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arXiv:2605.12867

Liouvillian spectral control for fast charging of quantum batteries

Hang Zhou, Jia-Wei Huang, Chuan-Cun Shu

quant-phSubmitted May 13, 2026• Announced May 14, 2026• 0 citations
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Abstract

Quantum batteries, which use quantum systems to store and deliver energy, are promising for next-generation energy storage. However, optimizing charging strategies and understanding the interplay between dissipation and quantum coherence remain open challenges. Here, we investigate steady-state charging in an open quantum battery and demonstrate that the charging timescale depends on the spectral gap of the Liouvillian operator governing dissipative dynamics. As a minimal example, we examine a three-level quantum battery realized in a single trapped ${}^{40}\mathrm{Ca}^{+}$ ion, where energy from an engineered thermal photon reservoir is coherently transferred to a long-lived metastable storage state. We find that long-term dynamics are confined to a low-dimensional manifold of slow Liouvillian modes, with their spectral structure determining the relaxation rate to the charged steady state. By adjusting experimentally accessible parameters, such as reservoir occupation and coherent coupling strength, the non-Hermitian Liouvillian spectrum can approach an exceptional point. This increases the spectral gap and accelerates the approach to steady state. As a result, this mechanism significantly enhances asymptotic charging power without relying on many-body collectivity or steady coherence. Our findings offer fundamental insights into open quantum thermodynamics and provide a path to efficient energy storage and fast-charging solutions in emerging quantum technologies.

Comments
11 pages, 8 figures. Hang Zhou and Jia-Wei Huang contributed equally to this work

