Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime

We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which cannot be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band, we predict an exponential relaxation at a rate different from that predicted by Fermi’s golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.

Figure 1

(a) Energy dispersion $\omega (\mathbf{k})/J$ and (b) density of states $D(E)$ for the square lattice tight-binding model with a black line highlighting the $\mathbf{k}$ points satisfying $\omega (\mathbf{k})=0$.

Figure 2

(a) Excited state population $|C_e(t){|}^2$ for a single QE for $g/J=0.1$ and different QE energies as depicted in the legend. Inset: Excited state population $|C_e(t){|}^2$ in logarithmic scale for $\mathrm{\Delta }=0$ to visualize the nonperturbative dynamics. (b),(c) Probability amplitude of the bath modes, $|C_{\mathbf{n}}|$, for positions $\mathbf{n}=(n_x,n_y)$ at a time $tJ=100$ for $\mathrm{\Delta }/J=-3$ and 0, respectively.

Figure 3

(a) Population of states $|{\mathrm{\Phi }}_{2,\pm }⟩$ [$|{\mathrm{\Phi }}_{4,\pm }⟩$] for a coupling $g=0.05J$ for positions ${\mathbf{n}}_{12}=(6,6)$ and (6,0),(0,6),(6,12),(12,6), respectively. (b)–(e) Bath probability amplitude at time $tJ=200$ for the initial states of panel (a) as depicted in the legend.