arXiv subjects

M. Kohler

Publications and source records attributed to M. Kohler.

5 recordsLinked to original sources

arXiv2020

On the rate of convergence of image classifiers based on convolutional neural networks

Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of the aposteriori probability a rate of convergence is shown which is independent of the dimension of the image. This proves that in image classification it is possible to circumvent the curse of dimensionality by convolutional neural networks.

stat.ML↗

arXiv2014

All-optical production and trapping of metastable noble gas atoms down to the single atom regime

The determination of isotope ratios of noble gas atoms has many applications e.g. in physics, nuclear arms control, and earth sciences. For several applications, the concentration of specific noble gas isotopes (e.g. Kr and Ar) is so low that single atom detection is highly desirable for a precise determination of the concentration. As an important step in this direction, we demonstrate operation of a krypton Atom Trap Trace Analysis (ATTA) setup based on a magneto-optical trap (MOT) for metastable Kr atoms excited by all-optical means. Compared to other state-of-the-art techniques for preparing metastable noble gas atoms, all-optical production is capable of overcoming limitations regarding minimal probe volume and avoiding cross-contamination of the samples. In addition, it allows for a compact and reliable setup. We identify optimal parameters of our experimental setup by employing the most abundant isotope Kr-84, and demonstrate single atom detection within a 3D MOT.

physics.atom-ph↗

arXiv2005

Creating and probing long-range order in atomic clouds

Ultracold atoms interacting with the optical modes of a high-Q optical ring cavity can synchronize their motion. The collective behavior makes the system interesting for quantum computing applications. This paper is devoted to the study of the collective coupling. We report on the first observation of a collective dynamics and on the realization of a laser, the gain mechanism of which is based on collective atomic recoil. We show that, if the atoms are subject to a friction force, starting from an unordered distribution they spontaneously form a moving density grating. Furthermore, we demonstrate that a 1D atomic density grating can be probed via Bragg scattering. By heterodyning the Bragg-reflected light with a reference beam, we obtain detailed information on phase shifts induced by the Bragg scattering process.

quant-ph↗

arXiv2005

Multiple Reflections and Diffuse Scattering in Bragg Scattering at Optical Lattices

We study Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers located at the antinodes of the standing wave. Light incident on this array at a well-defined angle is partially Bragg-reflected. We measure reflectivities as high as 30%. In contrast to a previous experiment devoted to the thin grating limit [S. Slama, et al., Phys. Rev. Lett. 94, 193901 (2005)] we now investigate the thick grating limit characterized by multiple reflections of the light beam between the atomic layers. In principle multiple reflections give rise to a photonic stop band, which manifests itself in the Bragg diffraction spectra as asymmetries and minima due to destructive interference between different reflection paths. We show that close to resonance however disorder favors diffuse scattering, hinders coherent multiple scattering and impedes the characteristic suppression of spontaneous emission inside a photonic band gap.

quant-ph↗

arXiv2005

Dimensional Crossover in Bragg Scattering from an Optical Lattice

We study Bragg scattering at 1D optical lattices. Cold atoms are confined by the optical dipole force at the antinodes of a standing wave generated inside a laser-driven high-finesse cavity. The atoms arrange themselves into a chain of pancake-shaped layers located at the antinodes of the standing wave. Laser light incident on this chain is partially Bragg-reflected. We observe an angular dependence of this Bragg reflection which is different to what is known from crystalline solids. In solids the scattering layers can be taken to be infinitely spread (3D limit). This is not generally true for an optical lattice consistent of a 1D linear chain of point-like scattering sites. By an explicit structure factor calculation we derive a generalized Bragg condition, which is valid in the intermediate regime. This enables us to determine the aspect ratio of the atomic lattice from the angular dependance of the Bragg scattered light.

quant-ph↗