Charging performance of quantum batteries based on intensity-dependent Dicke model

Recently, quantum battery based on various physical models from quantum optics model to spin model and its enhancement of charging performance have attracted increasing interest. It has been demonstrated that quantum entanglement is beneficial to the speedup of work extraction. In this paper, by an exact diagonalization approach, we investigate the charging performance of the field intensity-dependent Dicke model (also called intensity-dependent Dicke model) quantum battery, which consists of &lt;i&gt;N&lt;/i&gt; qubits collectively interacting with a single-mode cavity. The considered intensity-dependent Dicke model is a generalized Dicke model with a nonlinear-coupling fashion and different weights of energy conserved term and non-conserved term. Firstly, we consider the influences of energy non-conserved term (also called anti-rotating wave term) on the maximum stored energy and maximum charging power in quantum battery. It is shown that the maximum stored energy is not very sensitive to the increase of the weight of energy non-conserved term, but the maximum charging power undergoes a significant change with the increase of the weight of energy non-conserved term. We also show that the maximum charging power increases monotonically with the increase of coupling constant between qubits and cavity, but the maximum stored energy is not monotonically related to the increase of coupling constant. Then, we further examine in detail the characteristics of the maximum stored energy, charging time, energy quantum fluctuation and maximum charging power in the quantum battery under the same weight between energy conserved term and non-conserved term. By comparing the charging performances of quantum battery based on the single-photon-Dicke model with those based on the two-photon-Dicke model, we find that the performances, specifically, the charging time and maximum charging power of the intensity-dependent Dicke quantum battery are better than those of single-photon Dicke quantum battery, but weaker than those of two-photon Dicke quantum battery. Of particular interest is that the relationship of maximum charging power with large quantum cell number in intensity-dependent Dicke quantum battery has the same form as that in the two-photon Dicke quantum battery, i.e. their maximum values of charging power are both proportional to the large quantum cell number squared, specifically, &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ P_{\mathrm{max}}^{\mathrm{ID}}\propto N^2 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ P\mathrm{_{max}^{2ph}}\propto N^2 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, which are consistent with the upper bound given by the paper (Gyhm J, Šafránek D, Rosa D &lt;ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevLett.128.140501"&gt; 2022 &lt;i&gt;Phys. Rev. Lett.&lt;/i&gt; &lt;b&gt;128&lt;/b&gt; 140501&lt;/ext-link&gt;). It is worthwhile to mention that Dou et al. (Dou F Q, Zhou H, Sun J A &lt;ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevA.106.032212"&gt; 2022 &lt;i&gt;Phys. Rev. A&lt;/i&gt; &lt;b&gt;106&lt;/b&gt; 032212&lt;/ext-link&gt;) showed that using the quantum advantage of maximum charging power in the quantum battery based on cavity Heisenberg-spin-chain model &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ P\mathrm{_{max}}\propto N^2 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; can be obtained. Therefore, this study of the charging performance based on the intensity-dependent Dicke quantum battery may provide an alternative approach to the further research on quantum battery.