Strong Photon Nonlinearities and Photonic Mott Insulators

We show that photon nonlinearities in an electromagnetically induced transparency can be at least 1 order of magnitude larger than predicted in all previous approaches. As an application we demonstrate that in this regime they give rise to very strong photon-photon interactions which are strong enough to make an experimental realization of a photonic Mott insulator state feasible in arrays of coupled ultrahigh-$Q$ microcavities.

Figure 1

The level structure and the possible transitions of one atom: $\omega$ is the frequency of the cavity mode; $\Omega$ is the Rabi frequency of the driving by the laser; $g_{13}$ and $g_{24}$ are the parameters of the respective dipole couplings; and $\delta$, $\Delta$, and $\epsilon$ are detunings.

Figure 2

Mott insulator state for three polaritons in three cavities: (a) photon number $n_1$, (b) photon number fluctuation $F_1$, (c) differences between full and effective BH model, $\delta n_1$ (solid line) and $\delta F_1$ (dashed line), and (d) $n_1$ and $F_1$ as given by a solution of a master equation for the three site BH model (1) including damping $\Gamma$.

Figure 3

Mott insulator to superfluid transition for three polaritons in three cavities: (a) On-site potential $U$ (solid line) and hopping $J$ (dashed line); (b) number of photons in cavity 1, $n_1$ for the full model (solid line) and the effective BH model (dashed line); (c) fluctuations of the photon number in cavity 1, $F_1$ for the full model (solid line) and the effective BH model (dashed line); and (d) $n_1$ and $F_1$ as given by a solution of a master equation for the three site BH model (1) including damping $\Gamma$.