We present a novel approach called the intermediate rotating wave approximation (IRWA), which employs a time-averaging method to encapsulate the dynamics of light-matter interaction from strong to ultrastrong coupling regime. In contrast to the ordin
ary rotating wave approximation, this method addresses the co-rotating and counter-rotating terms separately to trace their physical consequences individually, and thus establishes the continuity between the Jaynes-Cummings model and the quantum Rabi model. We investigate IRWA in near resonance and large detuning cases. Our IRWA not only agrees well with both models in their respective coupling strengths, but also offers a good explanation for their differences.
State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized textit{propagating} pulse in free space and st
udy the probability $P_e(t)$ of finding the atom in the excited state at any time $t$. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $Lambdain[0,8pi/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then $P_e(t)$ can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single photon Fock state and coherent states and for various temporal shapes of the pulses.
