Kapitsa–Dirac effect
The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light. The effect was first predicted as the diffraction of electrons from a standing wave of light by Paul Adrien Maurice Dirac and Pyotr Kapitsa (or Peter Kapitza) in 1933. The effect relies on the wave–particle duality of matter as stated by the de Broglie hypothesis in 1924.
In 1924, French physicist Louis de Broglie postulated that matter exhibits a wave-like nature given by:
where λ is the particle wavelength, h is Planck's constant, and p is the particle momentum. From this, it follows that interference effects between particles of matter will occur. This forms the basis of the Kapitza–Dirac effect. Specifically, Kapitza–Dirac scattering operates in the Raman–Nath regime. This is to say that the interaction time of the particle with the light field is sufficiently short in duration such that the motion of the particles with respect to the light field can be neglected. Mathematically, this means the kinetic energy term of the interaction Hamiltonian can be neglected. This approximation holds if the interaction time is less than the inverse of the recoil frequency of the particle, . This is analogous to the thin lens approximation in optics. A coherent beam of particles incident on a standing wave of electromagnetic radiation (typically light) will be diffracted according to the equation:
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