Study On Dynamics Of PT Symmetry Cavity Arrays And Single-Photon Transmission

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 method.In this paper,the PT symmetry of four-body coupled cavities array and three-cavity coupled ring array is studied,wherein the PT phase transition of the two coupled systems is mainly discussed.For the four-body coupled cavities array,the transmission of a single photonic and its localization are discussed both in the cases of PT symmetry phase and in the cases of PT symmetry breaking.When we change the cavities in which losing and gain occur,it is found that the transmittance has considerably varied.For the three-cavity coupled ring array,we discussed the dynamics as adjusting the parameters.The reason that brings about the asymmetric distribution of the eigenmodes is analyzed.For the four-body coupled cavities array,two of the four eigenvalues show complex numbers as the system is in the PT symmetry phases.We computed the eigenstates for the two eigenmodes,it shows that the distribution of the single-photonic is symmetric in the case of PT symmetry phase.Otherwise,the distribution of the single-photonic is localized in the case of PT symmetry breaking.That is,the single-photonic will be localized in the gain cavity and the losing cavity for the two modes respectively.We got the quantum states by solving the Schr?dinger equation.The expressions of the eigenstates show that the transmission of the single photonic can be unidirectional.And such unidirectional behavior occurs not only in the PT symmetry phase but in the PT symmetry breaking phase.In the processing of adjusting parameters,the transmittance is affected considerably by the change of losing and gain cavities.Our analysis shows that there is also the localization for the single-photonic transmission in the three-cavity coupled ring array.And the asymmetry of the photonic transmittance is given.Differently,there are two critical values for the three-cavity coupled ring array to break the PT symmetry.The system will be in the PT symmetry breaking phase in the range between the two values.