Controlled manipulation of light by cooperative response of atoms in an optical lattice

We show that atoms in an optical lattice can respond cooperatively to resonant incident light and that such a response can be employed for precise control and manipulation of light on a subwavelength scale. Specific collective excitation modes of the system that result from strong light-mediated dipole-dipole interactions can be addressed by tailoring the spatial phase profile of the incident light. We demonstrate how the collective response can be used to produce optical excitations at well-isolated sites on the lattice.

Figure 1

The atomic excitation intensities $\overline{|e_j{|}^2}/{\max }_{j^{\prime }}\overline{|e_{j^{\prime }}{|}^2}$ resulting from the cooperative response of an optical lattice system to a phase-modulated incident field [Eq. (3)] with modulation period of six sites. The black dots indicate the positions of the populated sites. In (a), the atoms are perfectly confined at the center of each site and their wave functions have width $\ell =0$. (b) represents the response of a single stochastic realization of atomic positions sampled from a 2D Gaussian variables of width $0.12a$ centered on the lattice sites. Ensemble average responses over several thousand realizations of atomic positions are shown for (c), (e), (f) $\ell =0.12a$ and (d) $\ell =0.21a$. In (e), the incident field is detuned from the resonance of an isolated atom by $10\Gamma$, while the detuning is zero in all other cases. In (f), atoms were removed from 8/9 of the sites, resulting in an effective spacing of $a^{\prime }=3a$, thus suppressing the role of the other sites from the response and destroying the excitation pattern.