Radiative atom-atom interactions in optically dense media: Quantum corrections to the Lorentz-Lorenz formula

Abstract

Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account non-cooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and level shifts due to multiple scattering or reabsorption of spontaneously emitted photons. In the Markov limit a nonlinear and nonlocal single-atom density matrix equation is derived. To illustrate the effects of the quantum corrections we discuss amplified spontaneous emission and radiation trapping in a dense ensemble of initially inverted two-level atoms and the effects of radiative interactions on intrinsic optical bistability in coherently driven systems.

16 pages, 12 figures, subm. to PRA

References in corpus (2)

• Quantum field theory of cooperative atom response: Low light intensity
• Lorentz-Lorenz shift in a Bose-Einstein condensate

Cited by in corpus (30)

• The cooperative Lamb shift in an atomic nanolayer
• Photon storage in Lambda-type optically dense atomic media. II. Free-space model
• Collective atomic scattering and motional effects in a dense coherent medium
• Electromagnetically induced left-handedness in a dense gas of three level atoms
• Controlling dipole-dipole frequency shifts in a lattice-based optical atomic clock
• Many-body localization in waveguide QED
• Beyond lowest order mean field theory for light interacting with atom arrays
• Superradiance and subradiance in inverted atomic arrays
• Spontaneous emission and level shifts in absorbing disordered dielectrics and dense atomic gases: A Green's function approach
• Maximum refractive index of an atomic medium
• Direct single-shot observation of millimeter wave superradiance in Rydberg-Rydberg transitions
• Far-field resonance fluorescence from a dipole-interacting laser-driven cold atomic gas
• Superradiance in spin-$J$ particles: Effects of multiple levels
• Positive-P phase space method simulation in superradiant emission from a cascade atomic ensemble
• Population mixing due to dipole-dipole interactions in a 1D array of multilevel atoms
• Competition between finite-size effects and dipole-dipole interactions in few-atom systems
• Local field effect as a function of pulse duration
• Inelastic photon scattering via the intracavity Rydberg blockade
• Emission spectra and intrinsic optical bistability in a two-level medium
• Intensity effects of light coupling to one- or two-atom arrays of infinite extent
• Phase modulation induced by cooperative effects in electromagnetically induced transparency
• Slow light propagation in trapped atomic quantum gases
• Renormalization group analysis of near-field induced dephasing of optical spin waves in an atomic medium
• Master equation for multilevel interference in a superradiant medium
• Atomic-motion-induced spectroscopic effects nonlinear in atomic density in a gas
• Limits and possibilities of refractive index in atomic systems
• Spontaneous emission and atomic line shift in causal perturbation theory
• Theory of light-matter interactions in cascade and diamond type atomic ensembles
• Diagrammatic treatment of few-photon scattering from a Rydberg blockaded atomic ensemble in a cavity
• Propagation of radiation pulses through gas-plasma mixtures