Scrambling-Enhanced Quantum Battery Charging in Black Hole Analogues

TL;DR

The paper investigates scrambling-enhanced charging in a black-hole analogue realized by a 1D isotropic XY chain with position-dependent hopping that encodes curved spacetime. A scrambling-quench protocol changing the horizon parameter from $x_{h0}$ to $x_{ht}$ modulates the noncommutativity of the Hamiltonians, leading to higher maximal stored energy $E_{\max}$ and maximal power $P_{\max}$ when $x_{ht}>x_{h0}$, with the optimal charging time $\tau_{*}$ decreasing as scrambling strengthens; ergotropy aligns with stored energy due to near-ground-state final states, and OTOCs reveal exponential growth tied to scrambling intensity. The approach relies on a mapping to an effective Hubbard model with site-dependent hopping and uses bandwidth regularization to study robustness, finding that the qualitative advantage persists despite reduced scrambling strength. Experimentally, superconducting qubit arrays with tunable couplers can realize the XY chain and scrambling-quench dynamics, enabling verification of the predicted acceleration and energy-transfer improvements in quantum batteries. Overall, the work demonstrates how gravitational analogue scrambling can be engineered to optimize quantum-energy storage devices, with implications for quantum thermodynamics and information scrambling in engineered quantum systems.

Abstract

Black holes constitute nature's fastest quantum information scramblers, a phenomenon captured by gravitational analogue systems such as position-dependent XY spin chains. In these models, scrambling dynamics are governed exclusively by the hopping interactions profile, independent of system size. Utilizing such curved spacetime analogues as quantum batteries, we explore how the black hole scrambling affects charging via controlled quenches of preset scrambling parameters. Our analysis reveals that the intentionally engineered difference between post-quench and pre-quench scrambling parameters could significantly enhance both maximum stored energy $E_{\max}$ and peak charging power $P_{\max}$ in the quench charging protocol. Furthermore, the peaks of extractable work and stored energy coincide. This is because the system's evolution under a weak perturbation remains close to the ground state, resulting in a passive state energy nearly identical to the ground state energy. The optimal charging time $τ_*$ exhibits negligible dependence on the preset initial horizon parameter $x_{h0}$, while decreasing monotonically with increasing quench horizon parameter $x_{ht}$. This temporal compression confines high-power operation to regimes with strong post-quench scrambling $x_{ht} > x_{h0}$, demonstrating accelerated charging mediated by spacetime-mimicking scrambling dynamics.

Figures (8)

• Figure 1: Schematic diagram of the charging process: The quantum battery employs a nearest-neighbor hopping XY spin chain architecture. Green spheres represent individual spin qubits, interconnected by tunable couplers. Distinct coupling distribution groups are represented by unique colors.Notably, the coupling distribution during the charging process differs from that observed in the non-charging process.
• Figure 2: Variation of the fitted Lyapunov exponent $\lambda$ as a function of the horizon parameter $x_h$. We select metric function $f(x)=x^2(1-x_h/x)$ such that the Hawking temperature is given by $T=x_h/(4\pi)$. The theoretical chaos bound is represented by the blue curve, while the numerical data is depicted as green dots with red error bars. The size of system set L=250.
• Figure 3: The plot of maximum stored energy $E_{\text{max}}$ versus initial scrambling parameter $x_{h0}$ and quench scrambling parameter $x_{ht}$, with values represented by bar height or color (red to blue). The system size is set to $L = 250$.
• Figure 4: The plot of maximum ergotropy $\mathcal{E}_{\text{max}}$ versus initial scrambling parameter $x_{h0}$ and quench scrambling parameter $x_{ht}$, with values represented by bar height or color (red to blue). The system size is set to $L = 250$.
• Figure 5: Impact of quenched scrambling parameters on different performance metrics: (a) maximum charging power $P_{\text{max}}$ and (b) optimal charging time $\tau_{*}$. The system size is fixed at $L=250$.