2003/09/15 by R. Y. Chiao, T. H. Hansson, Tony Hansson +3 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Mechanical and Optical Resonators #Quantum Electrodynamics and Casimir Effect #cond-mat #physics.atom-ph #quant-ph
paper · pdf · doi:10.1103/physreva.69.063816
25 pages (revtex4), including 2 figures
arxiv created 2003/09/15 · openalex publication_date 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-P'erot resonator. With the atoms modeled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the nonlinear Kerr susceptibility is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.