Supersymmetry of the solution to the master equation between two-level atom and laser channel

Abstract

We propose a new Ket-Bra entangled state (KBES) method to solve the master equation of finite-level system. The KBES method can convert the master equation into Schrdinger-like equation which is easier to solve than the master equation, and Schrdinger equation in a certain form can also be used to solve the Schrdinger-like equation. Thus the KBES method has a wider application range. In the paper, we mainly study the master equation of the two-level atom. The corresponding master equation is solved by the KBES method, and for the first time we obtain the opera-sum solution of the atom. Furthermore, we compare this result with the well known solution that describes the laser channel. There is much analogousness between both opera-sum solutions, which show that there is some supersymmetry between Bose creation-annihilation operator and upper-down transition operators of atom. Finally, we further analyze the supersymmetry between the bose and atom system, and find that the spin-up and spin-down operator can be represented by the creation and annihilation operator repectively, which can be achieved in infinite ways. It is easy to understand that the bose operator is infinite-level while the spin operator is two-level, thus the creation-annihilation operator is super-complete for the spin operator. Thus the representation is not unique, and all of this directly shows and proves the supersymmetry.