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Quantum batteries, which use quantum systems to store and deliver energy,
are promising for next-generation energy storage. However, optimizing charging
strategies and understanding the interplay between dissipation and quantum
coherence remain open challenges. Here, we investigate steady-state charging
in an open quantum battery and demonstrate that the charging timescale depends
on the spectral gap of the Liouvillian operator governing dissipative dynamics.
As a minimal example, we examine a three-level quantum battery realized in
a single trapped 40Ca+{}^{40}\mathrm{Ca}^{+}40Ca+ ion, where energy from an
engineered thermal photon reservoir is coherently transferred to a long-lived
metastable storage state. We find that long-term dynamics are confined to
a low-dimensional manifold of slow Liouvillian modes, with their
spectral structure determining the relaxation rate to the charged
steady state. By adjusting experimentally accessible parameters,
such as reservoir occupation and coherent coupling strength, the non-Hermitian
Liouvillian spectrum can approach an exceptional point. This increases
the spectral gap and accelerates the approach to steady state. As a result,
this mechanism significantly enhances asymptotic charging power without
relying on many-body collectivity or steady coherence. Our findings offer
fundamental insights into open quantum thermodynamics and provide a path
to efficient energy storage and fast-charging solutions in emerging quantum
technologies.
Abstract We investigate the stabilization mechanism of open quantum batteries driven by a classical field in the weak or strong system-reservoir coupling regime. A protocol to improve the steady-state energy storage performance is proposed by engineering the spectral density of a band-gap environment which is described as the superposition of two inhomogeneous Lorentzian spectrums with different weights. We find out that the interplay between the battery-environment-bound state and the reservoir memory effect plays a crucial role in the stabilization performance against energy dissipation. The formation of the bound state and the non-Markovian effect will be strengthened by adjusting the weights of the environment spectral density. In the charging process, the classical field contributes to enhancing the steady ergotropy. Moreover, the manipulation of the spectrum weights results in the speedup scheme of carrying out the energy storage due to the existence of bound states. In the self-discharging process, increasing the spectral weight allows the battery to maintain a higher steady ergotropy. These results provide a practical approach to achieving optimal quantum batteries with better stabilization performance.
Fast charging of quantum batteries requires amplification of the energy transferred to a storage mode without uncontrolled gain or phenomenological non-Hermitian dynamics. Inspired by broken/unbroken dynamical regimes, we introduce a reservoir-engineered quantum battery in which a two-photon-driven charger and a battery mode are coupled through a lossy dissipative mediator. Eliminating the fast mediator yields a reduced two-mode Lindblad model with a complex dissipative coupling and renormalized damping rates. Its drift matrix has a pump-induced stability threshold: below threshold the seeded response is bounded, whereas above threshold a weak seed excites a growing mode and the battery occupation increases exponentially. Compared with a coherent beam-splitter charger--battery benchmark at equal effective coupling, the dissipative architecture reaches this broken regime at a lower pump amplitude. For the parameters studied here, this corresponds to about 61%61\%61% less critical pump power and opens a pump-power window in which dissipative charging is exponential while the coherent benchmark remains below threshold. In the broken dissipative regime, the growth is dominated by a seed-selected coherent battery displacement rather than incoherent fluctuation buildup, so a large fraction of the stored energy is directly extractable by a displacement operation. The broken-regime boundary is a dynamical stability threshold, not generally an exceptional point, and the full three-mode Lindblad model confirms the reduced description in the fast-mediator regime. Our results give a completely positive route to pump-efficient, low-threshold, and coherently addressable quantum energy storage using engineered reservoirs.
Suppressing coherent energy backflow while maintaining extractable energy in a stable nonequilibrium state remains a central challenge for quantum energy storage. Here, we introduce a reservoir-engineered dual-charger quantum battery architecture, in which nonequilibrium dissipation is exploited as a control resource to stabilize useful stored energy. A hot-reservoir-coupled driver supplies excitations, while a cold-reservoir-coupled cache biases the resonant three-body transition toward charging and suppresses the dressed-state coherences responsible for energy backflow. This mechanism establishes a population-inverted steady state with finite ergotropy and converts reversible charger--battery exchange into persistent energy storage. For uniformly spaced multilevel batteries, we show that the stored energy and ergotropy scale approximately linearly with the number of accessible levels, while the stored-energy utilization approaches unity. The accompanying stationary heat current provides a thermodynamic signature of the charging regime. Our results demonstrate dissipation engineering as a strategy for achieving stable and scalable quantum energy storage beyond transient coherent charging protocols.
A quantum battery charged through a lossy intermediate state faces a structural trade-off between charging speed and dissipation. We show that an exact algebraic cancellation removes it in a driven three-level cell: the radiatively decaying state is fed by a single bright amplitude, and a counterdiabatic field annuls the lone residual source that drives it, holding the lossy state identically empty. Charging is then lossless -- not one photon is emitted through the bridge -- at any one-photon detuning, coupling, linewidth, and speed down to the rotating-wave limit, with no adiabatic elimination, so the charging power is bounded by the drive amplitude (a quantum speed limit) rather than by dissipation. Crucially, this losslessness is independent of the reservoir: because the dark sector never engages the system-bath coupling, the emission vanishes exactly for an arbitrary spectral density, Markovian or not, as an exact damped-pseudomode treatment confirms to machine precision across all memory times. The entire non-Hermitian structure -- a Markovian second-order exceptional point that reservoir memory promotes to a third-order one, and the attendant dissipation phase diagram -- lives in the bright sector, from which the protocol is by construction exempt. This inverts dissipation-engineered charging, where an exceptional point or reservoir memory is a resource; here the lossy sector is never populated at all. The same dark-state structure protects the stored charge, converting fast radiative self-discharge into the slow metastable lifetime, with residuals quadratic in the control error. We detail experimental requirements and representative parameters for neutral alkaline-earth atoms, trapped ions, transmons, and defect centers.
We investigate the charging of a nonlinear quantum battery consisting of a single bosonic mode subject to a saturable nonlinearity, coherent driving, and dissipation. In contrast to Kerr-type anharmonicities, the saturable interaction induces a bounded and nonlinear distortion of the energy spectrum, leading to a progressive increase in the density of energy levels. We analyze the time evolution of the energy and ergotropy of the battery by solving a Lindblad master equation and show that the nonlinear spectral structure significantly affects both transient charging behavior and steady-state properties. Our results reveal that, for a broad range of parameters, the saturable nonlinearity enhances the maximum stored energy and modifies the ergotropy generation in the presence of losses. The interplay between dissipation and bounded spectral nonlinearity provides a controllable mechanism to tune energy storage and work extraction in bosonic quantum batteries.
Abstract We investigate the charging of a nonlinear quantum battery consisting of a single bosonic mode subject to a saturable nonlinearity, coherent driving, and dissipation. In contrast to Kerr-type anharmonicities, the saturable interaction induces a bounded and nonlinear distortion of the energy spectrum, leading to a progressive increase in the density of energy levels. We analyze the time evolution of the energy and ergotropy of the battery by solving a Lindblad master equation and show that the nonlinear spectral structure significantly affects both transient charging behavior and steady-state properties. Our results reveal that, for a broad range of parameters, the saturable nonlinearity enhances the maximum stored energy and modifies the ergotropy generation in the presence of losses. The interplay between dissipation and bounded spectral nonlinearity provides a controllable mechanism to tune energy storage and work extraction in bosonic quantum batteries.