Threshold for a Dicke superradiant burst in ordered atom arrays
In plain words
Excited atoms packed close enough emit a bright burst instead of glowing steadily. The minimum closeness needed in a regular array is predicted only approximately.
Precise statement
$N$ fully inverted two-level atoms in a $1\mathrm{D}$ or $2\mathrm{D}$ array with spacing $d$ and transition wavelength $\lambda$, coupled by free-space dipole-dipole interactions, single-atom decay rate $\gamma_{0}$. Determine the critical spacing $d_{c}(N)$ below which the peak emission rate exceeds $N\gamma_{0}$, and the scaling of the peak rate with N, beyond mean-field and cumulant methods. Answer: $d_{c}(N)/\lambda$ and exponents.
What would settle it
Exact or controlled numerics of the full master equation for N up to about 100 matched by tweezer-array measurements.
Status in the literature
A threshold was predicted with approximate methods (Masson and Asenjo-Garcia, Nature Communications 2022).