Scaling of energy and power in a large quantum battery-charger model

Abstract

We investigate a multi-qubit quantum battery-charger model, focusing on its potential emulation on a superconducting qubit chip. Using a large-spin representation, we first obtain the analytical form of the energy $E_B(t)$, power $P_B(t)$ and their maximum values, $E_B^{\max }$ and $P_B^{\max }$, of the battery part by means of the antiferromagnetic Holstein-Primakoff (AFM-HP) transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of $P_B^{\max }$ ensues. By further combining these with the ones obtained via exact diagonalization (ED), we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10,000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with growing number of charger qubits, or when both parts simultaneously grow, we classify the system size scalings of $E_B^{\max }$ and $P_B^{\max }$, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of $P_B^{\max }$ is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in superconducting qubit platforms, in particular ones that exhibit long-range couplings.

15 pages, 11 figures, newly added figures(Fig.3 and 11), major revision with the main conclusions unchanged

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• Variational quantum algorithm for ergotropy estimation in quantum many-body batteries
• Reservoir-assisted quantum battery charging at finite temperatures
• Cooperative isentropic charging of hybrid quantum batteries
• Quantum Charging Advantage in Superconducting Solid-State Batteries
• Cavity-Heisenberg spin-$j$ chain quantum battery and reinforcement learning optimization
• Magnetic Dipolar Quantum Battery with Spin-Orbit Coupling
• Excitation Spectra of one-dimensional spin-1/2 Fermi gas with an attraction
• Dissipative qutrit-mediated stable charging
• Cluster Ising quantum batteries can mimic super-extensive charging power