Imaging the collective excitations of an ultracold gas using statistical correlations

Advanced data analysis techniques have proved to be crucial for extracting information from noisy images. Here we show that principal component analysis can be successfully applied to ultracold gases to unveil their collective excitations. By analyzing the correlations in a series of images we are able to identify the collective modes which are excited, determine their population, image their eigenfunction, and measure their frequency. Our method allows to discriminate the relevant modes from other noise components and is robust with respect to the data sampling procedure. It can be extended to other dynamical systems including cavity polariton quantum gases or trapped ions.Comment: See also the supplementary material and the video abstrac

Modeling Pressure-Ionization of Hydrogen in the Context of Astrophysics

The recent development of techniques for laser-driven shock compression of hydrogen has opened the door to the experimental determination of its behavior under conditions characteristic of stellar and planetary interiors. The new data probe the equation of state (EOS) of dense hydrogen in the complex regime of pressure ionization. The structure and evolution of dense astrophysical bodies depend on whether the pressure ionization of hydrogen occurs continuously or through a ``plasma phase transition'' (PPT) between a molecular state and a plasma state. For the first time, the new experiments constrain predictions for the PPT. We show here that the EOS model developed by Saumon and Chabrier can successfully account for the data, and we propose an experiment that should provide a definitive test of the predicted PPT of hydrogen. The usefulness of the chemical picture for computing astrophysical EOS and in modeling pressure ionization is discussed.Comment: 16 pages + 4 figures, to appear in High Pressure Researc

The equation of state of solid nickel aluminide

The pressure-volume-temperature equation of state of the intermetallic compound NiAl was calculated theoretically, and compared with experimental measurements. Electron ground states were calculated for NiAl in the CsCl structure, using density functional theory, and were used to predict the cold compression curve and the density of phonon states. The Rose form of compression curve was found to reproduce the ab initio calculations well in compression but exhibited significant deviations in expansion. A thermodynamically-complete equation of state was constructed for NiAl. Shock waves were induced in crystals of NiAl by the impact of laser-launched Cu flyers and by launching NiAl flyers into transparent windows of known properties. The TRIDENT laser was used to accelerate the flyers to speeds between 100 and 600m/s. Point and line-imaging laser Doppler velocimetry was used to measure the acceleration of the flyer and the surface velocity history of the target. The velocity histories were used to deduce the stress state, and hence states on the principal Hugoniot and the flow stress. Flyers and targets were recovered from most experiments. The effect of elasticity and plastic flow in the sample and window was assessed. The ambient isotherm reproduced static compression data very well, and the predicted Hugoniot was consistent with shock compression data

Pump-probe detuning dependence of four-wave mixing pulse in an SOA

Four-wave mixing (FWM) between 2-ps pulses in a multiquantum-well semiconductor optical amplifier (SOA) is presented. The conjugate pulses are fully characterized using the frequency-resolved optical gating technique. The detuning between the pump and probe is varied, leading to a compression of the FWM signal from 3.71 to 2.77 ps as the detuning is increased from 5 to 25 nm. The output conjugate pulse is always broader than the injected probe signal due to gain saturation effects. A reshaping of the conjugate pulse is also measured. However, large nonlinearities are introduced to the frequency chirp across the pulse for large detunings which may degrade the performance of four-wave-mixing-based all-optical processing applications in SOAs

Quantum image classification using principal component analysis

We present a novel quantum algorithm for classification of images. The algorithm is constructed using principal component analysis and von Neuman quantum measurements. In order to apply the algorithm we present a new quantum representation of grayscale images.Comment: 9 page

Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur