Chaos and flights in the atom-photon interaction in cavity QED

We study dynamics of the atom-photon interaction in cavity quantum electrodynamics (QED), considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinear Hamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including L\'{e}vy flights and chaotic walkings of an atom in a cavity. It is shown that the translational motion, related to the atom recoils, is governed by an equation of a parametric nonlinear pendulum with a frequency modulated by the Rabi oscillations. This type of dynamics is chaotic with some width of the stochastic layer that is estimated analytically. The width is fairly small for realistic values of the control parameters, the normalized detuning $\delta$ and atomic recoil frequency $\alpha$. It is demonstrated how the atom-photon dynamics with a given value of $\alpha$ depends on the values of $\delta$ and initial conditions. Two types of L\'{e}vy flights, one corresponding to the ballistic motion of the atom and another one corresponding to small oscillations in a potential well, are found. These flights influence statistical properties of the atom-photon interaction such as distribution of Poincar\'{e} recurrences and moments of the atom position $x$. The simulation shows different regimes of motion, from slightly abnormal diffusion with $\sim\tau^{1.13}$ at $\delta =1.2$ to a superdiffusion with $\sim \tau^{2.2}$ at $\delta=1.92$ that corresponds to a superballistic motion of the atom with an acceleration. The obtained results can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning $\delta$.Comment: 16 pages, 7 figures. To be published in Phys. Rev.

Retinal Structure and Function in Achromatopsia : Implications for Gene Therapy

Purpose: To characterize retinal structure and function in achromatopsia (ACHM) in preparation for clinical trials of gene therapy. Design: Cross-sectional study. Participants: Forty subjects with ACHM. Methods: All subjects underwent spectral domain optical coherence tomography (SD-OCT), microperimetry, and molecular genetic testing. Foveal structure on SD-OCT was graded into 5 distinct categories: (1) continuous inner segment ellipsoid (ISe), (2) ISe disruption, (3) ISe absence, (4) presence of a hyporeflective zone (HRZ), and (5) outer retinal atrophy including retinal pigment epithelial loss. Foveal and outer nuclear layer (ONL) thickness was measured and presence of hypoplasia determined. Main Outcome Measures: Photoreceptor appearance on SD-OCT imaging, foveal and ONL thickness, presence of foveal hypoplasia, retinal sensitivity and fixation stability, and association of these parameters with age and genotype. Results: Forty subjects with a mean age of 24.9 years (range, 6e52 years) were included. Disease-causing variants were found in CNGA3 (n [ 18), CNGB3 (n ¼ 15), GNAT2 (n ¼ 4), and PDE6C (n ¼ 1). No variants were found in 2 individuals. In all, 22.5% of subjects had a continuous ISe layer at the fovea, 27.5% had ISe disruption, 20% had an absent ISe layer, 22.5% had an HRZ, and 7.5% had outer retinal atrophy. No significant differences in age (P ¼ 0.77), mean retinal sensitivity (P ¼ 0.21), or fixation stability (P ¼ 0.34) across the 5 SD-OCT categories were evident. No correlation was found between age and foveal thickness (P ¼ 0.84) or between age and foveal ONL thickness (P ¼ 0.12). Conclusions: The lack of a clear association of disruption of retinal structure or function in ACHM with age suggests that the window of opportunity for intervention by gene therapy is wider in some individuals than previously indicated. Therefore, the potential benefit for a given subject is likely to be better predicted by specific measurement of photoreceptor structure rather than simply by age. The ability to directly assess cone photoreceptor preservation with SD-OCT and/or adaptive optics imaging is likely to prove invaluable in selecting subjects for future trials and measuring the trials’ impact