Quantized Media with Absorptive Scatterers and Modified Atomic Emission Rates

Modifications in the spontaneous emission rate of an excited atom that are caused by extinction effects in a nearby dielectric medium are analyzed in a quantummechanical model, in which the medium consists of spherical scatterers with absorptive properties. Use of the dyadic Green function of the electromagnetic field near a a dielectric sphere leads to an expression for the change in the emission rate as a series of multipole contributions for which analytical formulas are obtained. The results for the modified emission rate as a function of the distance between the excited atom and the dielectric medium show the influence of both absorption and scattering processes.Comment: 6 pages, 4 figure

Langevin description of speckle dynamics in nonlinear disordered media

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies $\Omega$ below some $\Omega_{\mathrm{max}}$, provided that the nonlinearity exceeds some $\Omega$-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of $1/\Omega_\mathrm {max}$.Comment: 6 pages, 3 figure

Robustness of Decoherence-Free Subspaces for Quantum Computation

It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are stable to first order in time to a perturbation. Here this result is extended to the non-Markovian regime and generalized. In particular, it is shown that within both the semigroup and the non-Markovian operator sum representation, DF subspaces are stable to all orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal for quantum memory applications. For quantum computation, however, the stability result does not extend beyond the first order. Thus, to perform robust quantum computation in DF subspaces, they must be supplemented with quantum error correcting codes.Comment: 16 pages, no figures. Several changes, including a clarification of the derivation of the Lindblad equation from the operator sum representation. To appear in Phys. Rev

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in Phys. Rev.

Theoretical description of light scattering by a collection of nonlinear Kerr particles

We theoretically study multiple scattering of monochromatic light by a collection of spheres that can freely move in a background medium. The spheres contain an optical nonlinearity of the Kerr type. Employing diagrammatic methods we construct the iterative solution of the nonlinear scalar wave equation that describes the electromagnetic radiation field inside the sacttering medium. The ensuing diagrammatic series for the amplitude of the radiation field is averaged over all possible configurations of the scatterers. Subsequently, it is proved that the average amplitude satisfies a nonlinear equation that is the counterpart of the usual Dyson equation. For the case of point scatterers that do not absorb light we obtain solutions of our nonlinear Dyson equation. They predict that as a result of auto-Kerr and backscattering effects, the system can become unstable. Furthermore, we find that it is possible to bleach the scatterers. Finally, the influence of nonlinear absorption on the average amplitude is investigated.Nous présentons une étude théorique de la diffusion multiple d'une lumière monochromatique par un ensemble de sphères qui peuvent se déplacer librement dans un certain milieu. Les sphères possèdent une nonlinéarité optique de type Kerr. En utilisant les methodes diagrammatiques, nous construisons la solution itérative de l'équation d'onde scalaire nonlinéaire qui décrit le champ de rayonnement électromagnétique dans le milieu désordonné. On moyenne la série diagrammatique pour l'amplitude du champ rayonné sur toutes les configurations possibles des diffuseurs et on montre que l'amplitude moyenne obéit à une équation nonlinéaire qui est le pendant de l'équation de Dyson ordinaire. Dans le cas où les diffuseurs sont de petite taille et n'absorbent pas la lumière, nous trouvons des solutions de notre équation de Dyson nonlinéaire. Celles-ci montrent que, à la suite des effets auto-Kerr et des effets de la rétrodiffusion, le système peut devenir instable. Nous trouvons qu'il est également possible de “blanchir” les diffuseurs. Finalement l'influence de l'absorption nonlinéaire sur l'amplitude moyenne est analysée