Optimal control of a dissipative micromaser quantum battery in the ultrastrong coupling regime

TL;DR

This work tackles the problem of charging and stabilizing a quantum battery operating in the ultrastrong coupling regime under realistic dissipation. It models a micromaser battery where a cavity mode is sequentially charged by qubits via the Rabi Hamiltonian, and uses a GKLS master equation to capture open‑system dynamics during collisions. By applying quantum optimal control to the initial qubit population $q$ and the sequence of interaction times $\{\tau_k\}$, the authors show substantial gains in final ergotropy compared to a JC‑limit benchmark, and demonstrate that a measurement‑based passive feedback strategy can maintain stored ergotropy against dissipation. The results highlight dissipation as a resource for stabilization and establish practical guidelines for robust quantum energy storage in USC systems, with implications for superconducting and circuit‑QED platforms.

Abstract

We investigate the open system dynamics of a micromaser quantum battery operating in the ultrastrong coupling (USC) regime under environmental dissipation. The battery consists of a single-mode electromagnetic cavity sequentially interacting, via the Rabi Hamiltonian, with a stream of qubits acting as chargers. Dissipative effects arise from the weak coupling of the qubit-cavity system to a thermal bath. Non-negligible in the USC regime, the counter-rotating terms substantially improve the charging speed, but also lead, in the absence of dissipation, to unbounded energy growth and highly mixed cavity states. Dissipation during each qubit-cavity interaction mitigates these detrimental effects, yielding steady-state of finite energy and ergotropy. Optimal control on qubit preparation and interaction times enhances battery's performance in: (i) Maximizing the stored ergotropy trhough an optimized charging protocol; (ii) Stabilizing the stored ergotropy against dissipative losses through an optimized measurement-based passive-feedback strategy. Overall, our numerical results demonstrate that the interplay of ultrastrong light-matter coupling, controlled dissipation, and optimized control strategies enables micromaser quantum batteries to achieve both enhanced charging performance and long-term stability under realistic conditions.

Figures (6)

• Figure 1: Pictorial representation of the micromaser quantum battery. The battery, modeled as a single-mode cavity in the state $\rho_B$, interacts sequentially with a stream of identically prepared two-level systems (qubits) $\rho_q$. The qubits enter the cavity, exchange energy with the cavity field, and exit in the modified state $\rho_q'$. The wavy arrows indicate coupling to the environment, modeling dissipation of the cavity field. The sequential interactions, duration and qubit preparation, are designed to increase the amount of energy stored in the cavity field.
• Figure 2: Evolution of the closed quantum battery: (a) energy, (b) purity, and (c) ergotropy as functions of the number of collisions. Each curve corresponds to a different coupling strength in the USC regime, $g \in \{0.2,0.4,0.6,0.8\}$, with fixed parameters $c=1$, $q=0.5$, $\tau=10$, and $\omega=1$. In the closed-system regime, both the cavity energy and ergotropy increase without bound as the number of collisions grows, while the purity rapidly decreases, indicating that the battery evolves into strongly mixed states.
• Figure 3: Evolution of the open quantum battery: (a) energy, (b) purity, and (c) ergotropy as functions of the number of collisions. Each line corresponds to a different value of $g \in \{0.2,0.4,0.6,0.8\}$ in the USC regime, with fixed system parameters $c=1$, $q=0.5$, $\tau=10$, $\omega=1$, and environment parameters $\omega_c=3$, $\beta=450$, and $\eta=0.01$. Including dissipation during each qubit--cavity collision qualitatively changes the dynamics: energy and ergotropy converge to well-defined steady-state values, while purity decreases moderately with increasing $g$. The steady-state ergotropy remains nonzero, indicating that the energy stored in the cavity is at least partially extractable through unitary operations.
• Figure 4: Comparison of ergotropy in optimized and non-optimized protocols. (a) Optimized battery ergotropy as a function of the number of collisions (solid curves), compared with the non-optimized one resulting from the $\pi$-pulse protocol (dashed curves) defined by the Jaynes--Cummings prescription $\tau_k = \pi/(2 g \sqrt{k})$ with $q=0$. Blue curves correspond to $g=0.1$, while red curves correspond to $g=0.7$. The optimized protocol consistently achieves higher final ergotropy than the $\pi$-pulse protocol, demonstrating the effectiveness of the optimization. (b) Battery final ergotropy as a function of the coupling constant $g$, comparing optimized protocols (solid line) with $\pi$-pulse protocols (dashed line). Across all values of $g$, the optimized protocols consistently yield higher final ergotropy. Fixed parameters: $c=1$, $\omega=1$, $\omega_c=3$, $\eta=0.01$, and $\beta=450$.
• Figure 5: Wigner function of the battery state after the charging process for three different protocols. (a) Closed-system $\pi$-pulse protocol with $g=0.7$, $\tau_k = \pi/(2 g \sqrt{k})$, $q=0$, $c=1$, and $\omega=1$. (b) Open-system $\pi$-pulse protocol with the same system parameters and environmental parameters $\omega_c=3$, $\beta=450$, and $\eta=0.01$. (c) Optimized open-system protocol, corresponding to the optimal parameters used for $g=0.7$ in figure \ref{['fig:combined_ergotropy']}(a). Panel (a) exhibits small negativities typical of quantum coherence, while panels (b) and (c) show strictly non-negative distributions due to dissipative effects. Panels (a) and (b) display irregular, low-amplitude distributions near the origin, indicative of moderately excited battery states, whereas panel (c) shows a distribution with larger amplitudes displaced away from the origin, signaling a higher energy content and enhanced charging performance.