We report on a new implementation of the factorisation of numbers using Gauss sums which improves tremendously the efficiency to eliminate all ”ghost” factors. We show that by choosing randomly the terms in the Gauss sum, the required number of terms varies as ln N instead of 4 √ N . As an illustration, we present experimental results obtained by interfering thirty ultrashort laser pulses where we factorise 1, 340, 333, 404, 807. This new approach is totally general and can be implemented for all the experiments based on the Gauss sum. Introduction. – Factorisation of numbers has attracted a wide interest in pure arithmetics as well as for applications, particularly because it is much easier to multiply two large prime numbers than doing the reverse operation [1]. This difficulty is at the basis of encryption systems. A competition exists permanently to promote new algorithms in order to factorize large numbers. For instance, J. Franke (Bonn’s university) was able to factorize the RSA-640 (193 digits) in 5 months with 80 processors. Besides improving mathematical algorithms, several physical approaches to factorisation have been introduced [2,3]. In particular, quantum systems offer strong promises due to the large-scale parallelism offered by the use of entangled states. Indeed, the Shor’s factorisation algorithm is one of the two pillars of quantum computing [2]. Despite the difficulties to manipulate the required large number of qubits [4] and in particular to preserve them from decoherence [5–7], the factorisation of 15 has been achieved [3]. However, large scale demonstrations based on quantum algorithms are still not in view. Recently a very different approach based on Gauss Sums has been proposed theoretically [8, 9] and experimentally implemented by several groups in NMR [10,11], with cold atoms [12] and ultrashort pulses [13]. This method which presents strong interest as underlined by reference [14] is based on multiple-wave interferences with relative phases depending on the number N to be factorised and another integer l. These interferences reproduce the Gauss sum [15] given by:

We study optical field emission from silver nanotips, showing the combined influence of the illumination wavelength and the exact shape of the nanotip on the strong-field response. This is particularly relevant in the case of FIB milled nano tips, where the nanotip fabrication capabilities could become a new ingredient for the study of strong-field physics. The influence of the thermal load on the nanotip and its effect on the emission is studied as well by switching the repetition rate of the laser source from 1 kHz to 62 MHz, showing a clear transition towards the quenching of the strong-field emission.

We present the first demonstration of ultrafast laser-induced field emission from a carbon nanotube based nanotip, and measurement of the energy distribution of the electrons.

We investigate the possibility of using a scattering medium as a highly multimode platform for implementing quantum walks. We demonstrate the manipulation of a single photon propagating through a strongly scattering medium using wavefront-shaping technique. Measurement of the scattering matrix allows the wavefront of the photon to be shaped to compensate the distortions induced by multiple scattering events. The photon can thus be directed coherently to a specific output mode. Using this approach, we show how entanglement of a single photon across different modes can be manipulated despite the enormous wavefront disturbance caused by the scattering medium.

We present the first demonstration of ultrafast laser-induced field emission and measurement of the energy distribution of electrons from a nanotip based on a carbon nanotube (CNT). Our experimental setup extends the studies performed on conventional tungsten or gold tips by using this new innovative tip. The carbon tip consists of concentric carbon layers in the shape of a cone, and has been previously studied as a very good candidate for cold field emission. The first laser-induced field emission from a CNT-based nanotip has been observed and we measured the energy spectrum as well as the polarization dependance of the emission. We also characterize the damage threshold of the tip, when illuminated by a high repetition rate femtosecond laser. These first results are encouraging further studies of electron emission from CNT-based carbon nanotips.

We present an experiment studying the interaction of a strongly focused 25 fs laser pulse with a tungsten nanotip, investigating the different regimes of laser-induced electron emission. We study the dependence of the electron yield with respect to the static electric field applied to the tip. Photoelectron spectra are recorded using a retarding field spectrometer and peaks separated by the photon energy are observed with a 45% contrast. They are a clear signature of above threshold photoemission (ATP), and are confirmed by extensive spectrally resolved studies of the laser power dependence. Understanding these mechanisms opens the route to control experiment in the strong-field regime on nanoscale objects.

We demonstrate the control of entanglement of a single photon between several spatial modes propagating through a strongly scattering medium. Measurement of the scattering matrix allows the wavefront of the photon to be shaped to compensate the distortions induced by multiple scattering events. The photon can thus be directed coherently to a single or multi-mode output. Using this approach we show how entanglement across different modes can be manipulated despite the enormous wavefront disturbance caused by the scattering medium.

In this work, we use wavefront shaping methods to control non-classical states of light propagating through a multiply scattering medium. We experimentally show guiding of a single-photon into a selected single-mode fiber after propagation through the medium, and demonstrate generation of a one-photon entangled state.

We present a detailed theoretical analysis of biexciton state generation in InAs-GaAs quantum dots by strong, chirped laser pulses. Specifically, we derive an accurate analytical expression, which not only provides a clear physical picture of the process, but also allows identifications of laser parameter regimes where efficient biexciton generation should be possible, even at temperatures up to 80 K. The results are confirmed by numerical simulations, in very good agreement with the model proposed. A clear choice of parameters is proposed, which might pave the way towards the optimal design of high-fidelity sources of entangled photon pairs based on individual quantum dots

Propagation of ultrashort broadband pulses through a multiply scattering media result in complex spatio-temporal speckle pattern. Using spectral pulse shaping, we demonstrate the spatially localized temporal recompression of the output speckle to the Fourier-limit duration.

