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.
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