Figure 1

Notion of single-site addressing in an optical lattice. The atoms are fixed in the lattice sites while a laser beam traveling perpendicular to the interatomic axis is focused onto one site. The beam profile is given by a Gaussian envelope with a FWHM $\eta$ as given in Eq. (5). The parameters $a_l$ and $\eta$ match the experimental parameters of Ref. [9].Reuse & Permissions

Figure 2

The dipole-dipole interaction $J^{\mu \nu }$ (solid red line) and the collective damping rate ${\Gamma }^{\mu \nu }$ (blue dashed line) in units of $\gamma$ as a function of the interatomic separation $x^{\mu \nu }$ with ${\alpha }^{\mu \nu }=\frac{\pi }{2}$.Reuse & Permissions

Figure 3

(a) Incoherent part of the power spectrum for two atoms with ${\mathbf{R}}_{21}=a_l{\vec{e}}_x=0.82{\lambda }_0{\vec{e}}_x,{\alpha }^{12}=\pi /2,J^{12}\approx -0.09\gamma ,{\Gamma }^{12}\approx -0.11\gamma ,\Delta =\gamma ,\sigma =600\mathrm{nm}$, and ${\Omega }_1=0.1\gamma$. The detector is positioned in the $xy$ plane with $\theta =\measuredangle (\widehat{\mathbf{r}},{\mathbf{R}}_{21})\approx 0.92$. The solid red and dashed blue lines display the spectrum under single-atom addressing, i.e., ${\Omega }_2\approx 0.004{\Omega }_1\approx 0$, whereas, the dot-dashed green and dotted orange lines consider a broad laser beam with $0.1\gamma ={\Omega }_1\approx {\Omega }_2$. The dashed blue and the dotted orange lines, however, display the case where the collective parameters $J^{\mu \nu }$ and ${\Gamma }^{\mu \nu }$ artificially have been set to zero. (b) The degree of asymmetry as defined in Eq. (15) plotted as a function of the ratio ${\Omega }_2/{\Omega }_1$ for parameters as in (a) except for ${\Omega }_1=0.1\gamma \approx |J^{12}|\approx |{\Gamma }^{12}|$ (solid red line), ${\Omega }_1=0.5\gamma \approx 5|J^{12}|\approx 5|{\Gamma }^{12}|$ (dashed blue line), and ${\Omega }_1=1\gamma \approx 10|J^{12}|\approx 10|{\Gamma }^{12}|$ (dotted black line).Reuse & Permissions

Figure 4

Incoherent part of the power spectrum (a) and (b) with the corresponding atomic configurations in the lattice below (c) and (d), respectively. (a) Incoherent part of the power spectrum with parameters as in Fig. 3a. The solid red curve shows the spectrum for two atoms under single-atom addressing just as the solid red line in Fig. 3a. The dashed blue curve displays the spectrum of three atoms where the third atom is placed at ${\mathbf{r}}_3=-a_l{\vec{e}}_x$. This represents single-site addressing in a 1D optical lattice where the contributions of the nearest neighbors of the addressed atom are taken into account. For the 2D lattice, we place two more atoms at ${\mathbf{r}}_4=a_l{\vec{e}}_y$ and ${\mathbf{r}}_5=-a_l{\vec{e}}_y$ and find very similar features (dot-dashed green curve). The Mollow spectrum of a single atom also is given for comparison (dotted black curve). (b) Incoherent part of the power spectrum for two atoms (solid red curve), three atoms (dashed blue curve), and five atoms (dot-dashed green curve) with the parameters $\Delta =\gamma$ and ${\Omega }_0=0.5\gamma$. The positions of the atoms are ${\mathbf{r}}_1={\{0,0,0\}}^{\top },{\mathbf{r}}_2=a_l{\{\sqrt{2},0,0\}}^{\top },{\mathbf{r}}_3=a_l{\{-\sqrt{2},0,0\}}^{\top },{\mathbf{r}}_4=a_l{\{0,\sqrt{2},0\}}^{\top }$, and ${\mathbf{r}}_5=a_l{\{0,-\sqrt{2},0\}}^{\top }$ as illustrated in the picture below with $a_l=532$ and $\sigma =700\mathrm{nm}$ as in Refs. [8, 10]. The detector is positioned in the far-field zone at $\widehat{\mathbf{r}}=\widehat{r}\{0,1,0\}$. All the lines consider single-site addressing, which is compared to the Mollow line (dotted black curve). In (c) and (d), small black dots indicate lattice sites, colored dots indicate the atoms considered for plots of the corresponding color in (a) and (b), respectively, and the faint orange circle indicates the FWHM of the probe laser.Reuse & Permissions