Charging of a Quantum Battery by a Single-Photon Quantum Pulse

TL;DR

The paper studies charging a quantum harmonic-oscillator battery via a traveling single-photon pulse, mediated by a two-level system, in an open-quantum-system setting. Analytical solutions for the dynamics yield an optimal pulse shape that saturates the energy-storage bound set by TLS decay rates, i.e., an upper limit on stored energy. A quantum speed limit is established at the exceptional point where fastest non-oscillatory charging occurs, and there are closed-form expressions for the minimum time and the power-optimal envelope. The results are directly applicable to optical and microwave platforms with realistic pulse shaping and can be extended to few-photon charging.

Abstract

We study a minimal model for charging a quantum battery consisting of a two-level system (TLS) acting as a charger, coupled to a harmonic oscillator that serves as the quantum battery. A single-photon quantum pulse of light excites the TLS, which subsequently transfers its excitation to the isolated battery. The TLS may also decay into the electromagnetic environment. We obtain analytical solutions for the dynamics of the battery and determine the optimal pulse shape that maximizes the stored energy. The optimal pulse saturates a universal bound for the stored energy, determined by the TLS decay rates into the pulse and the environment. Furthermore, we derive the minimum charging time and establish a quantum speed limit at the exceptional point, where a critical transition occurs in the system's dynamics. We also present analytical expressions for the charging power and investigate the pulse duration that maximizes it.

Figures (7)

• Figure 1: Illustration (not to scale) of charging a harmonic oscillator as a battery with a single-photon pulse. $\Gamma$ ($\Gamma_\perp$) captures the interaction strength with the pulse (environment). The parameter $\omega_b$ denotes the frequency of the harmonic oscillator. The parameter $f$ is the coherent coupling strength governing the exchange of single excitations between the TLS and the harmonic oscillator.
• Figure 2: Optimal pulse shapes $\xi_{\mathrm{opt}}(\tau)$ for different values of $f/\Gamma$, plotted as a function of time. The coupling of the atom (charger) to the environment is set to $\Gamma_\perp = 0$.
• Figure 3: Time evolution and key features of $|\alpha_1^b(t)|^2$ for a optimal input pulse ($\Gamma_\perp = 0$ i.e. $f_{EP}=\Gamma/4$).
• Figure 4: (a) Normalized pulse shapes $\xi(\tau)$ on a timescale set by $\Gamma$, all satisfying $\Gamma T_\sigma = 2\sqrt{3}$. (b) Time-dependent excitation probability $|\alpha_1^b(t)|^2$ at the exceptional point (EP). We assume $\Gamma_\perp = 0$ and optimal coupling $f_{EP} = \Gamma/4$.
• Figure 5: Maximum excitation probability ($|\alpha_1^b(t_m)|^2$) as a function of the dimensionless quantities of $\Gamma T$ and $f/\Gamma$ for a Gaussian input pulse. The decay to the environment is (a) $\Gamma_\perp = 0$ (i.e. $f_{EP}=\Gamma/4$), (b) $\Gamma_\perp = 0.5\Gamma$ (i.e. $f_{EP}=3\Gamma/8$), and (c) $\Gamma_\perp = \Gamma$ (i.e. $f_{EP}=\Gamma/2$) . Vertical dashed lines in panels: guides for the eye at the EP.