Dynamical Criticality Behind Energy-Storage Singularities in Quantum Batteries

TL;DR

This paper reveals that dynamical criticality in momentum space governs energy-storage singularities in quantum batteries, linking dynamical quantum phase transitions to optimal charging channels and energy storage control.

Contribution

It introduces a mode-resolved framework connecting dynamical criticality and quantum-battery charging, demonstrating how DQPTs optimize energy storage at the microscopic level.

Findings

Dynamical critical momentum causes nonanalytic energy dependence on quench strength.

Critical modes exhibit maximal stored energy and zero power at DQPT times.

Charging signal-to-noise ratio sharply peaks at critical times, probing DQPT.

Abstract

Energy-storage singularities in quantum batteries are often associated with equilibrium quantum criticality. Here we show that, in quench-driven many-body batteries, such singularities can originate from dynamical criticality in momentum space. Using the transverse-field Ising chain as a representative free-fermion quantum battery, we develop a momentum-resolved description of the charging process. The long-time stored energy forms a dephasing plateau whose dependence on the quench strength becomes nonanalytic when a real dynamical critical momentum emerges. More generally, for free-fermion two-band quantum batteries, each momentum sector acts as an independent coherent charging channel, and the condition for a dynamical quantum phase transition (DQPT) is equivalent to perfect normalized charging of the critical mode. At the critical times, this mode has a vanishing Loschmidt amplitude, maximal normalized stored energy, and zero instantaneous power at the turning point between energy absorption and backflow. We further show that the single-mode charging signal-to-noise ratio (SNR) develops sharp signatures at the same critical times, providing a direct charging-based probe of DQPT. Thus, nonequilibrium criticality does not simply enhance the total stored energy or power, which remain shaped by noncritical modes, but reorganizes energy storage by selecting optimal microscopic charging channels. Our results establish a mode-resolved connection between DQPT and quantum-battery charging, suggesting a route toward controlling many-body energy storage through dynamical criticality.