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arXiv:2610.28373

Stable charged energy and phase transitions in an anisotropic Dicke quantum battery with Kerr nonlinearity

Shao-Fan He, Lv-Ting Gong, Fu-Quan Dou

quant-phSubmitted Oct 20, 2026• Announced Oct 21, 2026
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Abstract

Phase transitions (PTs) in quantum many-body systems offer a powerful route to manipulate the performance of quantum batteries (QBs). Here, we investigate an anisotropic Dicke QB with Kerr nonlinearity, focusing on the role of PTs in the charging process of the QB system. By analyzing how the Kerr nonlinearity reshapes the cavity level-spacing structure, we find that multiple near-degeneracies emerge at specific nonlinearity strengths. Away from the region of multiple near-degeneracies, the stable stored energy is governed primarily by the ergodic-nonergodic transition (ENET), whereas within this region it is controlled by first- and second-order dissipative phase transitions (DPTs). We employ Liouvillian spectral theory to quantify the critical slowing down associated with the DPTs, and use the Wigner function to characterize the properties of the cavity field in the vicinity of criticality. We optimize the charging process via reinforcement learning (RL) and reveal the physical mechanism underlying performance enhancement from the perspective of ergodic and nonergodic phase dynamics. Our results offer a feasible pathway for manipulating and optimizing quantum battery performance based on intrinsic PT behaviors.

Comments
13 pages,10 figures

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Phase transitions (PTs) in quantum many-body systems offer a powerful route to manipulate the performance of quantum batteries (QBs). Here, we investigate an anisotropic Dicke QB with Kerr nonlinearity, focusing on the role of PTs in the charging process of the QB system. By analyzing how the Kerr nonlinearity reshapes the cavity level-spacing structure, we find that multiple near-degeneracies emerge at specific nonlinearity strengths. Away from the region of multiple near-degeneracies, the stable stored energy is governed primarily by the ergodic-nonergodic transition (ENET), whereas within this region it is controlled by first- and second-order dissipative phase transitions (DPTs). We employ Liouvillian spectral theory to quantify the critical slowing down associated with the DPTs, and use the Wigner function to characterize the properties of the cavity field in the vicinity of criticality. We optimize the charging process via reinforcement learning (RL) and reveal the physical mechanism underlying performance enhancement from the perspective of ergodic and nonergodic phase dynamics. Our results offer a feasible pathway for manipulating and optimizing quantum battery performance based on intrinsic PT behaviors.
Quantum batteries are energy-storing devices, governed by quantum mechanics, that promise high charging performance thanks to collective effects. Because of its experimental feasibility, the Dicke battery-which comprises N two-level systems coupled to a common photon mode-is one of the most promising designs for quantum batteries. However, the chaotic nature of the model severely hinders the extractable energy (ergotropy). Here, we use reinforcement learning to optimize the charging process of a Dicke battery either by modulating the coupling strength, or the system-cavity detuning. We find that the ergotropy and quantum mechanical energy fluctuations (charging precision) can be greatly improved with respect to standard charging strategies by countering the detrimental effect of quantum chaos. Notably, the collective speedup of the charging time can be preserved even when nearly fully charging the battery.
A quantum battery (QB) is an energy storage and extraction device that is governed by the principles of quantum mechanics. Here we propose a three-level Dicke QB and investigate its charging process by considering three quantum optical states: a Fock state, a coherent state, and a squeezed state. The performance of the QB in a coherent state is significantly superior to that in a Fock or squeezed state. We show that the locked energy is positively related to the entanglement between the charger and the battery, and diminishing the entanglement increases the ergotropy. The role of quantum phase transitions in the charging process of the QB system is analyzed and we find that the behavior of maximum stored energy is jointly determined by ground and excited-state quantum phase transitions. We further demonstrate that, no matter what the initial state is, the stored energy can be completely extracted when NNN is small (N=10N=10N=10), far below the thermodynamic limit, and the charging power follows a behavior consistent with that of the stored energy.
High-power Dicke quantum batteries (QBs) typically exploit collective superradiance, whereas intrinsic matter-matter interactions are conventionally considered detrimental. Here, we propose a counterintuitive paradigm: these interactions can be controlled and repurposed as a synergistic resource to enhance charging power and capacity. In the low-excitation limit, transverse interactions induce collective spin squeezing, causing critical mode softening and an exponential enhancement of effective coupling, which significantly boosts charging power. At higher excitations, these interactions act as a macroscopic nonlinear torque. By appropriately aligning this torque, we effectively lower phase-space dynamical barriers, guiding the system along optimal rapid-charging paths. Importantly, this cooperative enhancement remains highly robust under realistic dissipation, outperforming ideal, dissipationless Dicke QBs in specific regimes. Our results provide a blueprint for exploiting matter interactions to design dissipation-resistant, high-performance many-body QBs.
We investigate the performances of multiphoton anisotropic Dicke quantum battery (QB), which couples a finite number NNN of identical and independent two-level systems (TLSs) to a unique cavity mode. Each transition of TLS is accompanied by the absorption or emission of lll photons from the cavity mode. In this model, the coupling constants of rotating and counterrotating wave terms are independent. Therefore, we utilize this interesting property to investigate the role of counterrotating wave terms and find that the higher the proportion of counterrotating wave terms, the higher the average power. Moreover, it is shown that the charging process is progressively faster by increasing the coupling strength from the weak to the ultrastrong and deep strong coupling regime. In the deep strong regime, the anti-Tavis-Cummings (ATC) coupling can almost achieve the optimal energy storage in a short time, which can be used to realize the feasibility of QB. Furthermore, we also analyze the effects of multiphoton interaction and single-multiphoton mixing process on the battery performances.
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.
Criticality is widely used to enhance energy storage in quantum batteries. Two criticalities are compared here, one spectral and one dynamical. We ask two questions. Where does the enhancement that criticality brings to a quenched battery come from? And does the best charging performance require a critical point or a critical time? In the anisotropic XY chain, whose dynamics decomposes into independent momentum sectors, the weight each sector transfers to its upper level organizes the response. A closing spectral gap reshapes that weight near the closing momentum, so the stored energy responds sharply and controllably to the quench parameters. What it supplies is tunability rather than a larger maximum. A dynamical quantum phase transition (DQPT) marks the time at which the evolving state becomes orthogonal to its initial state, where the stored energy stays smooth, and equals the energy maximum when the final precession frequencies coincide, as for a flat band away from the critical field. The interacting Ising chain has no momentum sectors, yet its energy maximum and its return peak separate by a tunable margin. Weak quenches reduce the stored energy to the static susceptibility of the quenched operator. These results identify what optimization acts on, the distribution of transition weights and the spread of precession frequencies, and turn the weak-quench response into a probe of the transition order.