From Superradiance to Superabsorption: An Exact Treatment of Non-Markovian Cooperative Radiation

TL;DR

The paper addresses how memory effects in a structured environment alter cooperative radiation from an ensemble of $N$ two-level atoms in a Lorentzian cavity. It develops exact results for $N=1$ and $N=2$ and then employs a pseudomode mapping with a weak symmetry to solve up to $N=10^3$ exactly, uncovering three regimes controlled by the spectral width $\lambda$: Markovian superradiant bursts, non-Markovian spontaneous superabsorption, and pulsed critical emission. It shows that the conventional $I_{\max}\propto N^2$ scaling degrades to a subquadratic $I_{\max}\propto N^{3/2}$ in the large-$N$ limit, while spontaneous reabsorption also scales superlinearly with $N$, highlighting a memory-driven enhancement of absorption. These results reveal a deep link between environmental memory and cooperativity, with potential implications for energy recycling and cavity-based non-Markovian quantum devices.

Abstract

We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to $10^3$ emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.

Figures (8)

• Figure 1: Visual representation of the physical model. $N$ identical two-level atoms interact with a resonant QED cavity mode with losses modeled by the spectral density \ref{['spectraldensity']}. The energy gap between the ground state $\hbox{$| g \rangle$}$ and the excited state $\hbox{$| e \rangle$}$ is given by $\omega_0$ (units of $\hbar=1$). The atoms are assumed to be close enough to experience the same phase of the electromagnetic field, but not so close as to interact significantly with each other. Orbital shapes are used for illustrative purposes only.
• Figure 2: Decay rate (left) and radiated intensity (right) for a single atom for $\lambda$ below, equal to, and above the critical value $\lambda_{\rm crit}=\sqrt{2}\gamma_0$. All quantities are in units of $\omega_0=1$.
• Figure 3: From left to right: canonical decay rates for $\lambda<\lambda_{\rm crit}$, $\lambda=\lambda_{\rm crit}$ and $\lambda>\lambda_{\rm crit}$, and corresponding radiated intensities. The value $\gamma_0 = 0.001\omega_0$ is chosen. At all times, at least one canonical decay rate is negative. For $\lambda<\lambda_{\rm crit}$ the radiated intensity also becomes negative during certain time intervals, indicating reabsorption. All quantities are in units of $\omega_0=1$.
• Figure 4: Decay rates $\tilde{\gamma}_m(t)$ (non-canonical) for jump operators $\tilde{L}_m$ given by powers of $J_\pm$. We see that $\tilde{\gamma}_1$ remains positive for all $t$ (left), leading to one-step decays throughout the Dicke state hierarchy (right, black arrows). The remaining decay rates, associated with higher-order powers of $J_\pm$, can be positive or negative depending on time, effectively resulting in lowering (solid arrows) and raising (dashed arrows) processes across the Dicke state hierarchy, respectively. The same values of $\lambda$ and $\gamma_0$ as in Fig. \ref{['Fig:2']} have been taken. All quantities are in units of $\omega_0=1$.
• Figure 5: Radiated intensity ($N=50$) for $\lambda$ below, above and equal to the critical value $\lambda_{\rm crit}$ (left), and $\lambda_{\rm crit}/\gamma_0$ as a function of $N$ (right). For $\lambda>\lambda_{\rm crit}$ (green line) a single burst is observed. For $\lambda<\lambda_{\rm crit}$ (blue line) there are times at which $I<0$, indicating reabsorption of excitations by the atoms. At $\lambda=\lambda_{\rm crit}$ (red line) pulsed emission without reabsorptions is observed. The value of $\lambda_{\rm crit}$ increases monotonically with $N$ from $N=2$ to $N=100$ (right plot). In these figures, the value $\gamma_0 = 0.001\omega_0$ is taken. All quantities are in units of $\omega_0 = 1$.