arXiv subjects
Publications and source records attributed to B. Girard.
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.
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.
Time Shaping of ultrashort visible pulses has been performed using a specially designed Acousto-Optic Programmable Dispersive Filter of 50% efficiency at the output of a two-stage noncollinear optical parametric amplifier. The set-up is compact and reliable. It provides a tunable shaped source in the visible with unique features: 4 ps shaping window with preserved tunability over 500-650 nm, and pulses as short as 30 fs. Several $μ$J output energy is easily obtained.