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 wav e due to fast modulation in time. The experiment, carried out with slow neu trons, achieved pulse widths of 33 n, and has been analyzed using time-depe ndent optics based on the nonrelativistic Schrodinger 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 modula tion 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 dem onstrate the operation of a time-of-flight spectrometer (FOTOF), and achiev e an energy resolution of 20 neV, which to our knowledge represents a new l imit for a TOF with slow neutrons. [S1050-2947(98)04312-1].