# The energetic cost of work extraction

## TL;DR

This paper investigates the maximum work that can be extracted from a qubit coupled to a waveguide acting as a quantum battery, highlighting the role of quantum coherence and ergotropy in the process.

## Contribution

It introduces a new autonomous model for quantum batteries using a qubit-waveguide system and establishes bounds on work extraction based on ergotropy and initial coherence.

## Key findings

- Work extraction is bounded by the qubit's ergotropy.
- Maximum work is achieved with sufficiently large battery charge.
- Quantum coherence influences work extraction when resources are limited.

## Abstract

We analyze work extraction from a qubit into a wave guide (WG) acting as a battery, where work is the coherent component of the energy radiated by the qubit. The process is stimulated by a wave packet whose mean photon number (the battery's charge) can be adjusted. We show that the extracted work is bounded by the qubit's ergotropy, and that the bound is saturated for a large enough battery's charge. If this charge is small, work can still be extracted. Its amount is controlled by the quantum coherence initially injected in the qubit's state, that appears as a key parameter when energetic resources are limited. This new and autonomous scenario for the study of quantum batteries can be implemented with state-of-the-art artificial qubits coupled to WGs.