Optimal Quantum Pumps

Abstract

We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In this regime the pump is characterized by the matrix of energy shift which we introduce as the dual to Wigner's time delay. The energy shift determines the charge transport, the dissipation, the noise, and the entropy production. We prove a general lower bound on dissipation in a quantum channel and define optimal pumps as those that saturate the bound. We give a geometric characterization of optimal pumps and show that they are noiseless and transport integral charge in a cycle. Finally we discuss an example of an optimal pump related to the Hall effect.

Transport and Dissipation in Quantum Pumps

“…If a pump operation is of the form (7.3), then dQ is the winding number of e iγ [3,7]. Alternatively, the curvature Eq.…”

“…Had we used this procedure to compute the quantitiesĖ j andQ j separately, each of them would be off by nonzero O(ω 2 ) terms (as can be seen in the snowplow and battery examples); nevertheless, the combinationĖ j − µQ j is computed correctly to order ω 2 . The reason is that in each quantum channel one has the following lower bound on the dissipation [7]:…”

“…This does not preclude the possibility that charge is quantized for reasons other than being a Chern number. In fact, one can geometrically characterize a class of periodic pump operations [7] for which the transported charge in a cycle, and not just its expectation value, is a non-random integer. It is to be cautioned that a small change of the scattering matrix will typically destroy this quantization.…”

Dissipation and noise in adiabatic quantum pumps

“…The problem of current noise in a quantum pump is closely connected with the problem of quantization of the charge pumped in one cycle 4,6,16,17,29 . On the other hand the noise in mesoscopic phase coherent conductors is interesting in itself [42][43][44]57 because it is very sensitive to quantum-mechanical interference effects and can give additional information about the scattering matrix.…”

“…Recently Avron et al 4 investigated adiabatic quantum pumping with the aim to formulate criteria for an "optimal pump". The term "optimal" means that such a pump is noiseless and transports integer charge in each cycle.…”