  We consider a minimal model of a quantum rotator composed of a single
particle confined in an harmonic potential and driven by two temperature-biased
heat reservoirs. In the case the particle potential is rendered asymmetric and
rotated an angle, a finite angular momentum develops, corresponding to a
directed rotary motion. At variance with the classical case, the thermal
fluctuations in the baths give rise to a non-vanishing average torque
contribution; this is a genuine quantum effect akin to the Casimir effect. In
the steady state the heat current flowing between the two baths is
systematically converted into particle rotation. We derive exact expressions
for the work rate and heat currents in the case where the system is driven by
an external time periodic mechanical force. We show, in agreement with previous
works on classical systems, that for this choice of external manipulation
protocol, the rotator cannot work either as a heat pump or as a heat engine. We
finally use our exact results to extend an ab-initio quantum simulation
algorithm to the out-of-equilibrium regime.
