Optimal Quantum Pumps

TL;DR

This paper investigates the properties of adiabatic quantum pumps operating on short time scales, introducing the energy shift matrix as a key tool to analyze charge transport, dissipation, and noise, and characterizing optimal pumps that minimize dissipation.

Contribution

It introduces the energy shift matrix as a dual to Wigner's time delay, provides a lower bound on dissipation, and characterizes optimal, noiseless quantum pumps.

Findings

Optimal pumps are noiseless and transport integral charge per cycle.

A geometric characterization of optimal pumps is provided.

An example related to the Hall effect illustrates the concepts.

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.