Bridging the daemonic gap en route to charge multi-mode batteries via a single auxiliary

TL;DR

The work addresses how to harness daemonic advantage in charging quantum batteries by evolving a battery and an auxiliary charger together under a JC-type interaction and then extracting work by tracing out the charger. It introduces and analyzes the daemonic gap and daemonic band, showing that gapless charging is achievable for a single-mode harmonic battery with a qubit charger, across several passive initial states, and that repeating the charging cycle enables full charging and access to the entire daemonic band. The authors extend the design to multi-mode batteries with a qudit charger, demonstrating that sequential charging cycles are essential to simultaneously charge multiple modes. These findings provide a pathway to robust, measurement-assisted energy storage in continuous- and discrete-variable quantum systems, with implications for scalable quantum batteries.

Abstract

We show that harnessing daemonic advantage is possible while charging a quantum battery by first time-evolving the battery collectively with an auxiliary charger, followed by an energy extraction via tracing out the charger. We define the difference between the minimum daemonic ergotropy and the maximum ergotropy of the battery as the daemonic gap at the time where the ergotropy of the battery is maximum. Considering a harmonic mode as the battery and a qubit as the auxiliary charger interacting via Jaynes-Cummings interaction, we show that the daemonic gap can be closed for specific initial passive states of the battery, including the ground state, truncated mixtures of low-lying states, and canonical thermal states. We further define the daemonic band as the difference between the maximum and the minimum daemonic ergotropy, and show that starting from the ground state of the single-mode battery, the daemonic band collapses. We also show that achieving a complete charging, along with accessing the full daemonic band, is possible for the single-mode battery using all of the other initial states by repeating the charging cycle and maximizing ergotropy in every round. We extend the battery-charger design to a multi-mode resonator battery and a qudit charger, and demonstrate, for a double-mode battery and a qutrit charger, that repeating the charging cycle is vital for simultaneously charging individual modes of the collective battery.

Figures (8)

• Figure 1: Charging cycle. The battery (charger) is initialized in the state $\rho_b^{\text{in}}$ ($\rho_a^{\text{in}}$). The operation $U_{ab}$ entangles the battery and the charger, resulting in the state $\rho_{ab}$. This is followed by a measurement and subsequent discarding of the charger, leaving the battery in the state $\rho_b$ with ergotropy $\mathcal{E}$.
• Figure 2: Variations of $\omega^{-1}\overline{\mathcal{E}}(t)$ and $\omega^{-1}\mathcal{E}(t)$ against $t$.
• Figure 3: (a) Landscape of $\mathcal{A}(\tau,M_a)$ on the $(r_0^{(0)},\alpha)$ plane, indicating that the minimum occurs at $\alpha=0,\pi$$\forall r_0^{(0)}$. (b) Variations of $\overline{\mathcal{E}}_{\min}(\tau)$, $\mathcal{E}^{\max}$, and $\mathcal{L}(\tau)$ (inset) as functions of $\beta$. The trends of $\mathcal{E}^{\max}$ and $\overline{\mathcal{E}}_{\min}(\tau)$ against $\beta$ are fitted to Eqs. (\ref{['eq:fitted_1']}) and (\ref{['eq:fitted_2']}) respectively, with the fitting parameters given by $c_0=1.77$, $c_1=3.75$, $\overline{c}_0=1.94$, $\overline{c}_1=3.442$. To generate both plots (a) and (b), we have fixed $\omega=1$, $d_b=11$ and $g=1$.
• Figure 4: Schematic representation of repeated application of $\Lambda(.)$ on the battery-charger setup. See Sec. \ref{['subsec:repeated_charging']}.
• Figure 5: Full charging by repeating charging cycle. Variations of $\mathcal{E}^{\max}$ with increasing charging rounds $m$, where the duration of the time evolution in the $m$th round is $\tau_{(m)}$. The chosen initial states are (a) ground state of $b$ and truncated mixtures of two lowest lying states, (b) truncated mixtures of three levels, and (c) canonical thermal states. For (a) and (b), we fix $\delta=0.1$, while for (c), $\delta=0$. To generate the plots, we have fixed $\omega=1$, $d_b=11$ and $g=1$.

Theorems & Definitions (8)

• proof
• proof
• proof
• proof
• proof
• proof
• proof
• proof