Matter-wave optics in the time domain: Results of a cold-neutron experiment

We report an observation of a change in the energy spectrum of a matter wave due to fast modulation in time. The experiment, carried out with slow neutrons, achieved pulse widths of 33 n, and has been analyzed using time-dependent optics based on the nonrelativistic Schrödinger equation. A good fit to the data is obtained. The modulation of a matter wave in time leads to a characteristic energy spread. These phenomena can be seen as a consequence of the time-energy uncertainty relation. In our case, the amplitude modulation is done by a rapid periodic opening and closing of a slit. In the time domain this causes a so-called “diffraction in time.” In this work we demonstrate the operation of a time-of-flight spectrometer (FOTOF), and achieve an energy resolution of 20 neV, which to our knowledge represents a new limit for a TOF with slow neutrons.