E. S. Kyoseva, D. G. Angelakis, and L. C. Kwek, “A single-interaction step implementation of a quantum search in coupled micro-cavities, Europhy. Lett. 89, 20005 (2010).

[CrossRef]

M. Kiffner and M. J. Hartmann, “Dissipation induced Tonks–Girardeau gas of photons,” Phys. Rev. A 81, 021806(R) (2010).

[CrossRef]

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

M. Paternostro, G. S. Agarwal, and M. S. Kim, “Solitonic behaviour in coupled multi atom–cavity systems,” New J. Phys. 11, 013059 (2009).

[CrossRef]

S. Schmidt and G. Blatter, “Strong coupling theory for the Jaynes–Cummings–Hubbard model,” Phys. Rev. Lett. 103, 086403 (2009).

[CrossRef]
[PubMed]

P. Pippan, H. G. Evertz, and M. Hohenadler, “Excitation spectra of strongly correlated lattice bosons and polaritons,” Phys. Rev. Lett. 80, 033612 (2009).

M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, “Polaritons and pairing phenomena in Bose–Hubbard mixtures,” Phys. Rev. Lett. 102, 135301 (2009).

[CrossRef]
[PubMed]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide,” Eur. Phys. J. D 55, 205–209 (2009).

[CrossRef]

J. Koch and K. Le Hur, “Superfluid-Mott insulator transition of light in the Jaynes–Cummings lattice,” Phys. Rev. A 80, 023811 (2009).

[CrossRef]

N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, “Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities,” Phys. Rev. A 77, 031803(R) (2008).

[CrossRef]

S.-C. Lei and R.-K. Lee, “Quantum phase transitions of light in the Dicke–Bose–Hubbard model,” Phys. Rev. A 77, 033827 (2008).

[CrossRef]

F. G. S. L. Brandao, M. J. Hartmann, and M. B. Plenio, “Light-shift-induced photonic nonlinearities,” New J. Phys. 10, 043010 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. P. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photonics Rev. 2, 527–556 (2008).

[CrossRef]

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).

[CrossRef]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

D. Rossini, R. Fazio, and G. E. Santoro, “Photon and polariton fluctuations in arrays of QED-cavities,” Europhys. Lett. 83, 47001 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “A polaritonic two-component Bose–Hubbard model,” New J. Phys. 10, 033011 (2008).

[CrossRef]

A. Kay and D. G. Angelakis, “Reproducing spin lattice models in strongly coupled atom-cavity systems,” Europhys. Lett. 84, 20001 (2008).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum Hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).

[CrossRef]
[PubMed]

M. Aichorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, “Quantum fluctuations, temperature, and detuning effects in solid-light systems,” Phys. Rev. Lett. 100, 216401 (2008).

[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

D. G. Angelakis, M. F. Santos, V. Yannopapas, and A. Ekert, “A proposal for the implementation of quantum gates with photonic-crystal waveguides,” Phys. Lett. A 362, 377–380 (2007).

[CrossRef]

F. M. Hu, L. Zhou, T. Shi, and C. P. Sun, “Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping,” Phys. Rev. A 76, 013819 (2007).

[CrossRef]

A.-C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

[CrossRef]
[PubMed]

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 031805(R) (2007).

[CrossRef]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

D. Rossini and R. Fazio, “Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities,” Phys. Rev. Lett. 99, 186401 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann and M. B. Plenio, “Strong photon nonlinearities and photonic Mott insulators,” Phys. Rev. Lett. 99, 103601 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).

[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).

[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).

[CrossRef]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

R. Fazio and H. S. J. van der Zant, “Quantum phase transitions and vortex dynamics in superconducting networks,” Phys. Rep. 355, 235–334 (2001).

[CrossRef]

A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).

[CrossRef]

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).

[CrossRef]

M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[CrossRef]

M. Paternostro, G. S. Agarwal, and M. S. Kim, “Solitonic behaviour in coupled multi atom–cavity systems,” New J. Phys. 11, 013059 (2009).

[CrossRef]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

M. Aichorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, “Quantum fluctuations, temperature, and detuning effects in solid-light systems,” Phys. Rev. Lett. 100, 216401 (2008).

[CrossRef]

E. S. Kyoseva, D. G. Angelakis, and L. C. Kwek, “A single-interaction step implementation of a quantum search in coupled micro-cavities, Europhy. Lett. 89, 20005 (2010).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum Hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).

