Superradiance and Subradiance in an Inhomogeneously Broadened Ensemble of Two-Level Systems Coupled to a Low-$Q$ Cavity

The collective spontaneous emission of a fully inverted inhomogeneously broadened ensemble of $N$ two-level systems coupled to a single-mode low-$Q$ cavity is investigated numerically using Monte Carlo wave function technique. An intrinsically bi-exponential emission dynamics is found when the time scales of superradiance ${\tau }_{\mathrm{sr}}$ and inhomogeneous dephasing $T_2^{*}\sim 1/\Delta {\omega }_{\mathrm{inh}}$ become comparable: a fast superradiant is followed by a slow subradiant decay. Experimental configurations using ensembles of quantum dots coupled to optical microcavities are proposed as possible candidates to observe the combined superradiant and subradiant energy relaxation.

Figure 1

An inhomogeneously broadened ensemble of $N$ two-level systems coupled to a single damped cavity mode: general schematic in frequency domain (a) and possible experimental configurations in semiconductor cavity QED such as semiconductor quantum dots in a microdisc cavity (b) or 2D-photonic crystal cavity (c), or semiconductor nanocrystals linked via spacer molecules to the surface of a metallic nanoshell cavity (d).

Figure 2

Temporal evolution of squared polarization $⟨J_{+}{J}_{-}⟩$ for an ensemble of 10 initially inverted atoms for different $\alpha$ on a linear scale (a) and a logarithmic scale (b) ($\alpha =10$ corresponds to superradiance; $\alpha =0$ represents uncorrelated spontaneous emission).

Figure 3

Temporal evolution of atomic energy $W$ and correlated part of atomic polarization $⟨J_{+}{J}_{-}{⟩}_{\mathrm{corr}}$ for different $\alpha$.

Figure 4

Dynamics of the probabilities $p_k(t)$ of having $k$ inverted atoms for $\alpha =1$ (at $t=0$ all 10 atoms are inverted).