  We study non-Markovian enhancement effects in the spontaneous emission of a
collective excitation in a linear chain of up to 100 qubits coupled to a 1D
waveguide. We find that for a critical separation of qubits, the system
exhibits super-superradiant (SSR) behavior leading to collective decay stronger
than the usual Dicke superradiance. Here, time-delayed coherent quantum
feedback effects are at play on top of the usual Dicke superradiance effects.
We find a linear scaling for the SSR decay rate with increasing qubit number
$N$ such that $\Gamma_{\rm SSR} \sim 2.277 N \gamma_0$, where $\gamma_0$ is the
single emitter decay rate to a one-dimensional waveguide, as opposed to
$\Gamma_{\rm Dicke}\sim N \gamma_0$ for Dicke superradiance. The SSR decay rate
can be tuned with qubit separation distance and may therefore have application
for quantum technologies.
