Loss of purity by wave packet scattering at low energies

We study the quantum entanglement produced by a head-on collision between two gaussian wave packets in three-dimensional space. By deriving the two-particle wave function modified by s-wave scattering amplitudes, we obtain an approximate analytic expression of the purity of an individual particle. The loss of purity provides an indicator of the degree of entanglement. In the case the wave packets are narrow in momentum space, we show that the loss of purity is solely controlled by the ratio of the scattering cross section to the transverse area of the wave packets.Comment: 7 pages, 1 figur

Physical Properties of a Pilot Sample of Spectroscopic Close Pair Galaxies at z ~ 2

We use Hubble Space Telescope Wide-Field Camera 3 (HST/WFC3) rest-frame optical imaging to select a pilot sample of star-forming galaxies in the redshift range z = 2.00-2.65 whose multi-component morphologies are consistent with expectations for major mergers. We follow up this sample of major merger candidates with Keck/NIRSPEC longslit spectroscopy obtained in excellent seeing conditions (FWHM ~ 0.5 arcsec) to obtain Halpha-based redshifts of each of the morphological components in order to distinguish spectroscopic pairs from false pairs created by projection along the line of sight. Of six pair candidates observed, companions (estimated mass ratios 5:1 and 7:1) are detected for two galaxies down to a 3sigma limiting emission-line flux of ~ 10^{-17} erg/s/cm2. This detection rate is consistent with a ~ 50% false pair fraction at such angular separations (1-2 arcsec), and with recent claims that the star-formation rate (SFR) can differ by an order of magnitude between the components in such mergers. The two spectroscopic pairs identified have total SFR, SFR surface densities, and stellar masses consistent on average with the overall z ~ 2 star forming galaxy population.Comment: 11 pages, 5 figures. Accepted for publication in Ap

Analysis of photon-atom entanglement generated by Faraday rotation in a cavity

Faraday rotation based on AC Stark shifts is a mechanism that can entangle the polarization variables of photons and atoms. We analyze the structure of such entanglement by using the Schmidt decomposition method. The time-dependence of entanglement entropy and the effective Schmidt number are derived for Gaussian amplitudes. In particular we show how the entanglement is controlled by the initial fluctuations of atoms and photons.Comment: 6 pages, 3 figure

S-wave quantum entanglement in a harmonic trap

We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultra-cold temperature, ground state entanglement is generated by the dominated s-wave interaction. Based on a regularized pseudo-potential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified s-wave scattering length inside the trap.Comment: 10 pages, 5 figures, to be apear in PR

Model for resonant photon creation in a cavity with time dependent conductivity

In an electromagnetic cavity, photons can be created from the vacuum state by changing the cavity's properties with time. Using a simple model based on a massless scalar field, we analyze resonant photon creation induced by the time-dependent conductivity of a thin semiconductor film contained in the cavity. This time dependence may be achieved by irradiating periodically the film with short laser pulses. This setup offers several experimental advantages over the case of moving mirrors.Comment: 9 pages, 1 figure. Minor changes. Version to appear in Phys. Rev.

Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.Comment: 12 files,6 figure