Collective Dissipative Charging and Energy Extraction in Quantum Batteries

Abstract

In this dissertation, we investigate the charging and discharging dynamics of a quantum battery composed of a collectively driven ensemble of $N$ identical two level systems coupled to a structured electromagnetic environment. The system is described using collective angular momentum operators in the Dicke basis, which provides a compact and physically transparent framework for analyzing collective light-matter interactions. Rather than treating dissipation as an unwanted source of loss, we explicitly use it as a mechanism for energy storage and work extraction. Starting from a coherently driven ensemble coupled to common reservoirs, we derive a master equation in Lindblad form under the Born-Markov and secular approximations. In the dressed-state basis, spontaneous emission induces irreversible transitions that can increase the energy stored in the bare basis. We obtain analytic expressions for the steady state, including the stored energy and the ergotropy, and identify parameter regimes where substantial collective coherence is generated. A central result of this work is the demonstration that, in the extensive regime where the total energy scales linearly with $N$ and relative fluctuations vanish, the charging power scales as $N^2$. This quadratic enhancement scaling exceeds the $N^{3/2}$ limit previously established for purely Hamiltonian charging protocols of noninteracting Dicke batteries in the same regime. We show that this enhancement is consistent with quantum speed limits for open-system dynamics and originates from collectively enhanced dissipative processes analogous to superradiance. We further analyze the extraction process and show that the charged steady state stores not only energy but a macroscopic collective dipole moment. This coherence enables rapid energy release through either collective spontaneous emission or stimulated emission driven by an external coherent field. In the appropriate large $N$ extensive regime, the stored energy can become fully extractable in principle, and the discharging power also exhibits $N^2$ scaling. These results establish that dissipative protocols can provide a genuine collective advantage over Hamiltonian schemes in the extensive regime, while also highlighting the interplay between enhanced collective power and the conditions required to achieve high extractable energy.