Study Of The Nonlinear Characteristics For Multi-level Coherent Systems

The interaction between light and atoms is an important topic of physical research.In quantum optics,quantum interference(or coherence)contributes to nonlinear effects,and quantum coherence can be achieved by using the interaction between multi-level atoms and light fields.Electromagnetic induced transparency(EIT)is a typical model of quantum coherence,which has the advantages of high dispersion and small absorption.Multi-level(three-level and more)atomic system is the physical basis of realizing quantum coherence,and its energy level structure is crucial to the generation of quantum interference.In this paper,the quantum coherence of three-level systems and their nonlinear and higher-order nonlinear characteristics are studied.At the same time,the double EIT characteristics of Tripod four-level coherent systems are studied.The specific content is as follows:1)The basic coherent properties and nonlinear response characteristics of-type and V-type three-level systems are studied.The coherent properties of the systems under different optical conditions are studied based on the complete density matrix equation.It is found that the same Rabi frequency will lead to the coherent population trapping(CPT)effect in the-type system,which forms a dark state at the optical resonance of the probe.Under the excitation of a strong light and a weak light,atoms will form a wide-band dark state that does not depend on the detuning of probe field,thus forming electromagnetic induced transparency(EIT).The quantum coherence in-type EIT is very strong.However,in the V-type three-level system,the quantum coherence is severely inhibited,so no CPT will occur,and only weak EIT will be formed,because the spontaneous radiation of the two excited energy levels causes serious damage to the quantum coherence.The third-order and fifth-order nonlinear effects in V-type EIT are studied.The results show that the nonlinear effects of V-type EIT system,including self-nonlinear and cross-nonlinear effects,are much smaller than those of-type EIT system.2)The basic coherence properties of Tripod-type four-level system are studied.The coherent properties of the system under different optical conditions are studied based on the complete density matrix equations.The distribution of atomic population number and its electric polarizability under different optical conditions were investigated.It is found that the CPT can be formed under the condition that the three light fields have the same Rabi frequency,and the double dark state can be formed at the resonance of the probe light.When a light field is much smaller than the other two,double EIT is obtained,which forms a double dark state in the overall frequency range of probe light,in which the weak field becomes the common probe field of double EIT.It is also shown that the electric polarizability of the weak field is much higher than that of the strong fields,so the linear and nonlinear responses of the medium are reflected by the former.The adjustment of the interaction between double EITs is also studied by the two-photon detuning of the signal and coupling fields.3)The influence of the interaction between double EITs on the third and fifth order nonlinearities in Tripod coherent systems is studied.We control the interaction between the double EITs by adjusting the two-photon detuning between the coupled and the signal lights.The results show that both the third and fifth order nonlinear responses are suppressed in the overlapped and near-overlapped states.In the non-overlapping state,both nonlinear responses are strengthened.In this case,the two-photon detuning growth has a great influence on the nonlinear effect and the increase amplitude is large.The influence of the intensity of coupling light field on the interaction between two EITs was further studied.It is found that the interaction is strengthened under the condition of increasing the coupling light field,resulting in the enhancement of the third-order and fifth-order nonlinear effects.It is also found that the nonlinear effect can be greatly improved under certain parameter conditions.It is also found that the cross-nonlinear effect is very strong in the Tripod coherent system,and its effect is usually larger than the self-nonlinear effect(which can be two orders of magnitude larger).At the same time,it is found that the interaction has little influence on the cross-nonlinear effect,far less than the self-nonlinear effect.