Fine splits of photon emission spectrum of hydrogen atom caused by transitions between different dressed states in intense high frequency laser field

The photon emission spectrum of the hydrogen atoms in an intensehigh-frequency laser pulse is simulated by using one-dimensionalsoft Coulomb potential. Regular fine structures appear on the twosides of both the odd and even multiples of photon energy of thelaser field besides the ordinary odd harmonic peaks. It is provedthat the splits of the fine structures are responsible forhyper-Raman lines and the energy spacing between the odd harmoniclines is equal to the difference in energy between the eigenstateswith the same parity of the time averaged Krameters-Henneberger (KH)potential. By analysing the features of the fine structures, we alsoverify that the so-called even order harmonics under thestabilization condition are indeed hyper-Raman lines caused by thetransitions between the dressed atomic states with different valuesof parity.