Quantum many-body phenomena in coupled cavity arrays

Laser and Photonics Reviews

Volumn 2, Issue 6, 2008, Pages 527-556

  Hartmann, Michael J ^a,b   Brandão, Fernando G S L ^b   Plenio, Martin B ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Cavity QED; Photon blockade; Polaritons; Quantum many body models

Indexed keywords

EID: 66749121168     PISSN: 18638880     EISSN: 18638899     Source Type: Journal    
DOI: 10.1002/lpor.200810046     Document Type: Article

References (115)

1. H.J. Metcalf and P. van derStraten, Laser Cooling and Trapping (Springer, New York, 1999).
2. A.J. Leggett, Bose-Einstein condensation in the alkali gases: some fundamental concepts, Rev. Mod. Phys. 73, 307 (2001).
3. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).
4. J.M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).
5. A. Zeilinger, Experiment and the foundations of quantum physics, Rev. Mod. Phys. 71, S288 (1999).
6. F. De Martini and C. Monroe, eds., Experimental Quantum Computation and Information (IOS Press, Amsterdam, 2002).
7. R.P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
8. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)
9. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold bosonic atoms in optical lattices, Phys. Rev. Lett. 81, 3108 (1998).
10. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature 415, 39 (2002).
11. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. W. Hänsch, and I. Bloch, Tonks-Girardeau gas of ultracold atoms in an optical lattice, Nature 429, 277 (2004).
12. 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 (2007).
13. Y. Makhlin, G. Schön, and A. Shnirman, Quantum-state engineering with Josephson-junction devices, Rev. Mod. Phys. 73, 357 (2001).
14. H.S. vanderZant, F.C. Fritschy, W.J. Elion, L.J. Geerligs, and J.E. Mooij, Field-induced superconductor-to-insulator transitions in Josephson-junction arrays, Phys. Rev. Lett. 69,2971 (1992).
15. A. van Oudenaarden and J.E. Mooij, One-dimensional Mott insulator formed by quantum vortices in Josephson junction arrays, Phys. Rev. Lett. 76, 4947 (1996).
16. F. Mintert and C. Wunderlich, Ion-trap quantum logic using long-wavelength radiation, Phys. Rev. Lett. 87, 257904 (2001).
17. D. Porras and J.I. Cirac, Effective quantum spin systems with trapped ions, Phys. Rev. Lett. 92, 207901 (2004).
18. D. Porras and J.I. Cirac, Bose-Einstein condensation and strong-correlation behavior of phonons in ion traps, Phys. Rev. Lett. 93, 263602 (2004).
19. A. Retzker, R. Thompson, D. Segal, and M.B. Plenio, Dou-ble wells, scalar fields and quantum phase transitions in ion traps, arXiv:0801.0623.
20. A. Friedenauer, H. Schmitz, J.T. Glückert, D. Porras, and T. Schätz, Simulating the quantum magnet, arXiv:0802.4072.
21. M.J. Hartmann, F.G. S.L. Brandão, and M.B. Plenio, Strongly interacting polaritons in coupled arrays of cavities, Nature Phys. 2, 849 (2006).
22. 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, R031805 (2007).
23. A.D. Greentree, C. Tahan, J.H. Cole, and L.C.L. Hollenberg, Quantum phase transitions of light, Nature Phys. 2, 856 (2006).
24. F. Illuminati, Quantum optics: light does matter, Nature Phys. 2, 803 (2006).
25. M.J. Hartmann and M. B. Plenio, Strong photon nonlinearities and photonic Mott insulators, Phys. Rev. Lett. 99, 103601 (2007).
26. F.G. S.L. Brandão, M.J. Hartmann, and M. B. Plenio, Light-shift-induced photonic nonlinearities, New J. Phys. 10,043010 (2008).
27. M.J. Hartmann, F.G.S.L. Brandão, and M.B. Plenio, Effective spin systems in coupled microcavities, Phys. Rev. Lett. 99, 160501 (2007).
28. 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).
29. A. Kay and D.G. Angelakis, Reproducing spin lattice models in strongly coupled atom-cavity systems, arXiv:0802.0488.
30. P. Li, Q. Gong, and G. Guo, Effective generation of Ising interaction and cluster states in coupled micro-cavities, arXiv:0712.3864.
31. J. Cho, D.G. Angelakis, and S. Bose, Simulation of high-spin Heisenberg chains in coupled cavities, arXiv:0802.3365.
