Non-abelian Geometric Quantum Energy Pump

TL;DR

This paper presents a novel non-abelian geometric quantum energy pump that uses a transitionless geometric drive to coherently transfer energy within degenerate subspaces, controlled by topology and initial states, with potential quantum technological applications.

Contribution

It introduces a non-abelian geometric energy pump based on transitionless driving and explores its control via topology and initial states, with proposed implementations in artificial atoms.

Findings

Energy transfer is governed by non-abelian Berry curvature.

Pumping power depends on initial state and Hamiltonian topology.

Potential applications include quantum transducers and phase measurement tools.

Abstract

We introduce a non-abelian geometric quantum energy pump realized by a transitionless geometric quantum drive--a time-dependent Hamiltonian supplemented by a counterdiabatic term generated by a prescribed trajectory on a smooth control manifold--that coherently transports states within a degenerate subspace. When the coordinates of the trajectory are independently addressable by external drives, the net energy transferred between drives is set by the non-abelian Berry-curvature tensor. The trajectory-averaged pumping power is separately controlled by the initial state and by the Hamiltonian topology through the Euler class. We outline an implementation with artificial atoms, which are realizable on various platforms including trapped atoms/ions, superconducting circuits, and semiconductor quantum dots. The resulting energy pump can serve as a quantum transducer or charger, and as a metrological tool for measuring phase coherences in quantum states.