Second Quantization and Floquet Quasienergies of the Parabolic Barrier

摘要

In this work we show how to find the Floquet quasienergies of a parabolic barrier Hamiltonian interacting with a periodic field mode using a convenient definition of ladder operators.Although these operators are not adjoint to each other in the configuration space,they,however,keep all the other properties of the usual ladder operators for the harmonic oscillator.We also use the Bargmann-Segal representation to find the eigenvalues and eigenfunctions of the parabolic barrier in a straightforward way.The use of second-order perturbation theory and the Bogoliubov-Tyablikov transformation enables us to obtain the Floquet shift by utilizing only the algebraic properties of these ladder operators.