KapitzaDirac

Kapitza-Dirac diffraction is the elastic diffraction of matter waves by a standing light wave. It was proposed in 1933 by Pyotr Kapitza and Paul Dirac as a quantum mechanical analogue of Bragg diffraction, showing that light can act as a spatial grating for particles such as electrons or atoms.

In the interaction, a nearly monochromatic, far-detuned laser field creates a spatially periodic potential U(x) ∝ cos^2(kx), which couples momentum states separated by 2ħk. A particle passing through the standing wave can exchange momentum in quanta of 2ħk, distributing the wave into discrete diffraction orders with final momentum p0 + 2nħk. Depending on pulse duration and intensity, the diffraction is described by the Raman–Nath regime (short pulses) or the Bragg regime (longer, resonant pulses).

Historically, Kapitza-Dirac diffraction was first conceived for electrons; later experiments demonstrated the effect with neutral atoms and ultracold atomic ensembles, including Bose-Einstein condensates, providing a versatile tool in atom optics. The phenomenon is central to optical lattices and atom interferometry, where laser standing waves act as beam splitters and mirrors for matter waves.

Beyond fundamental tests of quantum mechanics, Kapitza-Dirac diffraction underpins precision measurements, quantum simulations of lattice systems, and investigations of light–matter interactions. It also provides a clean platform to study diffractive scattering, decoherence, and motional state control in quantum gases.