Pumping heat with quantum ratchets

We describe how adiabatically rocked quantum electron ratchets can act as heat pumps. In general, ratchets may be described as non-equilibrium systems in which directed particle motion is generated using spatial or temporal asymmetry. In a rocked ratchet, which may also be described as a non-linear rectifier, an asymmetric potential is tilted symmetrically and periodically. The potential deforms differently during each half-cycle, producing a net current of particles when averaged over a full period of rocking. Recently, it was found that in the quantum regime, where tunnelling contributes to transport, the net current may change sign with temperature. Here we show that a Landauer model of an experimental tunnelling ratchet (Linke et al., Science 286 (1999) 2314) predicts the existence of a net heat current even when the net particle current goes through zero. We quantify this heat current and define a coefficient of performance for the ratchet as a heat pump, finding that more heat is deposited in each of the two electron reservoirs due to the process of rocking than is pumped from one reservoir to the other by the ratchet.