The Investigation On The Dressed State Perturbation Theory In The Two-level Cavity QED System

By combining the dressed state theory and perturbation theory, we propose the dressed state perturbation theory beyond the rotating wave approximation to analytically treat the strong coupling between two-level system (including atom, non-polar molecule and polar molecule) and quantized cavity field. Analytical expressions can be explicitly derived for both the ground-and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately. We discuss their effects on the stationary wave function, energy spectrums and time development of population separately, and compare them with numerical simulation results.1. Based on the analytical expressions of wave functions, we can see that the transition relations among the dressed states caused by the CRT and PDM. As for two-level atom and non-polar molecule, Rabi Hamiltonian has parity symmetry, CRT cause the transition among the dressed states in the same parity chain. However, as for polar molecule, the parity symmetry is broken with PDM, so the odd and even parity chain initially independent in the two-level atom Rabi model are coupled together by the PDM.2. Based on the analytical expressions of energy spectrums, on one hand, we can see that the dressed state origination of the energy levels. On the other hand, the separate contribution of CRT and PDM on the energy level shift can be shown. The first-order correction of energy is zero, and in the second-order correction of energy, the energy level shifts caused by CRT and PDM are approximately proportional to the square of coupling strength, and the energy level shift caused by PDM is exactly proportional to the square of normalized permanent dipole difference. We discuss the validity condition of the analytical method, by comparing with the numerical energy spectrums, our analytical results are in good agreement with the numerical results within the specific parameter regimes 0<λ/ωc<0.1,0≤α<1 and -1<δ/ωc<1. Also the Bloch-Siegert (BS) Shift caused by CRT and PDM are analyzed separately. For giant dipole molecule, the BS shift caused by PDM is greater than that caused by CRT.3. We investigate the population dynamical evolution of the system, our analytical results are in good agreement with the numerical results, which further justify the validity of our analytical method. Based on the analytical expression of population time development, we find that the frequency components are no longer the distinct Rabi frequency of JC model due to the CRT and PDM, but actually contain more frequency components. And from our analytical expressions, we can see the origination of transition relation among dressed states for every frequency component. The dominant frequency is caused by rotating wave term interaction, and the resident frequency components are caused by CRT and PDM. Besides, because of BS shift, the dominant frequency is smaller than the vacuum Rabi frequency of JC model. For fixed polar molecule with fixed a, the dominant frequency increases with λ. And for fixed λ, the dominant frequency decreases with a.4. We compare our analytical method with the results proposed by other researchers and discuss our merit and weakness. The merit is that our method can clearly give the transition relation among dressed states caused by CRT and PDM separately, their contributions on the energy shift, and the dressed state origination of every energy level. And the weakness is the application of perturbation theory makes the validity regime of coupling strength is smaller, but which is valid in the present accessible experiment regime.