Study Of The Single Photonic Scattering In PT-symmetry Cavity Array System

Since Bender and his collaborators discovered in 1998 that not all Hamiltonian of quantum systems is Hermitian,it has attracted the interest of many scholars.As we have known,all the eigenvalues of a hermitian operator are real numbers.And PT symmetry theory proves that the eigenvalues of Hamiltonian of non-Hermitian system can be real numbers.If the parameters of the system are adjusted properly,the PT phase transition will occur.In this case,the eigenvalues of the system becomes complex and PT symmetry breaks.The complete PT symmetry system does not exist in nature,but it can be simulated by using physical methods.There will be some related interesting phenomena,such as the scattering behaviour of the photonic.In this paper,we studied the single photonic scattering in an infinite number of trimer structures in a coupled cavities array system with PT symmetry.In the system,a passive and an active cavity couple to another cavity without loss and gain simultaneously,which is in the middle of the cavity array.Such three cavities can be regarded as the scattering target coupling to the unlimited number of cavities from two directions respectively.We mainly discussed the scattering of a single photonic for the non-atomic system and the atomic system.We adopted the discrete coordinate method to solve the Schrodinger equation,and obtained the eigenvalues and the wave functions of the system.The analytical expressions of reflectivity and transmittance are obtained as well.The characterstics of the reflectivity and transmittance are discussed as the parameters are modulated,as well as the dynamics bringing about all changes.The results show that single photonic is closely related to the dynamic characteristics of PT-symmetry when it is transported in a PT-symmetry system.That is to say,the transmittance curve is symmetrical;the reflectance curve is mirror-symmetrical.The amplification of the reflectance was obtained.As one two-level atom is prepared in the middle cavity,wherein it interacts with the scattering target,the shift of the reflectivity can be observed.Meanwhile the enhancement of reflectivity within some wave vector regions may not occur due to the atom’s compensation for the cavity loss and gain.Whether there is the atom interaction or not,the scattering target can be used as a photon switch to control the transmission of the photonic in the cavity array.