  The de Broglie wave nature of matter is a paradigmatic example of fundamental
quantum physics and enables precise measurements of forces, fundamental
constants and even material properties. However, even though matter-wave
interferometry is nowadays routinely realized in many laboratories, this feat
has remained an outstanding challenge for the vast class of native
polypeptides, the building blocks of life, which are ubiquitous in biology but
fragile and difficult to handle. Here, we demonstrate the quantum wave nature
of gramicidin, a natural antibiotic composed of 15 amino acids. Femtosecond
laser desorption of a thin biomolecular film with intensities up to 1~TW/cm$^2$
transfers these molecules into a cold noble gas jet. Even though the peptide's
de Broglie wavelength is as tiny as 350~fm, the molecular coherence is
delocalized over more than 20 times the molecular size in our all-optical
time-domain Talbot-Lau interferometer. We compare the observed interference
fringes for two different interference orders with a model that includes both a
rigorous treatment of the peptide's quantum wave nature as well as a quantum
chemical assessment of its optical properties to distinguish our result from
classical predictions. The successful realization of quantum optics with this
polypeptide as a prototypical biomolecule paves the way for quantum-assisted
molecule metrology and in particular the optical spectroscopy of a large class
of biologically relevant molecules.
