  Heat engines convert thermal energy into mechanical work both in the
classical and quantum regimes. However, quantum theory offers genuine
nonclassical forms of energy, different from heat, which so far have not been
exploited in cyclic engines to produce useful work. We here experimentally
realize a novel quantum many-body engine fuelled by the energy difference
between fermionic and bosonic ensembles of ultracold particles that follows
from the Pauli exclusion principle. We employ a harmonically trapped superfluid
gas of $^6$Li atoms close to a magnetic Feshbach resonance which allows us to
effectively change the quantum statistics from Bose-Einstein to Fermi-Dirac. We
replace the traditional heating and cooling strokes of a quantum Otto cycle by
tuning the gas between a Bose- Einstein condensate of bosonic molecules and a
unitary Fermi gas (and back) through a magnetic field. The quantum nature of
such a Pauli engine is revealed by contrasting it to a classical thermal engine
and to a purely interaction-driven device. We obtain a work output of several
$10^6$ vibrational quanta per cycle with an efficiency of up to $25\%$. Our
findings establish quantum statistics as a useful thermodynamic resource for
work production, shifting the paradigm of energy-conversion devices to a new
class of emergent quantum engines.
