Beyond Adiabatic Elimination: Multi-photon Processes

Situations in which there is a wide separation among energy or time scales present in a physical system pervade all of Physics. It is therefore of recurrent interest to develop techniques to obtain approximate, effective descriptions of the low energy or slow sector of the system.Adiabatic elimination technique is a very common or standard approximation method to solve these problems in quantum optics.However, adiabatic elimination technique in quantum optics often require the effective Hamiltonian of the system is hermitian.For a non-hermitian effective Hamiltonian system,we use non-adiabatic elimination method,such as a Markov approximation,singular perturbation and so on.Here, we first briefly introduce two methods to study multiphoton process :adiabatic elimination method and non adiabatic elimination method.Then discuss the exact solution of a A-type three level atom system multiphoton process coupling with external fields.Next we introduce the main idea and procedure of singular perturbation and we detailed derivation a second order and fourth order Hamiltonian of linear and non-hermitian effective Hamiltonian of a A-type three level atom system.And then we utilize the second order and fourth order Hamiltonian of the system to calculate the evolution of the population of the ground and excited states.Compared with the exact solution,the result of singular perturbation has a good degree of approximation.The method of singular perturbation is extended to two A-type three level identical atom system, we use this method to calculate the evolution of the population of the ground and target states.Compared with the Markov approximation solution,we find the result of singular perturbation has a good degree of approximation.