Electromagnetically Induced Transparency Effect Improves Quantum Battery Lifetime

TL;DR

The paper addresses decoherence-induced degradation in quantum batteries by integrating a four-level atom QB with a coupled-cavity array charger and employing electromagnetically induced transparency to create a dark state $|E_1\rangle$. This dark state, together with bound-state formation when the QB energy $E_1$ lies within the cavity-band, yields strong dissipation suppression and enables coherent energy transfer, described by the effective Hamiltonian $H_{\mathrm{eff}}=E_1|E_1\rangle\langle E_1|+J\sum_k(a_k^{\dagger}|g\rangle\langle E_1|+\mathrm{h.c.})$ with $J=g/\sqrt{N}$. The key results show that two bound states arise inside the band, producing Rabi-like oscillations and a significantly reduced decay rate $\kappa'$, with the ergotropy maximized when $\omega_0\approx\mathrm{Re}(E_1)$ and an optimal inter-cavity coupling $\xi$ further boosting performance. This work provides a concrete, experimentally accessible pathway to design high-efficiency QBs by suppressing environmental decoherence through EIT and bound-state engineering.

Abstract

Quantum battery (QB) is an application of quantum thermodynamics which uses quantum effects to store and transfer energy, overcoming the limitations of classical batteries and potentially improving performance. However, due to the interaction with the external environment, it will lead to decoherence and thus reduce the lifetime of QBs. Here, we propose suppressing the environmental dissipation in the energy-storage process of the QB by exploiting the electromagnetically-induced transparency (EIT) and bound states. By constructing a hybrid system composed of a four-level atom and a coupled-cavity array, two bound states are formed in the system when the energy of the QB is in the energy band of the cavity array. Due to the bound states and the EIT effect, the ambient dissipation is significantly suppressed, which improves the lifetime of the QB. In addition, we show that when the energy of the QB is in resonance with the cavity, the ergotropy of the QB reaches the maximum. Furthermore, there exists an optimal coupling strength between two neighbouring cavities which helps improve the performance of the QB. These discoveries may shed the light on the design of high-efficiency QBs.

Figures (7)

• Figure 1: Schematic illustration of charging QB model. (a) Structure of coupled cavities, (b)a four-level atom, where $|d\rangle$ is a metastable energy level, $|m\rangle$ is a auxiliary energy level and $|e\rangle$ is a excited state energy level. Two pulses are applied at the same time to induce the transitions of $|e\rangle \leftrightarrow |d\rangle$ and $|e\rangle \leftrightarrow |m\rangle$ with respectively Rabi frequency $\Omega_p$ and $\Omega_c$.
• Figure 2: The dependence of the energy of the bound states on the energy band and the energy $E_1$ of the QB. The blue solid line is the energy band $\omega_k=\omega_0-2\xi\cos (k)$ of the coupled-cavity array. The energies of the bound states denoted by the red and green dots are obtained by Eq. (\ref{['eq:15']}). The parameters used in the calculation are $\omega_0 = 20\xi$, $g = 0.3\xi$.
• Figure 3: Probability of the dark state $|E_1\rangle$ vs time $t$. (a) When $E_1$ is in the energy band of the coupled cavities, the analytical results obtained by Eq. (\ref{['eq:21']}) are denoted as the blue dots while the numerical results are denoted by the red solid line. In addition, the green dashed line is calculated using the Lindblad-form quantum master equation. The parameters are as follows, $E_1/\xi=35.327-0.032i$, $\omega_0 = 100\xi/3$, $\Omega_d=106\xi/3$, $\Omega_e=50\xi$, $\Omega_m=106\xi/3$, $\kappa=20\xi/3$, $\Omega_p=50\xi/3$, $\Omega_c=5\xi/3$, and the number of cavities $N=253$. (b) When $E_1$ is outside of the energy band of the coupled cavities, the numerical results denoted by green solid line are obtained by $E_1/\xi=66.6553 - 0.0287i$, $\omega_0 = 100\xi/3$, $\Omega_d=200\xi/3$, $\Omega_e=100\xi$, $\Omega_m=200\xi/3$, $\kappa=20\xi/3$, $\Omega_p=50\xi/3$, $\Omega_c=5\xi/3$, and $N=253$.
• Figure 4: The envelope of the probability of the dark state with/without two bound states vs time. The red dashed line denotes the case when there are two bound states. We use the function $\ln(P_{E_1})=-0.35309-2.6487\times10^{-2}\xi t$ to fit the data with the linear correlation coefficient $|r|$ = 0.99314. The blue solid line shows the case when there is no bound state with the corresponding linear correlation coefficient $|r|$ = 1.0000. Initially, the atom is in the state $\ket{m}$. The parameters are as follows, i.e., $E_1/\xi=35.327-0.032i$, $\Omega_d=106\xi/3$, $\Omega_e=50\xi$, $\Omega_m=106\xi/3$, $\kappa=20\xi/3$, $\Omega_p=50\xi/3$, $\Omega_c=5\xi/3$.
• Figure 5: The maximum ergotropy $\mathcal{W}_{\max}$ during the duration $[0,t_{\rm max}=15/\Omega_c]$ vs the coupling strength $\xi$ and the frequency $\omega_0$ of the cavity. The other parameters are $\Omega_d=21.2\Omega_c$, $\Omega_e=30\Omega_c$, $\Omega_m=21.2\Omega_c$, $\kappa=4\Omega_c$, $\Omega_p=10\Omega_c$, and $N=253$.