32. J. Cho, D.G. Angelakis, and S. Bose, Fractional quantum Hall state in coupled cavities, arXiv:0807.1802.
33. M.J. Hartmann and M.B. Plenio, Migration of bosonic particles across a Mott insulator to a superfluid phase interface, Phys. Rev. Lett. 100, 070602 (2008).
34. C.D. Ogden, E.K. Irish, and M. S. Kim, Dynamics in a coupled-cavity array, arXiv:0804.2882.
35. L. Zhou, J. Lu, and C.P. Sun, Coherent control of photon transmission: slowing light in a coupled resonator waveguide doped with Λ atoms, Phys. Rev. A 76, 012313 (2007).
36. 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).
37. L. Zhou, Y.B. Gao, Z. Song, and C.P. Sun, Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits, Phys. Rev. A 77, 013831 (2008).
38. M.J. Hartmann, F. G.S. L. Brandão, and M.B. Plenio, A polaritonic two-component Bose-Hubbard model, New J. Phys. 10, 033011 (2008).
39. D. Rossini and R. Fazio, Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities, Phys. Rev. Lett. 99, 186401 (2007).
40. M. Aichhorn, M. Hohenadler, C. Tahan, and P.B. Littlewood, Quantum fluctuations, temperature, and detuning effects in solid-light systems, Phys. Rev. Lett. 100, 216401 (2008).
41. 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).
42. 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).
43. J. Zhao, A.W. Sandvik, and K. Ueda, Insulator to superfluid transition in coupled photonic cavities in two dimensions, arXiv:0806.3603.
44. N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, Strongly correlated polaritons in a two-dimensional array of photonic crystal micro-cavities, Phys. Rev. A 77, 031803(R) (2008).
45. 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 fiber, Nature Phys., advance online publication, doi:10.1038/nphys1074
46. M. Paternostro, G.S. Agarwal, and M.S. Kim, Solitons in interacting Dicke models of coupled cavities with two-level systems, arXiv:0707.0846.
47. S.-C. Lei and R.-K. Lee, Quantum phase transitions of light in the Dicke-Bose-Hubbard model, Phys. Rev. A 77, 033827 (2008).
48. Y.-F. Xiao, J. Gao, X.-B. Zou, J.F. McMillan, X. Yang, Y.- L. Chen, Z.-F. Han, G.-C. Guo, and C.W. Wong, Coupled quantum electrodynamics in photonic crystal nanocavities, arXiv.org:0707.2632.
49. D. Rossini, R. Fazio, and G. Santoro, Photon and polariton fluctuations in arrays of QED-cavities, Europhys. Lett., in press, arXiv:0806.0942.
50. M.X. Huo, Y. Li, Z. Song, and C.P. Sun, Atomic entanglement versus visibility of photon interference for quantum criticality of a hybrid system, Phys. Rev. A 77, 022103 (2008).
51. D.G. Angelakis, M.F. Santos, V. Yannopapas, and A. Ekert, A proposal for the implementation of quantum gates with photonic-crystal coupled cavity waveguides, Phys. Lett. A 362,377 (2007).
52. D.G. Angelakis and A. Kay, Weaving light-matter qubits into a one way quantum computer, New J. Phys. 10, 023012 (2008).
53. S. Bose, D.G. Angelakis, and D. Burgarth, Transfer of a polaritonic qubit through a coupled cavity array, J. Mod. Opt. 54, 2307 (2007).
54. D.G. Angelakis, S. Mancini, and S. Bose, Steady state entanglement between hybrid light-matter qubits, arXiv.org:0711.1830.
55. J. Cho, D.G. Angelakis, and S. Bose, Heralded generation of two-photon polarization entanglement with coupled cavities, Phys. Rev. A 78, 022323 (2008).
56. 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.
57. D.K. Armani, T.J. Kippenberg, S.M. Spillane, and K.J. Vahala, Ultra-high-Q toroid micro-cavity on a chip, Nature 421,925 (2003).
58. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A.S. Parkins, H.J. Kimble, T.J. Kippenberg, and K.J. Vahala, Observation of strong coupling between one atom and a monolithic microresonator, Nature 443, 825 (2006).
59. P.E. Barclay, K. Srinivasan, O. Painter, B. Lev, and H. Mabuchi, Integration of fiber-coupled high-Q SiNx micro-disks with atom chips, Appl. Phys. Lett. 89, 131108 (2006).
60. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, High-Q photonic nanocavity in a two-dimensional photonic crystal, Nature 425, 944 (2003).
61. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E.L. Hu, and A. Imamoǧlu, Quantum nature of a strongly coupled single quantum dot-cavity system, Nature 445, 896 (2007).
62. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.- S. Huang, J. Majer, S. Kumar, S.M. Girvin, and R.J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature 431, 162 (2004).
63. M. Trupke, J. Goldwin, B. Darquié, G. Dutier, S. Eriksson, J. Ashmore, and E.A. Hinds, Atom detection and photon production in a scalable, open, optical microcavity, Phys. Rev. Lett. 99, 063601 (2007).
64. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, Strong atom-field coupling for BoseEinstein condensates in an optical cavity on a chip, Nature 450,272 (2007).
65. R.J. Thompson, G. Rempe, and H.J. Kimble, Observation of normal-mode splitting for an atom in an optical cavity, Phys. Rev. Lett. 68, 1132 (1992).
66. Q.A. Turchette, C.J. Hood, W. Lange, H. Mabuchi, and H.J. Kimble, Measurement of conditional phase shifts for quantum logic, Phys. Rev. Lett. 75, 4710 (1995).
67. K.M. Birnbaum, A. Boca, R. Miller, A.D. Boozer, T.E. Northup, and H.J. Kimble, Photon blockade in an optical cavity with one trapped atom, Nature 436, 87 (2005).
68. N. Stefanou and M. Modinos, Impurity bands in photonic insulators, Phys. Rev. B 57, 12127 (1998).
69. A. Yariv, Y. Xu, R.K. Lee, and A. Scherer, Coupledresonator optical waveguide: a proposal and analysis, Opt. Lett. 24, 711 (1999).
70. M. Marzani and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
71. M.J. Hartmann, M. Reuter, and M. B. Plenio, Excitation and entanglement transfer versus spectral gap, New J. Phys. 8,94 (2006).
72. M.B. Plenio, J. Hartley, and J. Eisert, Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom, New J. Phys. 6, 36 (2004).
73. M.P. A. Fisher, P. B. Weichman, G. Grinstein, and D.S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B 40, 546 (1989).
74. M.P.A. Fisher, G. Grinstein, and S.M. Girvin, Presence of quantum diffusion in two dimensions: universal resistance at the superconductor-insulator transition, Phys. Rev. Lett. 64,587 (1990).
75. J. Hubbard, Electron correlations in narrow energy bands, Proc. R. Soc. A 276, 238 (1963).
76. M. Fleischhauer, A. Imamǒglu, and J. P. Marangos, Electromagnetically induced transparency: optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).
77. H. Schmidt and A. Imamǒglu, Giant Kerr nonlinearities obtained by electromagnetically induced transparency, Opt. Lett. 21, 1936 (1996).
78. A. Imamǒglu, H. Schmidt, G. Woods, and M. Deutsch, Strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett. 79, 1467 (1997);
79. P. Grangier, D.F. Walls, and K.M. Gheri, Comment: strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett. 81, 2833 (1998);
80. A. Imamǒglu, H. Schmidt, G. Woods, and M. Deutsch, Erratum: strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett. 81, 2836 (1998).
81. M.J. Werner and A. Imam and Imamǒglu, Photon-photon interactions in cavity electromagnetically induced transparency, Phys. Rev. A 61, 011801(R) (1999).
82. K.M. Gehri, W. Alge, and P. Grangier, Quantum analysis of the photonic blockade mechanism, Phys. Rev. A 60, R2673 (1999).
83. S.M. Spillane, T. J. Kippenberg, K.J. Vahala, K. W. Goh, E. Wilcut, and H.J. Kimble, Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics, Phys. Rev. A 71,013817 (2005).
84. F. Dimer, B. Estienne, A.S. Parkins, and H.J. Carmichael, Proposed realisation of the Dicke-model quantum phase transition in an optical cavity QED system, Phys. Rev. A 75,013804 (2007).
85. A. Recati, P.O. Fedichev, W. Zwerger, and P. Zoller, Spincharge separation in ultracold quantum gases, Phys. Rev. Lett. 90, 020401 (2003).
86. L.-M. Duan, E. Demler, and M.D. Lukin, Controlling spin exchange interactions of ultracold atoms in optical lattices, Phys. Rev. Lett. 91, 090402 (2003).
87. M.A. Cazalilla and A.F. Ho, Instabilities in binary mixtures of one-dimensional quantum degenerate gases, Phys. Rev. Lett. 91, 150403 (2003).
