Storing Light with Subradiant Correlations in Arrays of Atoms

We show how strong light-mediated resonant dipole-dipole interactions between atoms can be utilized in a control and storage of light. The method is based on a high-fidelity preparation of a collective atomic excitation in a single correlated subradiant eigenmode in a lattice. We demonstrate how a simple phenomenological model captures the qualitative features of the dynamics and sharp transmission resonances that may find applications in sensing.

Figure 1

Schematic illustration and numerically calculated response. The atoms (one per site) are confined in a small square 2D $8\times 8$ array on the $yz$ plane. The linearly polarized (along $y$) incident light propagates along the positive $x$ direction driving the $|J=0,m_J=0⟩\to |J^{\prime }=1,m_J=\pm 1⟩$ transitions. The arrows represent the numerically calculated steady state atomic dipoles at each site. A real or synthetic magnetic field along the $z$ axis induces Zeeman shifts, effectively rotating the dipoles around the $z$ axis. For $({\delta }_{+}^z,{\delta }_{-}^z)=(0.1,0.3)\gamma$ (left panel) this rotation is small, but for $({\delta }_{+}^z,{\delta }_{-}^z)=(0.45,1.75)\gamma$ (driven at the resonance of the subradiant mode; right panel), the dipoles are oriented approximately normal to the lattice, representing a collective excitation eigenmode with a factor of 50 narrowed linewidth.

Figure 2

The dynamics of the total atomic polarization density in the lattice of $20\times 20$ sites for different Zeeman shifts and lattice heights. (a) Curves from slow to fast decay: $({\delta }_{+}^z,{\delta }_{-}^z,{\mathrm{\Delta }}_0)=(0,0,0)$, $(0.4,0.6,0)\gamma$, and $(1.1,1.1,0.65)\gamma$ ($s=50$). At $\gamma t=20$ (when each curve is normalized to one), the Zeeman shifts and the incident light are switched off. When the dipoles are oriented close to the $x$ axis (see Fig. 1 on right), the decay is slow (collective subradiance). For ${\delta }_{\pm }^z=0$ the dipoles are pointing along the $y$ axis and decay rapidly. An exponential fitting provides decay rates $0.79\gamma$, $0.16\gamma$, and $0.14\gamma$. (b) The curves from top: incident Gaussian beam with fixed atomic positions, plane-wave excitation for fixed atomic positions, for lattice with $s=50$, 20, 5, [$({\delta }_{+}^z,{\delta }_{-}^z,{\mathrm{\Delta }}_0)=(1.1,1.1,0.65)\gamma$], and for fixed atomic positions (${\delta }_{\pm }^z={\mathrm{\Delta }}_0=0$). The shaded lines around the curves represent the stochastic uncertainties of the excitation amplitudes due to the vacuum fluctuations of the atomic positions.

Figure 3

The resonance linewidth ${\upsilon }_P$ of the subradiant collective eigenmode where the atomic dipoles coherently point to the normal of the lattice. (a) The dependence on the lattice spacing $a$. The curves from top: arrays $5\times 5$, $10\times 10$, $15\times 15$, $20\times 20$, $25\times 25$. (b) The dependence on the number of atoms for $a=0.55\lambda$: $s=50$ (top curve), the atoms at fixed positions (lower curve). For instance, ${\upsilon }_P\simeq 1.0\times 10^{-3}\gamma$ for the $35\times 35$ lattice in the lower curve. In comparison, the most subradiant eigenmode in this case has a linewidth $1.5\times 10^{-4}\gamma$.

Figure 4

The spectrum of forward or back scattered light and Fano resonances for different orientations of the dipoles: $({\delta }_{+}^z,{\delta }_{-}^z)=(0.1,0.2)\gamma$ (the orientation not far from the lattice plane; narrow resonances), $(0.45,1.75)\gamma$ (the orientation approximately normal to the plane; broad resonances) for a lattice of fixed atomic positions and (a) $3\times 3$; (b) $20\times 20$ sites. Numerical simulation (blue, solid curves), two-mode model (red, dashed curves) with numerically calculated eigenvalues for the two dominant eigenmodes $({\delta }_P+i{\upsilon }_P)/\gamma \simeq -0.65+0.0031i$ ($20\times 20$), $-0.62+0.12i$ ($3\times 3$), and $({\delta }_I+i{\upsilon }_I)/\gamma \simeq -0.68+0.79i$ ($20\times 20$), $-0.59+0.83i$ ($3\times 3$). The scattering resonance is approximately at the effective resonance of the subradiant mode [Eq. (4a)] ${\mathrm{\Delta }}_P-\tilde{\delta }\simeq 0$.