## Interferometry: just in time!

There are many analogies between the interferometry of light and matter but there are also important experimental differences: while monochromatic light is easily provided by modern lasers, molecular beams have usually broad velocity distributions and low longitudinal coherence. Fortunately, the monochromaticity requirement can be overcome in time-domain interferometry, as illustrated below:

The simulation illustrates the idea for the simplified example of a double slit. When a cloud of particles with a finite velocity distribution is diffracted at a double slit the slow particles (left) follow the faster ones (right). The individual particles are distributed among the intensity maxima of the quantum interference pattern. The interference pattern of the fast particles on the fixed screen is depicted by the red pattern. Some time later the slow fraction is detected as the green pattern. Because of their extended flight time, the momentum transfer imparted by the double slit, translates into a wider peak separation of their interference pattern. If we collect all velocity classes on a fixed screen the fringe pattern will tend to wash out, even though there is high contrast in each velocity class. So how can we observe high-contrast interference when the molecular beam has a wide velocity distribution? The answer is: by imaging an extended region of space only for a very short time.

Physics textbooks teach us that the physics of diffraction at a double slit or grating can be understood by the overlap of elementary de Beoglie wavelets - which is correct. However, you can also predict where to find all far-field interference maxima using a more mechanistic picture: the double slit imparts a fixed momentum kick of  Δp=±n h/d to the traversing particle, which depends on Planck's constant h, and the separation between the two slits d, where n is an integer number.  This momentum transfer is independent of de Broglie wavelength and is a delocalized feature of the experimental geometry. The de Broglie wavelength then enters since it is inversely proportional to the forward velocity and thus determines the ratio between longiutudinal and transverse momentum.

However, at any give instant in time, the transverse evolution is the same for all particles, independent of their forward velocity. In the simulation one can imagine a camera taking a snap shot when the clouds pass the interaction region.