to highly excited states (e.g., rydberg states); Multiphoton ionization and excitation to highly excited states (eg, Rydberg states); Numerical integration of matrix elements; Optics; Photon interactions with atoms; Physics; Quantum optics; Rydberg wavepackets; Strong-field excitation of optical transitions in quantum systems; multi-photon processes; dynamic stark shift
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(99)00250-7

Analytical and numerical procedures for the calculation of atomic transition matrix elements in the interaction with linearly and circularly polarized laser light are presented. The laser—atom interaction is treated beyond the dipole approximation. The procedures are derived explicitly for hydrogen but may be readily generalized to other one-electron systems with, e.g., quantum defect type radial wavefunctions. The numerical procedure is programmed in Matlab and tested for main quantum numbers up to n = 30. The results clearly indicate when the dipole approximation breaks down in connection with laser excitation of angular Rydberg wavepackets.