Resonance : Its description, criteria and significance

Princeton University

Nick J. Schilder, Christophe Sauvan, Yvan R. P. Sortais +2 more

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\ensuremath{\rho}$. The ensemble is dense enough for the usual condition for homogenization, viz. $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, neither of the criteria for homogenization is fulfilled, meaning that the condition $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or nonradiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.

Brian J. Coffey

The effects of position-dependent dipole-dipole frequency shifts are included in a semiclassical description of resonance fluorescence from many two-level atoms in a volume small compared with a resonant wavelength. In general, these effects are drastic: They lead to loss of coherence long before cooperative effects become important. In samples for which the field of a uniform polarization is itself uniform we obtain criteria for the stability of the Bloch vector against dipolar-induced dephasing.

Frederic R. Morgenthaler

Sreenath K. Manikandan, Frank A. Wilczek

We propose simple quantitative criteria, based on counting statistics in resonant harmonic detectors, that probe the quantum mechanical character of radiation fields. They provide, in particular, practical means to test the null hypothesis that a given field is “maximally classical,” i.e., accurately described by a coherent state. We suggest circumstances in which that hypothesis plausibly fails, notably including gravitational radiation involving nonlinear or stochastic sourcing.

R. Lefèbvre