Quantum slit diffraction in space and in time of a Gaussian wave packet and semi-classical approximation

Mathieu Beau (1) , T.C. Dorlas (1)

1 STP-DIAS - School of Theoretical Physics [Dublin]

We revisit the famous problem of quantum slit diffraction of a three-dimensional Gaussian wave packet, taking into account the diffraction in time phenomenon for a reflective or absorbing slit. We first recall the theory of diffraction in space and in time to give an explicit integral formula for the single-slit propagator (for a two-dimensional aperture) assuming that the time of opening the aperture coincides with the time of emission of the particle. Then we derive a semiclassical expression for the amplitude when the parameter $\mu=m|\bold{r}|^2/(\hbar t)$ is large, where $\bold{r}$ is the position of the particle with mass $m$ detected on the screen at the time $t$. We also give corrections to the law giving the distance between two fringes in the Fraunhofer regime when the distances of the apparatus in the propagation direction are large compared to the size of the aperture of the slit. To conclude, we discuss the phenomenological consequences and we give a new perspective to investigate the quantum diffraction phenomenon particulary for the cold atom slit experiment.

Mots clés: matter waves; semiclassical theories and applications; beam optics; atom and neutron optics

Domaines: Physique Quantique [quant-ph]; Optique [physics.optics]

Mathieu Beau, T.C. Dorlas. Quantum slit diffraction in space and in time of a Gaussian wave packet and semi-classical approximation. 2013. ⟨hal-00875304v2⟩