“…2.3 , the critical components are the QD-cavity systems, which can perform the reflection operators, [ ] and [ ], to induce differences in the reflectances and phase shifts of the reflected photon, according to the hot or cold cavity. Therefore, the analysis of the interaction between a photon and an electron spin state in the QD is required to quantify the efficiency and reliability of the QD-cavity system under vacuum noise , for the operation of the QD-dipole, and leaky modes (sideband leakage and absorption) 11 , 20 , 22 , 54 – 56 , 84 , 85 . To figure out the affections of the vacuum noise and leaky modes in the QD-cavity system, we can calculate the quantum Langevin equations of a cavity field operator , a dipole operator of , and the input–output relations with vacuum noise and leaky modes from the Jaynes-Cummings Hamiltonian 11 , 20 , 22 , 54 – 56 , 84 , 85 , as follows: where ( ) is the input (output) field operator from the leaky modes, due to sideband leakage and absorption in the cavity mode, and is the vacuum noise operator for of .…”