Pumping Heat (reversibly) with Quantum Ratchets

A ratchet may be described as a non-equilibrium system 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 to produce directed particle motion. We have found experimentally that in rocked quantum electron ratchets high energy electrons travel, on average, in the opposite direction to low energy (tunnelling) electrons. This means that such a device can act as a heat pump, sifting hot and cold electrons. We have investigated the limiting efficiency of an idealised rocked quantum electron ratchet which is composed of an asymmetric resonant tunnelling structure connecting two reservoirs of two-dimensional electron gas at different temperatures and electro-chemical potentials. We have found that, in general, a quantum heat engine (or refrigerator) working between two reservoirs which are not in equilibrium (different temperatures and electro-chemical potentials) has no limiting efficiency lower than the Carnot value when a suitably chosen, sharp energy filter (such as a quantum dot) is used to connect the reservoirs.

Figure caption: An illustration of a hypothetical quantum electron ratchet, rocked using a square wave voltage of magnitude V. Shown tilted up (left figure) and tilted down (right figure), the ratchet is composed of an asymmetric quasi-0-dimensional quantum dot and two two-dimensional electron gas reservoirs which are connected via an adjustable resonant energy channel in the dot. The higher temperature of the right reservoir is indicated by wider shading on the energy axis, marked e, and the electro-chemical potentials of each reservoir are marked mL/R. The device can either cool the left reservoir by removing hot electrons and holes or alternately, by changing the energy e of the resonance, the ratchet can act as a heat engine, utilising the temperature gradient to pump electrons against the potential gradient, so exhibiting absolute negative resistance during each half cycle. Between these two regimes of operation these exists an energy at which transport of electrons between the reservoirs is reversible.

T.E. Humphrey, H. Linke, R. Newbury