Driven three-state model and its analytic solutions
- 1 February 1988
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 29 (2) , 487-509
- https://doi.org/10.1063/1.528041
Abstract
For an atom or molecule in which two transitions are driven by laser beams, a three‐state model is used. Transitions among the three states are caused only by the oscillating electric fields of the laser beams. The amplitudes and detunings of the two laser beams, which are various functions of the time, appear in the Schrödinger equation for the atom or molecule. In certain cases, the Schrödinger equation can be solved analytically, to find transition probabilities and the probability of no transition. This is done by using Clausen’s special function, or by assuming that the sum of the two detunings is zero at all times. Conditions for complete transfer of the population from the ground state to an excited state are obtained from the analytic solutions.Keywords
This publication has 23 references indexed in Scilit:
- A new class of analytic solutions of the two-state problemJournal of Physics A: General Physics, 1986
- Asymptotic Formulas for Zero-Balanced Hypergeometric SeriesSIAM Journal on Mathematical Analysis, 1984
- Eigenvalue problem of the square of the pulse area for two-level systemsPhysical Review A, 1984
- Two-level transition probabilities for asymmetric coupling pulsesPhysical Review A, 1981
- Coherent dynamics of-level atoms and molecules. III. An analytically soluble periodic casePhysical Review A, 1979
- Analytical solutions for laser excitation of multilevel systems in the rotating-wave approximationPhysical Review A, 1976
- The contiguous function relations for _{𝑝}𝐹_{𝑞} with application to Batemean’s 𝐽_{𝑛}^{𝑢,𝜈} and Rice’s 𝐻_{𝑛}(𝜁,𝑝,𝜈)Bulletin of the American Mathematical Society, 1945
- Ueber die Integration der linearen Differentialgleichungen durch Reihen.Journal für die reine und angewandte Mathematik (Crelles Journal), 1873
- Zur Theorie der linearen Differentialgleichungen mit veränderlichen Coefficienten.Journal für die reine und angewandte Mathematik (Crelles Journal), 1866
- Ueber die Fälle, wenn die Reihe von der Form y = etc. ein Quadrat von der Form z = etc. hat.Journal für die reine und angewandte Mathematik (Crelles Journal), 1828