Cooperative Effects in Closely Packed Quantum Emitters with Collective Dephasing

In a closely packed ensemble of quantum emitters, cooperative effects are typically suppressed due to the dephasing induced by the dipole-dipole interactions. Here, we show that by adding sufficiently strong collective dephasing, cooperative effects can be restored. Specifically, we show that the dipole force on a closely packed ensemble of strongly driven two-level quantum emitters, which collectively dephase, is enhanced in comparison to the dipole force on an independent noninteracting ensemble. Our results are relevant to solid-state systems with embedded quantum emitters such as color centers in diamond and superconducting qubits in microwave cavities and waveguides.

Figure 1

(a) Schematic illustration of a driven ensemble of randomly distributed identical TLEs in a 3D volume. (b) $\eta$ is plotted as a function of $\overline{r}/{\lambda }_0$ for $N=6$. The thick lines are the mean $\eta$ over 1000 random distributions and the shaded areas represent regions where 68% of the values for $\eta$ lie (see [38] for further details). Solid (dotted) line corresponds to ${\gamma }_c/\mathrm{\Gamma }=1.3\times {10}^4$ (${\gamma }_c=0$) for ${\mathrm{\Omega }}_0/\mathrm{\Gamma }={10}^3$. Inset plots the mean and the 68% confidence interval of $\overline{g}/\mathrm{\Gamma }$ and $2\overline{\mathrm{\Gamma }}/\mathrm{\Gamma }$ as a function of $\overline{r}/{\lambda }_0$.

Figure 2

Regions of CE for $N=2$ in the plane $({\mathrm{\Omega }}_0/\mathrm{\Gamma },{\gamma }_c/\mathrm{\Gamma })$ for different values of $\overline{r}/{\lambda }_0$. The contour line corresponds to $\eta =1$.

Figure 3

$⟨\eta ⟩$ is plotted as a function of $\overline{r}/{\lambda }_0$ for different values of $N$ using a rate equation approximation for $\overline{r}/{\lambda }_0<{10}^{-1}$ (averaged over 400 random configurations) and using a trajectory method simulation (averaged over 200 configurations) $\overline{r}/{\lambda }_0>{10}^{-1}$. (Inset) Enlargement of the region of CE.