Superradiant laser: Effect of long-ranged dipole-dipole interaction

We theoretically investigate the effect of long-ranged dipole-dipole interaction (LRDDI) on a superradiant laser (SL). This effect is induced from the atom-photon interaction in the dissipation process. In the bad-cavity limit usually performed to initiate SL, we demonstrate that cavity photon number oscillates as an inter-particle distance of the atoms varies. Similarly the atom-atom coherence alternates with signs, showing critical transitions alternatively in SL operations. This suggests a complexity of the collective effect emerging in a large ensemble of atoms. Therefore this effect in a SL can not be simply interpreted by only a part of the whole ensemble. We numerically solve for a steady state SL including the spatially-dependent LRDDI, and locate the maximal cavity photon number and the minimal spectral linewidth respectively at the optimal atomic separations in the setting of an equidistant atomic array. The scaling of a finite number of atoms shows an outperformed steady state SL than the one without LRDDI, which allows for probing narrow atomic transitions and is potentially useful for precision measurements and next generation optical clocks.