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Plasma wakefield acceleration is a promising technology to reduce the size of particle accelerators. Use of high energy protons to drive wakefields in plasma has been demonstrated during Run 1 of the AWAKE programme at CERN. Protons of energy 400 GeV drove wakefields that accelerated electrons to 2 GeV in under 10 m of plasma. The AWAKE collaboration is now embarking on Run 2 with the main aims to demonstrate stable accelerating gradients of 0.5-1 GV/m, preserve emittance of the electron bunches during acceleration and develop plasma sources scalable to 100s of metres and beyond. By the end of Run 2, the AWAKE scheme should be able to provide electron beams for particle physics experiments and several possible experiments have already been evaluated. This article summarises the programme of AWAKE Run 2 and how it will be achieved as well as the possible application of the AWAKE scheme to novel particle physics experiments., Comment: 21 pages, 8 figures. Submitted to Symmetry journal

We investigate the usage of a Schlieren imaging setup to measure the geometrical dimensions of a plasma channel in atomic vapor. Near resonant probe light is used to image the plasma channel in a tenuous vapor and machine learning techniques are tested for extracting quantitative information from the images. By building a database of simulated signals with a range of plasma parameters for training Deep Neural Networks, we demonstrate that they can extract from the Schlieren images reliably and with high accuracy the location, the radius and the maximum ionization fraction of the plasma channel as well as the width of the transition region between the core of the plasma channel and the unionized vapor. We test several different neural network architectures with supervised learning and show that the parameter estimations supplied by the networks are resilient with respect to slight changes of the experimental parameters that may occur in the course of a measurement., Comment: 26 pages, 13 figures, 1 table

We investigate the propagation of ultra-short laser pulses in atomic rubidium vapor. The pulses are intensive enough to ionize the atoms and are directly resonant with the 780 nm $D_2$ line. We derive a relatively simple theory for computing the nonlinear optical response of atoms and investigate the competing effects of strong resonant nonlinearity and ionization in the medium using computer simulations. A nonlinear self-channeling of pulse energy is found to produce a continuous plasma channel with complete ionization. We evaluate the length, width and homogeneity of the resulting plasma channel for various values of pulse energy and initial focusing to identify regimes optimal for applications in plasma-wave accelerator devices such as that being built by the AWAKE collaboration at CERN. Similarities and differences with laser pulse filamentation in atmospheric gases are discussed., Comment: 8 figures

We derive composite pulse sequences that achieve high-fidelity excitation of two-state systems in an optically dense, inhomogeneously broadened ensemble. The composite pulses are resistant to distortions due to the back-action of the medium they propagate in and are able to create high-fidelity inversion to optical depths $\alpha z>10$. They function well with smooth pulse shapes used for coherent control of optical atomic transitions in quantum computation and communication. They are an intermediary solution between single $\pi$-pulse excitation schemes and adiabatic passage schemes, being far more error tolerant than the former but still considerably faster than the latter., Comment: 9 pages, 4 figures, submitted to Phys. Rev. A

Photon-echo based optical quantum memory schemes often employ intermediate steps to transform optical coherences to spin coherences for longer storage times. We analyze a scheme that uses three identical chirped control pulses for coherence rephasing in an inhomogeneously broadened ensemble of three-level $\Lambda$-systems. The pulses induce a cyclic permutation of the atomic populations in the adiabatic regime. Optical coherences created by a signal pulse are stored as spin coherences at an intermediate time interval, and are rephased for echo emission when the ensemble is returned to the initial state. Echo emission during a possible partial rephasing when the medium is inverted can be suppressed with an appropriate choice of control pulse wavevectors. We demonstrate that the scheme works in an optically dense ensemble, despite control pulse distortions during propagation. It integrates conveniently the spin-wave storage step into memory schemes based on a second rephasing of the atomic coherences., Comment: 11 pages, 9 figures

Photon-echo based quantum memories use inhomogeneously broadened, optically thick ensembles of absorbers to store a weak optical signal and employ various protocols to rephase the atomic coherences for information retrieval. We study the application of two consecutive, frequency-chirped control pulses for coherence rephasing in an ensemble with a 'natural' inhomogeneous broadening. Although propagation effects distort the two control pulses differently, chirped pulses that drive adiabatic passage can rephase atomic coherences in an optically thick storage medium. Combined with spatial phase mismatching techniques to prevent primary echo emission, coherences can be rephased around the ground state to achieve secondary echo emission with close to unit efficiency. Potential advantages over similar schemes working with $\pi$-pulses include greater potential signal fidelity, reduced noise due to spontaneous emission and better capability for the storage of multiple memory channels., Comment: 12 pages, 13 figures, accepted for publication in Phys. Rev. A