Propagation of an ultrashort laser pulse through a scattering medium forms a speckle pattern in the spatio-spectral domain. This pattern arises from the contribution of the randomly phased electric fields associated with the different optical paths in the medium. Studying the speckle field provides information both about the diffusion properties of the medium and spatio-temporal control of the transmitted or scattered light. In this paper a spatio-temporal characterization of the near-IR 120 fs pulse transmitted through a thick strongly scattering medium is undertaken using spatially and spectrally resolved Fourier-transform interferometry (SSI). The advantages of SSI over conventional pulse measurement techniques are discussed. The diffusion properties of the scattering samples are measured. We find a good agreement between our measured diffusion properties and those obtained using another method. The implications of this measurement technique are discussed. (C) 2012 Optical Society of America

Motivated by recent experimental results, we present a detailed account of adiabatic population transfer in InGaAs/GaAs quantum dots by strong chirped laser pulses. Specifically, numerical simulations in very good agreement with experimental results allow for a clear physical picture of this process. An analytical expression is developed, which is used to analyze the strong-field adiabatic population transfer in the presence of the phonon environment. Optimal pulse parameters to achieve robust population transfer at temperatures as high as 80 K are identified and are confirmed by numerical simulations.

A comprehensive experimental analysis of spatio-temporal coupling effects inherent to the acousto-optic programmable dispersive filter (AOPDF) is presented. Phase and amplitude measurements of the AOPDF transfer function are performed using spatially and spectrally resolved interferometry. Spatio-temporal and spatio-spectral coupling effects are presented for a range of shaped pulses that are commonly used in quantum control experiments. These effects are shown to be attributable to a single mechanism: a group-delay--dependent displacement of the shaped pulse. The physical mechanism is explained and excellent quantitative agreement between the measured and calculated coupling speed is obtained. The implications for quantum control experiments are discussed.

The energy states in semiconductor quantum dots are discrete as in atoms, and quantum states can be coherently controlled with resonant laser pulses. Long coherence times allow the observation of Rabi flopping of a single dipole transition in a solid state device, for which occupancy of the upper state depends sensitively on the dipole moment and the excitation laser power. We report on the robust population inversion in a single quantum dot using an optical technique that exploits rapid adiabatic passage from the ground to an excited state through excitation with laser pulses whose frequency is swept through the resonance. This observation in photoluminescence experiments is made possible by introducing a novel optical detection scheme for the resonant electron hole pair (exciton) generation.

Pulses of light propagating through multiply scattering media undergo complex spatial and temporal distortions to form the familiar speckle pattern. There is much current interest in both the fundamental properties of speckles and the challenge of spatially and temporally refocusing behind scattering media. Here we report on the spatially and temporally resolved measurement of a speckle field produced by the propagation of an ultrafast optical pulse through a thick strongly scattering medium. By shaping the temporal profile of the pulse using a spectral phase filter, we demonstrate the spatially localized temporal recompression of the output speckle to the Fourier-limit duration, offering an optical analogue to time-reversal experiments in the acoustic regime. This approach shows that a multiply scattering medium can be put to profit for light manipulation at the femtosecond scale, and has a diverse range of potential applications that includes quantum control, biological imaging and photonics.

This paper investigates the origin of a quantum interference observed when NO(2) is dissociatively ionized by short pulses of ultraviolet light. We describe time-resolved measurements of NO(+), O(+), and NO(2)(+) ions produced following the interaction of NO(2) with a approximately 70 fs duration pulse centered close to 400 nm and a subsequent time-delayed probe pulse close to 269, 205, or 400 nm. A quantum beat oscillation with a period of 524 fs and a characteristic damping time of 8 ps is observed on all transient ion signals. We investigate the effect of tuning the central wavelength of the excitation pulse over a 12 nm range, and we discuss the potential importance of three possible multiphoton pathways involving one, two, and three pump photons. We conclude that the ionization pathway responsible for the beat signal is most likely due to a process involving the absorption of two pump photons and two probe photons. This presents an interesting problem with respect to the interpretation of the mechanism responsible for the quantum interference signature since the electronic states of NO(2) reached at the two-photon level are all thought to be extremely short-lived and to dissociate on a time scale that is far shorter than the characteristic damping time of the oscillatory signals. We suggest that a possible explanation for the observed dynamics is associated with a minor dissociation channel of the (2)(2)B(2) state of NO(2) through its interaction with the longer lived (2)(2)A(1) state.

Time shaping of ultra-short UV pulses has been performed using a specially designed acousto-optic programmable dispersive filter in KDP material. A time shaping window up to 5 ps has been obtained in the 260–410 nm range. A temporal/spectral characterization of shaped pulses on this broad UV spectral range is presented. The efficiency at shorter wavelength is limited by two-photon absorption. However several µJ is obtained at the output of the device allowing chemistry coherent control experiment.