Quantum Signatures in Laser-Driven Relativistic Multiple Scattering

The dynamics of an electronic Dirac wave packet evolving under the influence of an ultraintense laser pulse and an ensemble of highly charged ions is investigated numerically. Special emphasis is placed on the evolution of quantum signatures from single to multiple scattering events. We quantify the occurrence of quantum relativistic interference fringes in various situations and stress their significance in multiple-particle systems, even in the relativistic range of laser-matter interaction.

Figure 1

(a) Overview: Contour plots at $t=7.645$, 8.195, 9.495, and 12.095 a.u. corresponding to times before the first scattering, shortly after it, at the lower point of return, and after the second scattering, close to the upper point of return. The four dashed rectangles (some only partly visible) mark the dynamical grid boundaries for each of these situations. The thick dots indicate the positions of two ${\mathrm{S}\mathrm{n}}^{50+}$ ions, which are located right on the horizontal axis at positions 16.5 and 30.0 a.u. The solid line depicts the trajectory of the expectation value of the particle’s spatial coordinate. We omit any enlarged view of the initially Gaussian packet at $t=7.645\mathrm{a}.\mathrm{u}.$, but provide them for the other three cases as follows: (b) enlarged view at $t=8.195\mathrm{a}.\mathrm{u}.$ showing single scattering fringes shortly after the scattering event; (c) enlarged view at $t=9.495\mathrm{a}.\mathrm{u}.$ that depicts the same single scattering fringes somewhat later in order to illustrate the growth of the distance between any two fringes [compare with (b)]; (d) enlarged view at $t=12.095\mathrm{a}.\mathrm{u}.$ which displays interference from two separate scattering events with crossed fringes on the left side and on the right side the unperturbed structure from the first scattering event. In all cases, 20 contour lines are shown for $|\psi {|}^2$ with constant steps within $-1.15\ge \log |\psi {|}^2\ge -4$.

Figure 2

(a) Overview: Contour plots at time $t=12.270\mathrm{a}.\mathrm{u}.$ after two scatterings at an ensemble of six ${\mathrm{S}\mathrm{n}}^{50+}$ ions (thick dots) centered symmetrically around a further one at position (0,30) a.u. The dashed rectangle marks the grid boundary and the solid line depicts the trajectory of the expectation value of the electron’s spatial coordinate. (b) This enlarged view of the wave packet in (a) illustrates how the two scattering events at seven ions modify the regularity in the interference pattern. In both graphs, 20 contour lines are shown for $|\psi {|}^2$ with constant steps within $-1.15\ge \log |\psi {|}^2\ge -4$.