Superradiance in dense atomic samples

TL;DR

This work develops a Holstein-Primakoff and mean-field approach to superradiance in dense atomic ensembles with dipolar interactions, deriving master equations for both strong and weak reservoir coupling. In the weak-coupling regime, the results recover Dicke superradiance with enhanced intensity and shortened emission times due to collective effects, scaled by the interatomic coupling parameter $\alpha$. In the strong-coupling regime, a novel comb of ultra-short superpulses emerges, enveloped by a shorter overall emission timescale, with internal pulse spacing set by $\omega_0$ and the coupling $\alpha$. The study highlights the critical roles of dipolar interactions and reservoir coupling in shaping collective emission and points to experimental avenues for engineering dense-sample radiation with potential applications in lasers and quantum sensing.

Abstract

Here we present an approach to the problem of superradiance in dense atomic samples, when dipolar interactions arise between atoms. Our treatment consists of the sequential use of the Holstein-Primakoff and mean-field approximations, from which we derive master equations for the strong and weak couplings of the sample with the reservoir. We find, in both cases, that the radiation emission presents remarkable features, with characteristic emission times much shorter and intensities much higher than those of Dicke superradiance. In particular, for strong sample-reservoir coupling, a whole comb of superpulses occurs within an envelope with the above-mentioned characteristic emission times much shorter and intensities much higher than those of Dicke superradiance.

Figures (8)

• Figure 1: Plot of the scaled (a) mean energy $\varepsilon(t)/\omega_{0}$ and (b) intensity $\mathcal{I}(t)/(\gamma\omega_{0})$ against $\gamma t$, for $N=10^{4}$, $\omega_{0}=10^{6}\gamma$, and $g=10^{2}\gamma$.
• Figure 2: Plot of the scaled (a) mean energy $\varepsilon(t)/\omega_{0}$ and (b) intensity $\mathcal{I}(t)/(\gamma\omega_{0})$ against $\gamma t$, for $N=10^{4}$, $\omega_{0}=10^{5}\gamma$, and $g=10^{2}\gamma$.
• Figure 3: Plot of the scaled (a) mean energy $\varepsilon(t)/\omega_{0}$ and (b) intensity $\mathcal{I}(t)/(\gamma\omega_{0})$ against $\gamma t$, for $N=10^{4}$, $\omega_{0}=10^{6}\gamma$, and $g=10^{3}\gamma$.
• Figure 4: Plot of the scaled (a) mean energy $\varepsilon(t)/\omega_{0}$ and (b) intensity $\mathcal{I}(t)/(\gamma\omega_{0})$ against $\gamma t$, for $N=10^{6}$, $\omega_{0}=10^{6}\gamma$, and $g=10^{2}\gamma$.
• Figure 5: Plot of the scaled (a) mean energy $\varepsilon(t)/\omega_{0}$ and (b) intensity $\mathcal{I}(t)/(\gamma\omega_{0})$ against $\gamma t$, for $N=10^{7}$, $\omega_{0}=10^{6}\gamma$, and $g=10^{2}\gamma$.