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arXiv:0704.2575 · Physical Review Letters

Strong Photon Nonlinearities and Photonic Mott Insulators

Michael J. Hartmann, Martin Bodo Plenio

Published Sep 4, 2007• 114 citations
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Abstract

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.

DOI
10.1103/physrevlett.99.103601

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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.
We propose a new method to produce self- and cross-Kerr photonic nonlinearities, using light-induced Stark shifts due to the interaction of a cavity mode with atoms. The proposed experimental set-up is simpler than in previous approaches, while the strength of the nonlinearity obtained with a single atom is the same as in the setting based on electromagnetically induced transparency. Furthermore our scheme can be applied to engineer effective photonic nonlinear interactions whose strength increases with the number of atoms coupled to the cavity mode, leading to photon–photon interactions several orders of magnitude larger than previously considered possible.
Coupling light to ensembles of strongly interacting particles has emerged as a promising route toward achieving few photon nonlinearities. One specific way to implement this kind of nonlinearity is to interface light with highly excited atomic Rydberg states by means of electromagnetically induced transparency, an approach which allows freely propagating photons to acquire synthetic interactions of hitherto unprecedented strength. Here, we present an overview of this rapidly developing field, from classical effects to quantum manifestations of the nonlocal nonlinearities emerging in such systems. With an emphasis on underlying theoretical concepts, we describe the many experimental breakthroughs so far demonstrated and discuss potential applications looming on the horizon.
Quantum limit of dissipation-free photon-photon interactions at the few photon level is studied in the context of giant Kerr nonlinearities in cavity electromagneti cally induced transparency (EIT). It is shown that photon-photon interaction is largest when the cavity contains a sing le atom. In contrast to conventional nonlinearities, increasing the number of atoms cannot in crease the interaction strength but will in general degrade the performance by enhancing di spersion. In the non-perturbative regime, the single-atom photon-photon interaction can be limited by lossy states excited from long-lived EIT states. Asymptotically, in the strong coupling limit, photon-photon interaction is determined by the single photon-atom coupling strength. Photon blockade occurs for single atoms but only partial blockade can occur for low dispersion and not at all in the high-dispersion limit of the multi-atom case.
All optical devices based on nonlinear effects that use low-level power pumping acquire a great importance in optical communications systems and photonic processing. These optical devices can be implemented by means of different structures and materials. For instance, Fabry-Perot vertical microcavities, whispering gallery based microcavities or hybrid system of photonic crystal microcavities can improve their performance and so make possible a real implementation. In this research work we review the properties of optical media with three-level systems in which electromagnetically induced transparency has been induced. We analyse the effect of including such kind of material in an optical microcavity of the order of wavelenghts. Transmission properties like as the quality factor, the peak of transmission, the power of the coupling field in these microcavities with very small volume and very high non-linear Kerr coefficients will be analysed. Their application for developing new all-optical photonic devices for the next generation of all-optical networks, optical packets switching networks, and quantum information processing will be presented.
The propagation of light in strongly coupled atomic media takes place through the formation of polaritons-hybrid quasiparticles resulting from a superposition of an atomic and a photonic excitation. Here we consider the propagation under the condition of electromagnetically induced transparency and show that a novel many-body phenomenon can appear due to strong, dissipative interactions between the polaritons. Upon increasing the photon-pump strength, we find a first-order transition between an opaque phase with strongly broadened polaritons and a transparent phase where a long-lived polariton branch with highly tunable occupation emerges. Across this nonequilibrium phase transition, the transparency window is reconstructed via nonlinear interference effects induced by the dissipative polariton interactions. Our predictions are based on a systematic diagrammatic expansion of the nonequilibrium Dyson equations which can be controlled, even in the nonperturbative regime of large single-atom cooperativities, provided the polariton interactions are sufficiently long-ranged. Such a regime can be reached in photonic crystal waveguides thanks to the tunability of interactions, allowing us to observe the interaction-induced transparency transition even at low polariton densities.