Thermodynamics of a biophotomimetic nonreciprocal quantum battery

Abstract

We propose a theoretical model of a fully functional nonreciprocal quantum battery inspired by the architecture of bacterial light-harvesting complexes. We assign functional roles to collective quantum optical subradiant and superradiant states and introduce a unimodal cavity to assist storage. The transition rates are obtained from an effective non-Hermitian Hamiltonian, tailored to the battery geometry which are fed into a master equation to unravel the time evolution. We investigate the complete thermodynamic performance including storage, leakage, ergotropy, work extraction, flux, and power. We observe optimization at different ring sizes, each peaking at its specific energetic function. Strong coupling between the ring and central system enhances the battery's ability to store energy but reduces the ability of power output. The ergotropy exceeds capacity and approaches it linearly with increasing system size, with an optimal small-size regime that disappears under strong coupling.

Figures (5)

• Figure 1: (a) Schematic representation of the quantum battery. The manifold $\{|+\rangle, |-\rangle, |g\rangle\}$ is coupled to a charging reservoir at temperature $T_c$, while the states $\{|\alpha\rangle, |\beta\rangle\}$ are coupled to a unimodal cavity at a temperature $T_w$. The red arrows denote charging, the green arrows denote leakage, and the blue arrows denote storage. (b) Light-harvesting-inspired geometry of $N_R$ number of two-level systems (whose decay rate is $\Gamma$) arranged in the form of an equally spaced symmetric ring and coupled to a central two-level system (detuning $\Delta$, decay rate $\Gamma_0$). The collective eigenstates of the coupled system give rise to bright (superradiant, $|+\rangle$) and dark (subradiant, $|-\rangle$) states and can be estimated from Eq. (2).
• Figure 2: Scaled decay rates of the bright state, $\Gamma_{+}/\Gamma$, and the dark state, $\Gamma_{-}/\Gamma$, evaluated using Eq. (\ref{['eq:eigenvalues_split_rearranged']}). Parameters used are $\Omega=0.5$, $\Gamma=0.8$, $\Delta=0.5$, $J_d=2$, $\Gamma_d=0.0002$, and $\Gamma_0=0.5\tilde{\Gamma}_m$. We have set $\hbar,k_B\to 1$ so that natural units are employed in the numerics.
• Figure 3: (a) Stored-to-charged energy, $\langle H_S\rangle / \langle H_C\rangle$ as a function of the battery's dimensionless time evolution ($t\Gamma_+$) and ring-levels and central system coupling strength $J_d$. (b) Leaked-to-stored energy, $\langle H_L\rangle / \langle H_S\rangle$. (c) Stored passive-to-charged passive energy, $\langle H_S^{+}\rangle / \langle H_C^{+}\rangle$. (d) Leaked passive-to-stored passive energy, $\langle H_L^{+}\rangle / \langle H_S^{+}\rangle$. (e-h) Same quantities as in (a-d) shown as contour plots vs. number of ring levels $N_R$ and $J_d$.
• Figure 4: Variation of thermodynamic observables with the number of ring levels $N_R$ in the quantum battery model, (a) ergotropy, (b) work, (c) steady-state flux $j$, (d) output power and (e) capacity. (f) capacity Vs ergotropy with the number of ring levels $N_R$ and ring-levels and central system coupling strength $J_d$. To make each thermodynamic quantity dimensionless, these are plotted relative to the quantity's value with the smallest ring size $N_R =3$ and is denoted by a superscript, $^0$.
• Figure 5: Variation of thermodynamic observables with the number of ring levels $N_R$ and ring-levels and central system coupling strength $J_d$ in the quantum battery model, (a) capacity Vs ergotropy, (b) capacity (c) ergotropy, (d) work, (e) steady-state flux $j$ and (f) output power. To make each thermodynamic quantity dimensionless, these are plotted relative to the quantity's value with the smallest ring size $N_R =3$ and is denoted by a superscript, $^0$ at each value of $J_d$