Renormalization group methods in quantum optics

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Abstract
The velocity-dependent spontaneous emission of a two-level atom in a Fabry-Pérot cavity in the strong-coupling regime and the deflection of a beam of two-level atoms in a classical standing wave inside a cavity are discussed using a renormalization group approach. In this way we are able to renormalize the leading-order solutions for both problems through calculations of the corrections at first order. In fact, the first-order terms are not bounded for large times and no sense can be attached to this higher-order correction unless small times are considered. These are like the divergences of quantum field theory. To make them harmless, the condition for the Raman-Nath regime is recovered. The renormalization group methods permit one to eliminate those divergences generating a renormalized leading-order wave function without any condition of applicability. For the spontaneous emission of a two-level atom in a Fabry-Pérot cavity in the strong regime, using a Hamiltonian without losses, it is shown that the unperturbed levels are shifted by a term proportional to the zeroth-order Bessel function with an argument yielded by the ratio of the Rabi frequency and the Doppler-shifted frequency of the mode of the cavity. When the detuning is zero, the correction to the leading-order wave function is not present and known results are recovered. For the beam of two-level atoms in a classical standing wave, when the detuning is much larger than the Rabi frequency, it is shown that the renormalization group equation, which gives the correction for the renormalized leading-order wave function, is a time-dependent Schrödinger equation for a free particle that induces a spreading of the initial Gaussian wave packet.