Few-photon Transport In A Waveguide Coupled With Cavity Optomechanics

Within few-photon scattering experiments and theoretical studies,the waveguide geometry is often modeled as an infinite or semi-infinite collection of harmonic oscillators coupled to one or more discrete-energy-level quantum systems.Commonly in these studies the transport properties for the waveguide geometries are almost always assumed to depend only on the specific types of discrete-energy-level quantum systems and not on the waveguide properties.Under appropriate conditions,a local defect in an optical waveguide induces a highly asymmetric transmission line shape,characteristic of Fano interference.Therefore,waveguides with local defects on mirrored lines of symmetry are modeled as partial transmission elements.In this paper,a waveguide with partial transmission elements coupled with cavity optomechanics is constructed to study the characteristics of photon transmission in this waveguide.In this paper,Firstly,the basic physical models of waveguide with partial transmission elements and cavity optomechanics are introduced,and the Hamiltonian of the two systems are given respectively.Secondly,In order to facilitate the comparison with the photon transport properties in a waveguide coupled with cavity optomechanics,we set up the system with the cavity in the waveguide,and obtained the time evolution equation of the single photon wave packet and the analytical expression of the single photon dynamics shows that the partial transmission element affects the lifetime of the cavity field and changes the spectral position of resonance of the effective system.At the end of the thesis,we study the waveguide coupled with cavity optomechanics.The results show that in the waveguide with cavity optomechanics,the probability of finding single photon in cavity optomechanics decreases with the increase of the coupling coefficient,and the time of the center of the wave packet approaching the cavity optomechanical system is faster.At the same time,with the increase of the coupling coefficient of the system,the transmission spectrum and the reflection spectrum will shift to the left,and the frequency of the wave that resonates with the phonon is easier to be transmitted.