[CrossRef]
[PubMed]

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).

[CrossRef]

A. Kay and D. G. Angelakis, “Reproducing spin lattice models in strongly coupled atom-cavity systems,” Europhys. Lett. 84, 20001 (2008).

[CrossRef]

D. G. Angelakis, M. F. Santos, V. Yannopapas, and A. Ekert, “A proposal for the implementation of quantum gates with photonic-crystal waveguides,” Phys. Lett. A 362, 377–380 (2007).

[CrossRef]

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 031805(R) (2007).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, “Polaritons and pairing phenomena in Bose–Hubbard mixtures,” Phys. Rev. Lett. 102, 135301 (2009).

[CrossRef]
[PubMed]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

S. Schmidt and G. Blatter, “Strong coupling theory for the Jaynes–Cummings–Hubbard model,” Phys. Rev. Lett. 103, 086403 (2009).

[CrossRef]
[PubMed]

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum Hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).

[CrossRef]
[PubMed]

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 031805(R) (2007).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. P. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photonics Rev. 2, 527–556 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “A polaritonic two-component Bose–Hubbard model,” New J. Phys. 10, 033011 (2008).

[CrossRef]

F. G. S. L. Brandao, M. J. Hartmann, and M. B. Plenio, “Light-shift-induced photonic nonlinearities,” New J. Phys. 10, 043010 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).

[CrossRef]

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum Hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).

[CrossRef]
[PubMed]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).

[CrossRef]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).

[CrossRef]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

D. G. Angelakis, M. F. Santos, V. Yannopapas, and A. Ekert, “A proposal for the implementation of quantum gates with photonic-crystal waveguides,” Phys. Lett. A 362, 377–380 (2007).

[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

P. Pippan, H. G. Evertz, and M. Hohenadler, “Excitation spectra of strongly correlated lattice bosons and polaritons,” Phys. Rev. Lett. 80, 033612 (2009).

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

D. Rossini, R. Fazio, and G. E. Santoro, “Photon and polariton fluctuations in arrays of QED-cavities,” Europhys. Lett. 83, 47001 (2008).

[CrossRef]

D. Rossini and R. Fazio, “Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities,” Phys. Rev. Lett. 99, 186401 (2007).

[CrossRef]
[PubMed]

R. Fazio and H. S. J. van der Zant, “Quantum phase transitions and vortex dynamics in superconducting networks,” Phys. Rep. 355, 235–334 (2001).

[CrossRef]

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[CrossRef]

M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).

[CrossRef]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide,” Eur. Phys. J. D 55, 205–209 (2009).

[CrossRef]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).

[CrossRef]

M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[CrossRef]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide,” Eur. Phys. J. D 55, 205–209 (2009).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide,” Eur. Phys. J. D 55, 205–209 (2009).

[CrossRef]

M. Kiffner and M. J. Hartmann, “Dissipation induced Tonks–Girardeau gas of photons,” Phys. Rev. A 81, 021806(R) (2010).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “A polaritonic two-component Bose–Hubbard model,” New J. Phys. 10, 033011 (2008).

[CrossRef]

F. G. S. L. Brandao, M. J. Hartmann, and M. B. Plenio, “Light-shift-induced photonic nonlinearities,” New J. Phys. 10, 043010 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. P. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photonics Rev. 2, 527–556 (2008).

[CrossRef]

M. J. Hartmann and M. B. Plenio, “Strong photon nonlinearities and photonic Mott insulators,” Phys. Rev. Lett. 99, 103601 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, “Polaritons and pairing phenomena in Bose–Hubbard mixtures,” Phys. Rev. Lett. 102, 135301 (2009).

[CrossRef]
[PubMed]

P. Pippan, H. G. Evertz, and M. Hohenadler, “Excitation spectra of strongly correlated lattice bosons and polaritons,” Phys. Rev. Lett. 80, 033612 (2009).

M. Aichorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, “Quantum fluctuations, temperature, and detuning effects in solid-light systems,” Phys. Rev. Lett. 100, 216401 (2008).

[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).

[CrossRef]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

F. M. Hu, L. Zhou, T. Shi, and C. P. Sun, “Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping,” Phys. Rev. A 76, 013819 (2007).

[CrossRef]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).

[CrossRef]

A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).

