Ultrastrong coupling regime of the two-photon quantum Rabi model: a Numerical Approach

Abstract In this paper, some physical observables such as the energy spectra and time dynamics as well as the photon statistics of the two-photon quantum Rabi model in the ultrastrong coupling regime are numerically explored. The main aim of this work is to show the effect of the number of cavity fock states N on the spectral properties, particularly the special feature spectral collapse at critical coupling gc=ꞷc/2. We have shown that for a large number of cavity fock states the numberof discrete energy levels decreases down to only one at the collapse point. Secondly, we have simulated the time dynamics behaviors as well as the photon statistics, at the final state, of the two-photon quantum Rabi model in the ultrastrong coupling regime. PACS numbers: 03.67.Lx, 85.25.Dq, 42.50.Dv