Dressed-atom model interaction

An example of evolution to a related science is atom photonics, in which the thermal motions of neutral atoms in a vacuum are controlled using optical nearfields [71]. Theoretical studies have examined single-atom manipulation based on the dressed photon model [72], and experimental studies have involved the first successful guidance of an atom through a hollow optical fiber [73]. Recent studies have examined atom-detecting devices [74], atom deflectors [75], and an atomic funnel [76]. Atom photonics will open up a new field of science that examines the interactions between dressed photons and single atoms. 

In Section 9.3 we have used this truncated dressed state picture to discuss photoabsorption and subsequent relaxation in a model described by a zero-order basis that includes the following states a molecular ground state with one photon of frequency doorway state with no-photons, l, 0), and a continuous manifold of states /) that drives the relaxation. This model is useful for atomic spectroscopy, however, in molecular spectroscopy applications it has to be generalized in an essential way—by accounting also for molecular nuclear motions. In the following section we make this generalization before turning to consider effects due to interaction with the thermal environment. 

An interesting possibility offered by the realization of the self-assembled crystals discussed above is to utilize them as floating mesoscopic lattice potentials to trap other particles, which can be atoms or polar molecules of a different species. We show below that within an experimentally accessible regime of parameters extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of the extra-particles dressed by the lattice phonons. 

Consider a simple example such as Friedrichs model, which corresponds to an excited atom interacting with a continuous photon field. Two cases are possible. The first one is when the frequency associated to the atom is outside the spectral range of the continuum. This case corresponds to integrable systems. We can then easily define a dressed excited state in terms of the density matrix. 

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