[CrossRef]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).

[CrossRef]
[PubMed]

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).

[CrossRef]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

A.-C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).

[CrossRef]
[PubMed]

A. Kay and D. G. Angelakis, “Reproducing spin lattice models in strongly coupled atom-cavity systems,” Europhys. Lett. 84, 20001 (2008).

[CrossRef]

M. Kiffner and M. J. Hartmann, “Dissipation induced Tonks–Girardeau gas of photons,” Phys. Rev. A 81, 021806(R) (2010).

[CrossRef]

M. Paternostro, G. S. Agarwal, and M. S. Kim, “Solitonic behaviour in coupled multi atom–cavity systems,” New J. Phys. 11, 013059 (2009).

[CrossRef]

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).

[CrossRef]

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).

[CrossRef]

J. Koch and K. Le Hur, “Superfluid-Mott insulator transition of light in the Jaynes–Cummings lattice,” Phys. Rev. A 80, 023811 (2009).

[CrossRef]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

E. S. Kyoseva, D. G. Angelakis, and L. C. Kwek, “A single-interaction step implementation of a quantum search in coupled micro-cavities, Europhy. Lett. 89, 20005 (2010).

[CrossRef]

E. S. Kyoseva, D. G. Angelakis, and L. C. Kwek, “A single-interaction step implementation of a quantum search in coupled micro-cavities, Europhy. Lett. 89, 20005 (2010).

[CrossRef]

J. Koch and K. Le Hur, “Superfluid-Mott insulator transition of light in the Jaynes–Cummings lattice,” Phys. Rev. A 80, 023811 (2009).

[CrossRef]

S.-C. Lei and R.-K. Lee, “Quantum phase transitions of light in the Dicke–Bose–Hubbard model,” Phys. Rev. A 77, 033827 (2008).

[CrossRef]

S.-C. Lei and R.-K. Lee, “Quantum phase transitions of light in the Dicke–Bose–Hubbard model,” Phys. Rev. A 77, 033827 (2008).

[CrossRef]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide,” Eur. Phys. J. D 55, 205–209 (2009).

[CrossRef]

M. Aichorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, “Quantum fluctuations, temperature, and detuning effects in solid-light systems,” Phys. Rev. Lett. 100, 216401 (2008).

[CrossRef]

A.-C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).

[CrossRef]
[PubMed]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).

[CrossRef]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, “Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities,” Phys. Rev. A 77, 031803(R) (2008).

[CrossRef]

N. Na and Y. Yamamoto, “Generation of indistinguishable single photons and polarization-entangled photon-pairs via polaritonic superfluid to Mott-insulator quantum phase transition,” arXiv:0804.1829.

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).

[CrossRef]

M. Paternostro, G. S. Agarwal, and M. S. Kim, “Solitonic behaviour in coupled multi atom–cavity systems,” New J. Phys. 11, 013059 (2009).

[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

P. Pippan, H. G. Evertz, and M. Hohenadler, “Excitation spectra of strongly correlated lattice bosons and polaritons,” Phys. Rev. Lett. 80, 033612 (2009).

F. G. S. L. Brandao, M. J. Hartmann, and M. B. Plenio, “Light-shift-induced photonic nonlinearities,” New J. Phys. 10, 043010 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “A polaritonic two-component Bose–Hubbard model,” New J. Phys. 10, 033011 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann and M. B. Plenio, “Strong photon nonlinearities and photonic Mott insulators,” Phys. Rev. Lett. 99, 103601 (2007).

[CrossRef]
[PubMed]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. P. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photonics Rev. 2, 527–556 (2008).

[CrossRef]

D. Rossini, R. Fazio, and G. E. Santoro, “Photon and polariton fluctuations in arrays of QED-cavities,” Europhys. Lett. 83, 47001 (2008).

[CrossRef]

D. Rossini and R. Fazio, “Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities,” Phys. Rev. Lett. 99, 186401 (2007).

[CrossRef]
[PubMed]

J. Zhao, A. W. Sandvik, and K. Ueda, “Insulator to superfluid transition in coupled photonic cavities in two dimensions,” arXiv:0806.3603.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

D. Rossini, R. Fazio, and G. E. Santoro, “Photon and polariton fluctuations in arrays of QED-cavities,” Europhys. Lett. 83, 47001 (2008).

