Spatio-temporal shaping of a free-electron wave function via coherent light–electron interaction

The past decade has witnessed a quantum revolution in the field of computation, communication and materials investigation. A similar revolution is also occurring for free-electron based techniques, where the classical treatment of a free electron as a point particle is being surpassed toward a deeper exploitation of its quantum nature. Adopting familiar concepts from quantum optics, several groups have demonstrated temporal and spatial shaping of a free-electron wave function, developing theoretical descriptions of light-modulated states, as well as predicting and confirming fascinating phenomena as attosecond self-compression and orbital angular momentum transfer from light to electrons. In this review, we revisit the milestones of this development and the several methods adopted for imprinting a time-varying phase modulation on an electron wave function using properly synthesized ultrafast light fields, making the electron an exquisitely selective probe of out-of-equilibrium phenomena in individual atomic/nanoscale systems. We discuss both longitudinal and transverse phase manipulation of free-electrons, where coherent quantized exchanges of energy, linear momentum and orbital angular momentum mediating the electron–light coupling are key in determining their spatio-temporal redistribution. Spatio-temporal phase shaping of matter waves provides new routes toward image-resolution enhancement, selective probing, dynamic control of materials, new quantum information methods, and exploration of electronic motions and nuclear phenomena. Emerging as a new field, electron wave function shaping allows adopting familiar quantum optics concepts in composite-particle experiments and paves the way for atomic, ionic and nuclear wave function engineering with perspective applications in atomic interferometry and direct control of nuclear processes.

The nucleon momentum distribution in light nuclei

The nucléon momentum distribution in light nuclei is studied by means of a single particle potential model which consists of an attractive harmonic oscillator potential Va=½mω²r² and also of a repulsive one of the form Vr=B/r², Β > 0. The latter simulates to some extend effects which would result if short range correlations were included (e.g. by a Jastrow factor) in a nuclear wave function, having as uncorrelated part a Slater determinant of harmonic oscillator orbitals. The main advantage of this model is that it leads to fairly simple analytic expressions for the momentum distribution of light nuclei and also for the density distributions and the elastic form factors. These expressions are quite useful in obtaining, for example, the asymptotic form of η(k) for large k from which it is seen that the steep decrease of the nucléon momentum distribution observed with the harmonic oscillator model in this region is improved. Numerical results using various least squares fittings are obtained and discussed for a number of nuclei of the 1s, 1p shell.

Recent progress of the sign problem in the Onishi formula

The Hartree-Fock-Bogoliubov (HFB) method is one of the major methods to study a nuclear wave function. We discuss the sign problem in the Onishi formula, which emerges in calculating the overlap between two HFB wave functions. The origin of this problem is elucidated by expanding the overlap as a polynomial function. This article is based on Ref.[1].

Initial state and thermalization in the Color Glass Condensate framework

In this review, I present the description of the early stages of heavy ion collisions at high energy in the Color Glass Condensate framework, from the pre-collision high energy nuclear wave function to the point where hydrodynamics may start becoming applicable.