A topologically protected quantum dynamo effect in a driven spin-boson model

TL;DR

This paper introduces a topologically protected quantum dynamo effect in a driven spin-boson system, where energy from driving is converted into a coherent bosonic field, linked to the system's topology, with potential realizations in mesoscopic and atomic systems.

Contribution

It demonstrates a topologically protected quantum dynamo effect in a driven spin-boson model, connecting work conversion to the system's topology and providing a new method for coherent energy transfer.

Findings

The dynamo effect opposes changes in the external drive, akin to Faraday's law.

Work from spin manipulation converts into coherent bosonic mode displacement.

The effect is topologically protected and realizable in experimental systems.

Abstract

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of Faraday's law of induction, justifying the term 'quantum dynamo effect'. For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, the effect thus corresponds to a work-to-work conversion and allows to interpret this transmitted energy into the bath as work. We study this effect, its performance and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.