88. A. Imamǒglu, High efficiency photon counting using stored light, Phys. Rev. Lett. 89, 163602 (2002).
89. D.F. V. James and P.G. Kwiat, Atomic-vapor-based high efficiency optical detectors with photon number resolution, Phys. Rev. Lett. 89, 183601 (2002).
90. U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005).
91. J.K. Freericks and H. Monien, Strong-coupling expansions for the pure and disordered Bose-Hubbard model, Phys. Rev. B 53, 2691 (1996).
92. T. Moriya and K. Ueda, Antiferromagnetic spin fluctuation and superconductivity, Rep. Prog. Phys. 66, 1299 (2003).
93. H.J. Briegel and R. Raussendorf, Persistent entanglement in arrays of interacting particles, Phys. Rev. Lett. 86, 910 (2001).
94. A.S. Sørensen and K. Mølmer, Entangling atoms in bad cavities, Phys. Rev. A 66, 022314 (2002).
95. D.F. V. James, Quantum computation with hot and cold ions: an assessment of proposed schemes, Fortschr. Phys. 48,823 (2000).
96. R. Raussendorf and H.J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
97. D. Gross and J. Eisert, Novel schemes for measurement-based quantum computation, Phys. Rev. Lett. 98, 220503 (2006).
98. K.M. R. Audenaert and M. B. Plenio, When are correlations quantum? - verification and quantification of entanglement by simple measurements, New J. Phys. 8, 266 (2006).
99. S.G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice (Kluwer, Boston, 2002).
100. D.G. Angelakis, P.L. Knight, and E. Paspalakis, Photonic crystals and inhibition of spontaneous emission: an introduction, Contemp. Phys. 45, 303 (2004).
101. H. Altug and J. Vuckoic, Two-dimensional coupled photonic crystal resonator arrays, Appl. Phys. Lett. 84, 161 (2004).
102. M. Bayindir, B. Temelkuran, and E. Ozbay, Propagation of photons by hopping: a waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals, Phys. Rev. B 61, R11855 (2000).
103. M. Bayindir, B. Temelkuran, and E. Ozbay, Tight-binding description of the coupled defect modes in three-dimensional photonic crystals, Phys. Rev. Lett. 84, 2140 (2000)
104. F.H. Julien and A. Alexandrou, Controlling artificial atoms, Science 20, 1429 (1998).
105. A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P.M. Petroff, and A. Imamam̌glu, Deterministic coupling of single quantum dots to single nanocavity modes, Science 308,1158 (2005).
106. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Ultrahigh-Q photonic double-heterostructure nanocavity, Nature Mater. 4, 207 (2005).
107. A.M. Armani, A. Srinivasan, and K.J. Vahala, Soft lithographic fabrication of high Q polymer microcavity arrays, Nano Lett. 7, 6 (2007).
108. T.J. Kippenberg, S.M. Spillane, B. Min, and K.J. Vahala, Demonstration of ultra-high-Q small mode volume toroid micro-cavities on a chip, Appl. Phys. Lett. 85, 6113 (2004).
109. S.M. Spillane, T.J. Kippenberg, O.J. Painter, and K.J. Vahala, Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics, Phys. Rev. Lett. 91, 043902 (2003).
110. B. Dayan, A.S. Parkins, T. Aoki, E.P. Ostby, K.J. Vahala, and H.J. Kimble, A photon turnstile dynamically regulated by one atom, Science 319, 1062 (2008).
111. M. Trupke, E.A. Hinds, S. Eriksson, E.A. Curtis, Z. Moktadir, E. Kukharenka, and M. Kraft, Microfabricated high-finesse optical cavity with open access and small volume, Appl. Phys. Lett. 87, 211106 (2005).
112. http://www3.imperial.ac.uk/ccm/research/coldatoms/cavity.
113. M.A. Sillanpää, J.I. Park, and R. W. Simmonds, Coherent quantum state storage and transfer between two phase qubits via a resonant cavity, Nature 449, 438 (2007).
114. J. Majer, J.M. Chow, J.M. Gambetta, J. Koch, B.R. Johnson, J.A. Schreier, L. Frunzio, D.I. Schuster, A.A. Houck, A. Wallraff, A. Blais, M.H. Devoret, S.M. Girvin, and R.J. Schoelkopf, Coupling superconducting qubits via a cavity bus, Nature 449, 443 (2007).
115. J.M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff Climbing the Jaynes-Cummings ladder and observing its n nonlinearity in a cavity QED system, Nature 454, 315 (2008).