# Topologically protected quantization of work

## TL;DR

This paper demonstrates a topological effect that quantizes the average work done on a particle in a periodically driven potential, linking it to a topological invariant called the first Chern number, thus ensuring robustness against perturbations.

## Contribution

It introduces a topological mechanism for quantizing work in a driven system, connecting physical work to topological invariants in space-time.

## Key findings

- The average work equals the first Chern number in a space-time lattice.
- The quantization is topologically protected and robust.
- Illustrated with an atom coupled to electromagnetic waves.

## Abstract

The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this amount of work, when averaged over a single temporal period of the potential, can take any value in a continuous fashion. Here we present a topological effect inducing the quantization of the average work. We find that this work is equal to the first Chern number calculated in a unit cell of a space-time lattice. Hence, this quantization of the average work is topologically protected. We illustrate this phenomenon with the example of an atom whose center of mass motion is coupled to its internal degrees of freedom by electromagnetic waves.