Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect

Bragg scattering has been observed for free electrons using a standing wave of light. Both the rocking curve and the angular electron distribution have been measured. The results of a numerical simulation to the Schrödinger equation are consistent with our experimental data. Unlike the diffraction regime which uses thin crystals, the Bragg regime requires the use of thick crystals. We point out several applications in atom optics that could be realized in electron optics.

Figure 1

Comparing two regimes of the Kapitza-Dirac effect. Electrons passing through a narrow laser waist (left) are exposed to photons with larger angular uncertainty, allowing for diffraction into many different orders. For a wide laser waist (right), momentum and energy can be conserved only for Bragg scattering.

Figure 2

Top: the electron beam profile with the laser beam off. Bottom: when the laser light is on, the electrons which are incident at the Bragg angle, with a transverse momentum component of $-1\mathrm{\hbar }k$, are scattered to the positive first order.

Figure 3

The qualitative difference between the dependence on incident angle for a focused laser beam (triangles) and an unfocused laser beam (dots) shows that the Bragg regime is approached. The dotted and solid lines are theoretical calculations.

Figure 4

Experimental data of the rocking curves for the $+1\mathrm{s}\mathrm{t}$ (open circles) and the $-1\mathrm{s}\mathrm{t}$ (closed circles) orders at 5 W and the $+2\mathrm{n}\mathrm{d}$ (open squares) and the $-2\mathrm{n}\mathrm{d}$ (closed squares) at 9 W. The centers of the 2nd order rocking curves are approximately twice as far apart as those of the 1st order, as they should be.

Figure 5

The laser beam profile of the $\mathrm{N}\mathrm{d}:\mathrm{Y}\mathrm{A}\mathrm{G}$ at distances of 0.5, 2.8, and 17 m from the laser port is given left to right, respectively. The beam diameter for the left figure is 8 mm.