[CrossRef]

D. G. Angelakis, M. F. Santos, V. Yannopapas, and A. Ekert, “A proposal for the implementation of quantum gates with photonic-crystal waveguides,” Phys. Lett. A 362, 377–380 (2007).

[CrossRef]

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 031805(R) (2007).

[CrossRef]

S. Schmidt and G. Blatter, “Strong coupling theory for the Jaynes–Cummings–Hubbard model,” Phys. Rev. Lett. 103, 086403 (2009).

[CrossRef]
[PubMed]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

F. M. Hu, L. Zhou, T. Shi, and C. P. Sun, “Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping,” Phys. Rev. A 76, 013819 (2007).

[CrossRef]

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).

[CrossRef]

M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, “Polaritons and pairing phenomena in Bose–Hubbard mixtures,” Phys. Rev. Lett. 102, 135301 (2009).

[CrossRef]
[PubMed]

M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, “Polaritons and pairing phenomena in Bose–Hubbard mixtures,” Phys. Rev. Lett. 102, 135301 (2009).

[CrossRef]
[PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

F. M. Hu, L. Zhou, T. Shi, and C. P. Sun, “Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping,” Phys. Rev. A 76, 013819 (2007).

[CrossRef]

M. Aichorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, “Quantum fluctuations, temperature, and detuning effects in solid-light systems,” Phys. Rev. Lett. 100, 216401 (2008).

[CrossRef]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).

[CrossRef]

N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, “Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities,” Phys. Rev. A 77, 031803(R) (2008).

[CrossRef]

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

J. Zhao, A. W. Sandvik, and K. Ueda, “Insulator to superfluid transition in coupled photonic cavities in two dimensions,” arXiv:0806.3603.

N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, “Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities,” Phys. Rev. A 77, 031803(R) (2008).

[CrossRef]

R. Fazio and H. S. J. van der Zant, “Quantum phase transitions and vortex dynamics in superconducting networks,” Phys. Rep. 355, 235–334 (2001).

[CrossRef]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).

[CrossRef]

A.-C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).

[CrossRef]
[PubMed]

N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, “Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities,” Phys. Rev. A 77, 031803(R) (2008).

[CrossRef]

N. Na and Y. Yamamoto, “Generation of indistinguishable single photons and polarization-entangled photon-pairs via polaritonic superfluid to Mott-insulator quantum phase transition,” arXiv:0804.1829.

D. G. Angelakis, M. F. Santos, V. Yannopapas, and A. Ekert, “A proposal for the implementation of quantum gates with photonic-crystal waveguides,” Phys. Lett. A 362, 377–380 (2007).

[CrossRef]

J. Zhao, A. W. Sandvik, and K. Ueda, “Insulator to superfluid transition in coupled photonic cavities in two dimensions,” arXiv:0806.3603.

F. M. Hu, L. Zhou, T. Shi, and C. P. Sun, “Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping,” Phys. Rev. A 76, 013819 (2007).

[CrossRef]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–279 (2007).

[CrossRef]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide,” Eur. Phys. J. D 55, 205–209 (2009).

[CrossRef]

E. S. Kyoseva, D. G. Angelakis, and L. C. Kwek, “A single-interaction step implementation of a quantum search in coupled micro-cavities, Europhy. Lett. 89, 20005 (2010).

[CrossRef]

D. Rossini, R. Fazio, and G. E. Santoro, “Photon and polariton fluctuations in arrays of QED-cavities,” Europhys. Lett. 83, 47001 (2008).

[CrossRef]

A. Kay and D. G. Angelakis, “Reproducing spin lattice models in strongly coupled atom-cavity systems,” Europhys. Lett. 84, 20001 (2008).

[CrossRef]

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. P. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photonics Rev. 2, 527–556 (2008).

[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).

[CrossRef]

D. E. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. D. Lukin, and E. A. Demler, “Crystallization of strongly interacting photons in a nonlinear optical fibre,” Nat. Phys. 4, 884–889 (2008).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).

[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).

[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dotcavity system,” Nature 445, 896–899 (2007).

[CrossRef]
[PubMed]

A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. Girvin, and R. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).

[CrossRef]
[PubMed]

F. G. S. L. Brandao, M. J. Hartmann, and M. B. Plenio, “Light-shift-induced photonic nonlinearities,” New J. Phys. 10, 043010 (2008).

