Supersymmetry as an Algebraic Approach to the Jaynes-Cumming Model with Stark Shift and Kerr-Like Medium

Abstract

According to of supersymmetry which states that in the standard model, each particle has a partner with a spin that differs by half of a unit. So fermions partners are bosons and vice versa. Supersymmetry has been introduced to many one-dimensional quantum systems, radial Shrödinger equation and for the known model Jaynes-Cummings model. Since bosonic and fermionic are so related to the photon of two level-system. of course using supersymmetry theory will be beneficial. Here, supersymmetry arguments are used to derive the wave function of Jaynes-Cummings model describes a two-level system (atom) interacts with a cavity field of single mode over a multi-photon transition where a Kerr-like medium and Stark term are considered. The supersymmetric operators related to the atomic system are introduced to diagonalize the Hamiltonian with a canonical transformation technique. Also, the eigenvalues spectrum and eigenvectors are exactly given. Then, alot of physics phenomena can be investigated and supersymmetry arguments can be applied on different optical systems.