Charging Dicke and Tavis--Cummings quantum batteries with a $\mathcal{PT}$-symmetric lossy--gain cavity pair

We study how a parity--time-symmetric photonic environment changes the charging of Dicke and Tavis--Cummings quantum batteries. For atoms prepared in the collective ground state the excitation number grows as the square of the charging time, with a coefficient set by the initial mean photon number;