Collective Quantum Batteries and Charger-Battery Setup in Open Quantum Systems: Impact of Inter-Qubit Interactions, Dissipation, and Quantum Criticality

TL;DR

This work investigates three two-qubit open-quantum-system configurations to assess quantum battery performance under dissipation and interactions. It analyzes (i) two central spins with XXX or DM couplings to independent spin baths, (ii) a two-qubit collective decoherence battery driven by a squeezed thermal bath with distance- and temperature-dependent effects, and (iii) a charger–battery setup where a central-spin charger interacts with an XY-spin-chain bath near a quantum critical point. Key findings show that XXX coupling can yield higher long-time ergotropy despite an initial rapid discharge, collective decoherence slows ergotropy decay and preserves coherence, and criticality at the charger end ($$\lambda_c = 1$$) leads to rapid ergotropy dissipation and reduced charging effectiveness. These results highlight strategies for robust quantum batteries in realistic environments and underscore how bath-induced criticality can modulate energy storage dynamics in open quantum systems.

Abstract

Quantum batteries have emerged as promising platforms for exploring energy storage and transfer processes governed by quantum mechanical laws. In this work, we study three models of two-qubit open quantum systems. The first model comprises two central spins immersed in spin baths, and both central spins are collectively considered as quantum batteries. The impact of inter-qubit interactions on the performance of the quantum battery is investigated. In the second model, a two-qubit model interacting with a squeezed thermal bath serves as a collective quantum battery, where the impact of inter-atomic distance and the bath temperature on the battery's performance is explored. Furthermore, a two-qubit model is used, where one qubit is modeled as a battery and the other as a charger. The charger in this model interacts with an anisotropic spin-chain bath, which is conducive to quantum criticality. It is demonstrated that this criticality has a substantial impact on the quantum battery's storage capacity.

Figures (10)

• Figure 1: Variation of the ergotropy for the two central spin quantum battery for both DM and Heisenberg XXX interactions. The parameters are taken to be: $\omega_1= 1.15, \omega_2 = 1.25, \omega_a = 1.1, \omega_b = 1.2, g_{12} = 0.75, \epsilon_1 = \epsilon_2 = 0.5, \beta_a = 4, \beta_b = 1$, and $M= N= 8$.
• Figure 2: Variation of the charging power $\mathcal{P}(t)$, Eq. \ref{['eq_charging_power']}, and average (dis-)charging power $\overline{\mathcal{P}}$, Eq. \ref{['eq_avg_charging_power']}, for the two central spin quantum battery for both DM and Heisenberg XXX interactions. The triangle and square markers show the average (dis-)charging power for DM and XXX inter-qubit interactions, respectively. The parameters are taken to be: $\omega_1= 1.15, \omega_2 = 1.25, \omega_a = 1.1, \omega_b = 1.2, g_{12} = 0.75, \epsilon_1 = \epsilon_2 = 0.5, \beta_a = 4, \beta_b = 1$, and $M= N= 8$.
• Figure 3: Ergotropy dynamics for the two-qubit collective decoherence quantum battery. The initial two-qubit state is considered a product state $\ket{0+}$. (a) and (b) correspond to a squeezed thermal bath at temperature $T=5$ with squeezing parameters $r = 0.5$ and $\Phi = \tfrac{\pi}{4}$, while Figures (c) and (d) show the vacuum bath case. Subplots (a) and (c) depict results for $k_{0}r_{ij}=0.1$ (collective decoherence) and (b) and (d) are for $k_{0}r_{ij}=1.2$ (independent dissipation). The other parameters are: $\omega_{1} = \omega_{2} = 1.0$, $\mu r_{ij} = 0$, $\Gamma_{1} = \Gamma_{2} = 0.05$.
• Figure 4: Variation of ergotropy with the interatomic distance $r_{ij}$ at a given time $t = 2$ for the two-qubit collective decoherence battery. The initial state of the two qubits is taken to be the Bell-state $\frac{1}{\sqrt{2}}\left(\ket{01} - \ket{10}\right)$. The squeezed thermal bath parameters are: (a) $T=5$, $r=0.5$, $\phi = \frac{\pi}{4}$, and (b) $T=0.4$, $r=0.5$, $\phi=\frac{\pi}{4}$. Further, $\omega_{1} = \omega_{2} = 1.0$, $\mu r_{ij} = 0$, $\Gamma_{1} = \Gamma_{2} = 0.05$.
• Figure 5: Variation of ergotropy with temperature for the 2-qubit system in interaction with a squeezed thermal bath at time $t=2$ with squeezing parameters $r = 0.5$ and $\Phi = \tfrac{\pi}{4}$. (a) depicts results for $k_{0}r_{ij}=0.05$ (collective decoherence) and (b) for $k_{0}r_{ij}=1.1$ (independent dissipation). The other parameters are: $\omega_{1} = \omega_{2} = 1.0$, $\mu r_{ij} = 0$, $\Gamma_{1} = \Gamma_{2} = 0.05$.