Controlled Dark-State Energy Storage and Work Extraction in V-Type Quantum Batteries

Abstract

The performance of a quantum battery depends not only on its ability to retain stored energy against unwanted discharge but also on the amount of useful work that can be extracted from it. Here, we investigate these complementary aspects in an ensemble of V-type qutrits coupled to a lossy cavity. By applying a finite splitting pulse to the two excited states of each qutrit, cavity-bright excitations are converted into atomic dark states, whose populations remain protected upon restoring degeneracy, even while the light-matter coupling remains active. Simulations with finite-duration pulses reveal a capture window governed by the competition among energy transfer, bright-to-dark conversion, and photon leakage. We further show that if the energy is stored in the fully symmetric atomic subspace, the passive energy is bounded by twice the transition energy for number of atoms $N\geq2$. Consequently, if the stored energy scales extensively with $N$, the ratio of extractable work to stored energy approaches unity in the thermodynamic limit. Comparing different initial preparations at equal mean input energy, we find that coherent-state can yield greater finite-time ergotropy despite capturing less energy, whereas Fock-state favors greater extractable work in the stationary component. Our results demonstrate how controlled dark-state population trapping in an atom-cavity coupled system can protect stored energy while providing a conditional route toward high extractable work.

The paper asks whether cavity-charged quantum batteries can retain excitations in dark states while preserving extractable work. It studies $N$ identical V-type qutrits with equal, in-phase coupling to a lossy cavity. A uniform excited-state splitting pulse mixes bright and dark states; restoring degeneracy freezes the dark population without switching off the cavity coupling. An exact conservation law establishes post-pulse dark-population protection. Permutation symmetry confines the atomic state to a subspace of dimension $\binom{N+2}{2}$. Counting low-energy states in the full atomic Hilbert space then gives $E_{\rm pass}\leq2\omega$ for $N\geq2$, hence $\mathcal E\geq\max[0,E_a-2\omega]$. Consequently, the globally extractable fraction approaches unity **conditional on extensive retained energy**. This extends an existing rank-based extractability argument. Lindblad simulations with cavity photon loss examine finite square pulses of area $\pi$, with timing chosen from the pulse-free bright-population peak. Small-system calculations show competition among charging, conversion and leakage; for $N=3$, $\delta=0.2\omega$ and $\kappa=0.01\omega$, capture peaks near $g_0=0.1\omega$. At equal mean input energy, coherent cavity preparation can produce higher finite-time ergotropy despite storing less energy, whereas Fock preparation generally gives greater stationary-component ergotropy in the sampled useful-storage regime. Protection assumes matched couplings, restored degeneracy and cavity-only dissipation. Atomic noise and imperfections are not assessed. Counter-rotating interactions are combined with a local photon-loss model, whose stationary bright sector need not be the bare ground state. Zero-mode projection represents the full long-time state only if other populated modes decay. Extraction assumes unrestricted global atomic unitaries; explicit loads, control costs and interaction-energy accounting remain outside the analysis.