2019/12/05 by Chon‐Fai Kam, Yang Chen, Kam, Chon-Fai +1
Chemistry · Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Physical sciences #Laser-Matter Interactions and Applications #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectroscopy and Laser Applications
paper · pdf · doi:10.48550/arxiv.1912.02377
openalex publication_date 2019/12/05 · openalex created_date 2019/12/13 · openalex updated_date 2026/07/28
We study the dynamics of a nonlinear two-level crossing model with a cubic modification of the linear Landau-Zener diabatic energies. The solutions are expressed in terms of the bi-confluent Heun functions --- the generalization of the confluent hypergeometric functions. We express the finial transition probability as a convergent series of the parameters of the nonlinear laser detuning, and derive analytical approximations for the state populations in terms of parabolic cylinder and Whittaker functions. Tractable closed-form expressions are derived for a large part of the parameter space. We also provide simple method to determine the transition point which connects local solutions in different physical limits. The validity of the analytical approximations is shown by comparison with numerical results of simulations.