Saturable nonlinearities in a driven-dissipative bosonic quantum battery

Abstract

We investigate the charging of a nonlinear quantum battery consisting of a single bosonic mode subject to a saturable nonlinearity, coherent driving, and dissipation. In contrast to Kerr-type anharmonicities, the saturable interaction induces a bounded and nonlinear distortion of the energy spectrum, leading to a progressive increase in the density of energy levels. We analyze the time evolution of the energy and ergotropy of the battery by solving a Lindblad master equation and show that the nonlinear spectral structure significantly affects both transient charging behavior and steady-state properties. Our results reveal that, for a broad range of parameters, the saturable nonlinearity enhances the maximum stored energy and modifies the ergotropy generation in the presence of losses. The interplay between dissipation and bounded spectral nonlinearity provides a controllable mechanism to tune energy storage and work extraction in bosonic quantum batteries.

Figures (5)

• Figure 1: Eigenvalues $E_n = \omega n + n\chi / (1 + nn_s)$ of the nonlinear QB as a function of $n_s$ for $\chi = \omega = 1$.
• Figure 2: Energy $E(\tau) = \text{Tr}[H_B\rho(\tau)]$ (continuous lines) and ergotropy $\mathcal{E}(\tau)$ (dashed lines) of the nonlinear QB as a function of time $\tau$ for several values of the saturable parameter $n_s$. The orange dots denote the maximum values for $n_s = 0.3$ and $n_s = 1.5$. The other parameters used for this plot are given by $\omega = 1$, $\Delta = 0.1$, $\chi = 1$, $\alpha = 0.5$ and $\gamma = 0.2$.
• Figure 3: Maximum values of the energy $E(\tau) = \text{Tr}[h_B\rho(\tau)]$ of the nonlinear QB as a function of the saturable parameter $n_s$ for $\gamma = 0.2$ (continuous blue) and $\gamma = 0.4$ (dashed orange). The other parameters are the same as in Fig. \ref{['fig1']} with the exception of $\tau$ which takes the maximum value of 100 in this plot.
• Figure 4: Wigner function $W(\beta)$ during charging for several times. For this plot we take $n_s = 1$, $\alpha = 0.3$ and $\gamma = 0.01$. Other parameters are the same as in Fig. \ref{['fig2']}.
• Figure 5: Energy $E_{ss}(\infty) = \text{tr}(h_b\rho_{ss})$ and ergotropy $\mathcal{E}_{ss}(\infty) = \text{tr}(h_b\rho_{ss}) - \text{tr}(h_b\sigma_{ss})$ of the steady state $\rho_{ss}$, where $\sigma_{ss}$ is the passive state of $\rho_{ss}$, as a function of $n_s$. Other parameters are the same as in Fig. \ref{['fig2']}.