[CrossRef]

M. Paternostro, G. S. Agarwal, and M. S. Kim, “Solitonic behaviour in coupled multi atom–cavity systems,” New J. Phys. 11, 013059 (2009).

[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “A polaritonic two-component Bose–Hubbard model,” New J. Phys. 10, 033011 (2008).

[CrossRef]

D. G. Angelakis, M. F. Santos, V. Yannopapas, and A. Ekert, “A proposal for the implementation of quantum gates with photonic-crystal waveguides,” Phys. Lett. A 362, 377–380 (2007).

[CrossRef]

R. Fazio and H. S. J. van der Zant, “Quantum phase transitions and vortex dynamics in superconducting networks,” Phys. Rep. 355, 235–334 (2001).

[CrossRef]

N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, “Strongly correlated polaritons in a two-dimensional array of photonic crystal microcavities,” Phys. Rev. A 77, 031803(R) (2008).

[CrossRef]

J. Koch and K. Le Hur, “Superfluid-Mott insulator transition of light in the Jaynes–Cummings lattice,” Phys. Rev. A 80, 023811 (2009).

[CrossRef]

E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008).

[CrossRef]

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 031805(R) (2007).

[CrossRef]

M. Kiffner and M. J. Hartmann, “Dissipation induced Tonks–Girardeau gas of photons,” Phys. Rev. A 81, 021806(R) (2010).

[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Heralded generation of entanglement with coupled cavities,” Phys. Rev. A 78, 022323 (2008).

[CrossRef]

F. M. Hu, L. Zhou, T. Shi, and C. P. Sun, “Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping,” Phys. Rev. A 76, 013819 (2007).

[CrossRef]

M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, “Quantum phase transitions in photonic cavities with two-level systems,” Phys. Rev. A 77, 053819 (2008).

[CrossRef]

S.-C. Lei and R.-K. Lee, “Quantum phase transitions of light in the Dicke–Bose–Hubbard model,” Phys. Rev. A 77, 033827 (2008).

[CrossRef]

M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[CrossRef]

S. Schmidt and G. Blatter, “Strong coupling theory for the Jaynes–Cummings–Hubbard model,” Phys. Rev. Lett. 103, 086403 (2009).

[CrossRef]
[PubMed]

M. J. Hartmann and M. B. Plenio, “Strong photon nonlinearities and photonic Mott insulators,” Phys. Rev. Lett. 99, 103601 (2007).

[CrossRef]
[PubMed]

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum Hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).

[CrossRef]
[PubMed]

M. Aichorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, “Quantum fluctuations, temperature, and detuning effects in solid-light systems,” Phys. Rev. Lett. 100, 216401 (2008).

[CrossRef]

M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, “Polaritons and pairing phenomena in Bose–Hubbard mixtures,” Phys. Rev. Lett. 102, 135301 (2009).

[CrossRef]
[PubMed]

P. Pippan, H. G. Evertz, and M. Hohenadler, “Excitation spectra of strongly correlated lattice bosons and polaritons,” Phys. Rev. Lett. 80, 033612 (2009).

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

[CrossRef]
[PubMed]

I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, “Fermionized photons in an array of driven dissipative nonlinear cavities,” Phys. Rev. Lett. 103, 033601 (2009).

[CrossRef]
[PubMed]

D. Rossini and R. Fazio, “Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities,” Phys. Rev. Lett. 99, 186401 (2007).

[CrossRef]
[PubMed]

A.-C. Ji, X. C. Xie, and W. M. Liu, “Quantum magnetic dynamics of polarized light in arrays of microcavities,” Phys. Rev. Lett. 99, 183602 (2007).

[CrossRef]
[PubMed]

A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).

[CrossRef]

E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15–37 (2003).

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).

[CrossRef]

The notation al is used to denote exact (photons) and approximated (polaritons) bosonic particles.

J. Zhao, A. W. Sandvik, and K. Ueda, “Insulator to superfluid transition in coupled photonic cavities in two dimensions,” arXiv:0806.3603.

A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. E. Tureci, and A. Imamoglu, “Non-equilibrium phase transition in driven-dissipative nonlinear cavity arrays,” arXiv:0904.4437.

N. Na and Y. Yamamoto, “Generation of indistinguishable single photons and polarization-entangled photon-pairs via polaritonic superfluid to Mott-insulator quantum phase transition,” arXiv:0804.1829.