Abstract

Recently, there has been growing interest in the creation of artificial magnetic fields for uncharged particles, such as cold atoms or photons. These efforts are partly motivated by the resulting desirable features, such as transport along edge states that is robust against backscattering. We analyze how the optomechanical interaction between photons and mechanical vibrations can be used to create artificial magnetic fields for photons on a lattice. The ingredients required are an optomechanical crystal, i.e., a free-standing photonic crystal with localized vibrational and optical modes, and two laser beams with the right pattern of phases. One of the two schemes analyzed here is based on optomechanical modulation of the links between optical modes, while the other is a lattice extension of optomechanical wavelength-conversion setups. We analyze both schemes theoretically and present numerical simulations of the resulting optical spectrum, photon transport in the presence of an artificial Lorentz force, edge states, and the photonic Aharonov–Bohm effect. We discuss the requirements for experimental realizations. Finally, we analyze the completely general situation of an optomechanical system subject to an arbitrary optical phase pattern and conclude that it is best described in terms of gauge fields acting in synthetic dimensions. In contrast to existing nonoptomechanical approaches, the schemes analyzed here are very versatile, since they can be controlled fully optically, allowing for time-dependent in situ tunability without the need for individual electrical addressing of localized optical modes.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Controllable photon and phonon localization in optomechanical Lieb lattices

Liang-Liang Wan, Xin-You Lü, Jin-Hua Gao, and Ying Wu
Opt. Express 25(15) 17364-17374 (2017)

Diamond optomechanical crystals

Michael J. Burek, Justin D. Cohen, Seán M. Meenehan, Nayera El-Sawah, Cleaven Chia, Thibaud Ruelle, Srujan Meesala, Jake Rochman, Haig A. Atikian, Matthew Markham, Daniel J. Twitchen, Mikhail D. Lukin, Oskar Painter, and Marko Lončar
Optica 3(12) 1404-1411 (2016)

References

  • View by:
  • |
  • |
  • |

  1. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
    [Crossref]
  2. A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
    [Crossref]
  3. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
    [Crossref]
  4. A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
    [Crossref]
  5. E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
    [Crossref]
  6. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
    [Crossref]
  7. A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
    [Crossref]
  8. G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
    [Crossref]
  9. C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
    [Crossref]
  10. M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
    [Crossref]
  11. M. Bhattacharya and P. Meystre, “Multiple membrane cavity optomechanics,” Phys. Rev. A 78, 041801 (2008).
    [Crossref]
  12. A. Xuereb, C. Genes, and A. Dantan, “Strong coupling and long-range collective interactions in optomechanical arrays,” Phys. Rev. Lett. 109, 223601 (2012).
    [Crossref]
  13. A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
    [Crossref]
  14. M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14, 125005 (2012).
    [Crossref]
  15. U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
    [Crossref]
  16. D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
    [Crossref]
  17. W. Chen and A. A. Clerk, “Photon propagation in a one-dimensional optomechanical lattice,” Phys. Rev. A 89, 033854 (2014).
    [Crossref]
  18. M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical Dirac physics,” New J. Phys. 17, 023025 (2015).
    [Crossref]
  19. J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
    [Crossref]
  20. M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
    [Crossref]
  21. R. O. Umucalılar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
    [Crossref]
  22. K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6, 782–787 (2012).
    [Crossref]
  23. M. Hafezi and P. Rabl, “Optomechanically induced non-reciprocity in microring resonators,” Opt. Express 20, 7672–7684 (2012).
    [Crossref]
  24. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
    [Crossref]
  25. S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
    [Crossref]
  26. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
    [Crossref]
  27. Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
    [Crossref]
  28. A. Bermudez, T. Schaetz, and D. Porras, “Synthetic gauge fields for vibrational excitations of trapped ions,” Phys. Rev. Lett. 107, 150501 (2011).
    [Crossref]
  29. M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
    [Crossref]
  30. H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
    [Crossref]
  31. L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
    [Crossref]
  32. G. Heinrich, J. G. E. Harris, and F. Marquardt, “Photon shuttle: Landau-Zener-Stückelberg dynamics in an optomechanical system,” Phys. Rev. A 81, 011801 (2010).
    [Crossref]
  33. A. R. Kolovsky, “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling,” Europhys. Lett. 93, 20003 (2011).
    [Crossref]
  34. C. E. Creffield and F. Sols, “Comment on ‘Creating artificial magnetic fields for cold atoms by photon-assisted tunneling’ by Kolovsky A. R.,” Europhys. Lett. 101, 40001 (2013).
    [Crossref]
  35. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
    [Crossref]
  36. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
    [Crossref]
  37. C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
    [Crossref]
  38. D. R. Hofstadter, “Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,” Phys. Rev. B 14, 2239–2249 (1976).
  39. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 (Butterworth-Heinemann, 1980).
  40. Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485–491 (1959).
    [Crossref]
  41. O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
    [Crossref]
  42. A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
    [Crossref]
  43. M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).
  44. B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).
  45. H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
    [Crossref]
  46. S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
    [Crossref]
  47. V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” arXiv:1409.5375 (2014).
  48. J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.
  49. H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
    [Crossref]
  50. K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
    [Crossref]

2015 (1)

M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical Dirac physics,” New J. Phys. 17, 023025 (2015).
[Crossref]

2014 (6)

W. Chen and A. A. Clerk, “Photon propagation in a one-dimensional optomechanical lattice,” Phys. Rev. A 89, 033854 (2014).
[Crossref]

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

2013 (7)

C. E. Creffield and F. Sols, “Comment on ‘Creating artificial magnetic fields for cold atoms by photon-assisted tunneling’ by Kolovsky A. R.,” Europhys. Lett. 101, 40001 (2013).
[Crossref]

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref]

2012 (11)

