Dissipative dynamics of an open quantum battery in the BTZ spacetime

We consider how charging performances of a quantum battery, modeled as a two-level system, are influenced by the presence of vacuum fluctuations of a quantum field satisfying the Dirichlet, transparent, and Neumann boundary conditions in the BTZ spacetime. The quantum battery is subjected to an external static driving which works as a charger. Meanwhile, the quantum field is assumed to be coupled to both longitudinal and transverse spin components of the quantum battery including decoherence and pure dephasing mechanisms. Charging and discharging dynamics of the quantum battery are derived by extending the previous open quantum system approach in the relativistic framework to this more general scenario including both the driving and multiple coupling. Analytic expressions for the time evolution of the energy stored are presented. We find that when the driving amplitude is stronger/weaker than the energy-level spacing of the quantum battery the pure dephasing dissipative coupling results in better/worse charging performances than the decoherence dissipative coupling case. We also find that higher local Hawking temperature helps to improve the charging performance under certain conditions compared with the closed quantum battery case, implying the feasibility of energy extraction from vacuum fluctuations in curved spacetime via dissipation in charging protocol. Different boundary conditions for quantum field may lead to different charging performance. Furthermore, we also address the charging stability by monitoring the energy behaviour after the charging protocol has been switched off. Our study presents a general framework to investigate relaxation effects in curved spacetime, and reveals how spacetime properties and field boundary condition affect the charging process, which in turn may shed light on the exploration of the spacetime properties and thermodynamics via the charging protocol.