From Mott transitions to interacting relativistic theories with light: A brief history of photonic quantum simulators

I will start by reviewing our early works for observing photon-blockade induced Mott transitions in coupled cavity QED systems [1]. After briefly touching on the idea of simulating spin-models and the Fractional Hall effect [2], I will analyze more recent developments in realizing continuous 1D models in nonlinear optical fibers exhibiting electromagnetically induced transparency nonlinearities. Here the concept of the ``photonic Luttinger liquid'' will be introduced, along with a proposal to observe spin-charge separation with polarized photons in a nonlinear slow light set up [3]. I will continue by presenting our recent efforts in simulating 1D lattice models in the non-relativistic regime, such as the sine-Gordon and Bose-Hubbard [4], and the efforts for simulations of out of equilibrium phenomena using driven systems [5,6]. I will conclude by presenting ongoing work on interacting relativistic models (Thirring)[7]. Possible experimental implementations in quantum optical systems such as photonic crystals, optical fibers coupled to cold atoms, and Circuit QED will be discussed.\\[4pt] [1] D.G. Angelakis, M.F. Santos and S. Bose, Phys. Rev. A \textbf{76}, 031805(R) (2007); D.G. Angelakis, Reports in Progress in Phys., IOP (2012) to appear.\\[0pt] [2] J. Cho, D.G. Angelakis, Phys. Rev. Lett \textbf{101}, 246809 (2008).\\[0pt] [3] D.G. Angelakis, M.-X. Huo, E. Kyoseva and L.C.Kwek, Phys. Rev. Lett. \textbf{106}, 153601 (2011).\\[0pt] [4] M.-X. Huo, D.G. Angelakis, Phys. Rev. A \textbf{85} 023821 (2012)\\[0pt] [5] T. Gruzic, S. R. Clark, D. G. Angelakis. Dieter Jacksh, New Jour,. of Phys. \textbf{14}, 103025 (2012). [6] P. Das, C. Noh, D.G. Angelakis, arXiv:1208.0313.\\[0pt] [7] D.G. Angelakis, M.-X. Huo, D. Chang, L.C. Kwek, V. Korepin arXiv:1207.7272.