Lifetime scaling of the most subradiant state in 2D arrays
In plain words
Some collective states of atom arrays emit light extremely slowly and could store photons. How their lifetime grows with array size and how disorder shortens it are not known for 2D arrays.
Precise statement
Square array of $N$ two-level atoms with $d/\lambda < 1/2$. Determine the exponent $\alpha$ in $\gamma_{\min} \sim \gamma_0 N^{-\alpha}$ for the most subradiant collective mode, and its degradation with positional disorder $\sigma/d$ and atomic motion. Answer: $\alpha$ and the critical $\sigma$ where scaling is lost.
What would settle it
Numerical diagonalization of the non-Hermitian coupled-dipole matrix with disorder averaging, plus lifetime measurements in tweezer or lattice arrays.
Status in the literature
In $1\mathrm{D}$, $\gamma_{\mathrm{min}} \sim N^{-3}$ was found (Asenjo-Garcia et al., PRX 2017); $2\mathrm{D}$ finite arrays lack an agreed exponent.