Gauge Fields, Geometric Phases, and Quantum Adiabatic Pumps

TL;DR

This paper explores the geometric interpretation of quantum adiabatic pumping using gauge fields, highlighting its relation to Berry's phase and proposing experimental demonstrations of non-Abelian gauge effects in nanoscale devices.

Contribution

It introduces a gauge field framework for understanding quantum pumping, connecting it to geometric phases and suggesting experimental setups to observe non-Abelian gauge phenomena.

Findings

Quantum pumping can be described by gauge fields on parameter space.

The geometric representation clarifies the role of Berry's phase and non-Abelian effects.

Potential experimental demonstration using STM tunneling through magnetic atoms.

Abstract

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when two or more system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. We make explicit the similarities and differences with Berry's geometric phase. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.