Factorization of numbers with Gauss sums: I. Mathematical background

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.Comment: 21 pages, 8 figure

A charge-driven feedback loop in the resonance fluorescence of a single quantum dot

Semiconductor quantum dots can emit antibunched, single photons on demand with narrow linewidths. However, the observed linewidths are broader than lifetime measurements predict, due to spin and charge noise in the environment. This noise randomly shifts the transition energy and destroys coherence and indistinguishability of the emitted photons. Fortunately, the fluctuations can be reduced by a stabilization using a suitable feedback loop. In this work we demonstrate a fast feedback loop that manifests itself in a strong hysteresis and bistability of the exciton resonance fluorescence signal. Field ionization of photogenerated quantum dot excitons leads to the formation of a charged interface layer that drags the emission line along over a frequency range of more than 30 GHz. This internal charge-driven feedback loop could be used to reduce the spectral diffusion and stabilize the emission frequency within milliseconds, presently only limited by the sample structure, but already faster than nuclear spin feedback

Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.Comment: 22 pages, 7 figure

Photon noise suppression by a built-in feedback loop

Visionary quantum photonic networks need transform-limited single photons on demand. Resonance fluorescence on a quantum dot provides the access to a solid-state single photon source, where the environment is unfortunately the source of spin and charge noise that leads to fluctuations of the emission frequency and destroys the needed indistinguishability. We demonstrate a built-in stabilization approach for the photon stream, which relies solely on charge carrier dynamics of a two-dimensional hole gas inside a micropillar structure. The hole gas is fed by hole tunneling from field-ionized excitons and influences the energetic position of the excitonic transition by changing the local electric field at the position of the quantum dot. The standard deviation of the photon noise is suppressed by nearly 50 percent (noise power reduction of 6 dB) and it works in the developed micropillar structure for frequencies up to 1 kHz. This built-in feedback loop represents an easy way for photon noise suppression in large arrays of single photon emitters and promises to reach higher bandwidth by device optimization.Comment: 17 pages, 4 figure

Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

Precision spectral manipulation of optical pulses using a coherent photon echo memory

Photon echo schemes are excellent candidates for high efficiency coherent optical memory. They are capable of high-bandwidth multi-pulse storage, pulse resequencing and have been shown theoretically to be compatible with quantum information applications. One particular photon echo scheme is the gradient echo memory (GEM). In this system, an atomic frequency gradient is induced in the direction of light propagation leading to a Fourier decomposition of the optical spectrum along the length of the storage medium. This Fourier encoding allows precision spectral manipulation of the stored light. In this letter, we show frequency shifting, spectral compression, spectral splitting, and fine dispersion control of optical pulses using GEM

GINA - A Polarized Neutron Reflectometer at the Budapest Neutron Centre

The setup, capabilities and operation parameters of the neutron reflectometer GINA, the recently installed "Grazing Incidence Neutron Apparatus" at the Budapest Neutron Centre, are introduced. GINA, a dance-floor-type, constant-energy, angle-dispersive reflectometer is equipped with a 2D position-sensitive detector to study specular and off-specular scattering. Wavelength options between 3.2 and 5.7 {\AA} are available for unpolarized and polarized neutrons. Spin polarization and analysis are achieved by magnetized transmission supermirrors and radio-frequency adiabatic spin flippers. As a result of vertical focusing by the five-element (pyrolytic graphite) monochromator the reflected intensity from a 20x20 mm sample has doubled. GINA is dedicated to studies of magnetic films and heterostructures, but unpolarized options for non-magnetic films, membranes and other surfaces are also provided. Shortly after its startup, reflectivity values as low as 3x10-5 have been measured on the instrument. The facility is now open for the international user community, but its development is continuing mainly to establish new sample environment options, the spin analysis of off-specularly scattered radiation and further decrease of the background