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

A. Xuereb, C. Genes, and A. Dantan, “Strong coupling and long-range collective interactions in optomechanical arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14, 125005 (2012).
[Crossref]

U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6, 782–787 (2012).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
[Crossref]

M. Hafezi and P. Rabl, “Optomechanically induced non-reciprocity in microring resonators,” Opt. Express 20, 7672–7684 (2012).
[Crossref]

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

2011 (8)

A. Bermudez, T. Schaetz, and D. Porras, “Synthetic gauge fields for vibrational excitations of trapped ions,” Phys. Rev. Lett. 107, 150501 (2011).
[Crossref]

A. R. Kolovsky, “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling,” Europhys. Lett. 93, 20003 (2011).
[Crossref]

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

R. O. Umucalılar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
[Crossref]

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

2010 (4)

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[Crossref]

G. Heinrich, J. G. E. Harris, and F. Marquardt, “Photon shuttle: Landau-Zener-Stückelberg dynamics in an optomechanical system,” Phys. Rev. A 81, 011801 (2010).
[Crossref]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
[Crossref]

2009 (3)

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

2008 (2)

M. Bhattacharya and P. Meystre, “Multiple membrane cavity optomechanics,” Phys. Rev. A 78, 041801 (2008).
[Crossref]

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

2006 (1)

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

1976 (1)

D. R. Hofstadter, “Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,” Phys. Rev. B 14, 2239–2249 (1976).

1959 (1)

Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485–491 (1959).
[Crossref]

Aharonov, Y.

Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485–491 (1959).
[Crossref]

Aidelsburger, M.

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

Akram, U.

U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
[Crossref]

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

Arcizet, O.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Atala, M.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

Aycock, L. M.

B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).

Badolato, A.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

Balet, L.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Barak, G.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Barreiro, J. T.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

Bermudez, A.

A. Bermudez, T. Schaetz, and D. Porras, “Synthetic gauge fields for vibrational excitations of trapped ions,” Phys. Rev. Lett. 107, 150501 (2011).
[Crossref]

Beveratos, A.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Bhattacharya, M.

M. Bhattacharya and P. Meystre, “Multiple membrane cavity optomechanics,” Phys. Rev. A 78, 041801 (2008).
[Crossref]

Bloch, I.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

Boada, O.

O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
[Crossref]

Bohm, D.

Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485–491 (1959).
[Crossref]

Braive, R.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Brendel, C.

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” arXiv:1409.5375 (2014).

Burton, W. C.

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Cappellini, G.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Carusotto, I.

R. O. Umucalılar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
[Crossref]

Catani, J.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Celi, A.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
[Crossref]

Chan, J.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Chang, D. E.

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

Chen, C. J.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Chen, W.

W. Chen and A. A. Clerk, “Photon propagation in a one-dimensional optomechanical lattice,” Phys. Rev. A 89, 033854 (2014).
[Crossref]

Chen, Y.-A.

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

Clerk, A. A.

W. Chen and A. A. Clerk, “Photon propagation in a one-dimensional optomechanical lattice,” Phys. Rev. A 89, 033854 (2014).
[Crossref]

Compton, R. L.

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

Creffield, C. E.

C. E. Creffield and F. Sols, “Comment on ‘Creating artificial magnetic fields for cold atoms by photon-assisted tunneling’ by Kolovsky A. R.,” Europhys. Lett. 101, 40001 (2013).
[Crossref]

Dalmonte, M.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Dantan, A.

A. Xuereb, C. Genes, and A. Dantan, “Strong coupling and long-range collective interactions in optomechanical arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

Demler, E. A.

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

Diehl, S.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

Dong, C.

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Faez, S.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

Fallani, L.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Fan, J.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

Fan, S.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6, 782–787 (2012).
[Crossref]

Fang, K.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6, 782–787 (2012).
[Crossref]

Fiore, A.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Fiore, V.

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

Francardi, M.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Gavartin, E.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Genes, C.

A. Xuereb, C. Genes, and A. Dantan, “Strong coupling and long-range collective interactions in optomechanical arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

Genkina, D.

B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).

Gerardino, A.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Girvin, S. M.

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[Crossref]

Goldman, N.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

Groblacher, S.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Gröblacher, S.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

Habraken, S. J. M.

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

Hafezi, M.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

M. Hafezi and P. Rabl, “Optomechanically induced non-reciprocity in microring resonators,” Opt. Express 20, 7672–7684 (2012).
[Crossref]

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

Halperin, B. I.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Harris, J. G. E.

G. Heinrich, J. G. E. Harris, and F. Marquardt, “Photon shuttle: Landau-Zener-Stückelberg dynamics in an optomechanical system,” Phys. Rev. A 81, 011801 (2010).
[Crossref]

Heinrich, G.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

G. Heinrich, J. G. E. Harris, and F. Marquardt, “Photon shuttle: Landau-Zener-Stückelberg dynamics in an optomechanical system,” Phys. Rev. A 81, 011801 (2010).
[Crossref]

Hennessy, K.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Hofstadter, D. R.

D. R. Hofstadter, “Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,” Phys. Rev. B 14, 2239–2249 (1976).

Högerle, C.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

Holmes, C. A.

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

Houck, A. A.

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[Crossref]

Hu, E.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

Hur, K. L.

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[Crossref]

Imamoglu, A.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

Inguscio, M.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Jimenez-Garcia, K.

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

Juzeliunas, G.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

Kennedy, C. J.

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

Ketterle, W.

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Kiravittaya, S.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Koch, J.

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[Crossref]

Kolovsky, A. R.

A. R. Kolovsky, “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling,” Europhys. Lett. 93, 20003 (2011).
[Crossref]

Krause, A.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Kubala, B.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

Kumar, S.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Kuzyk, M. C.

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

Kwong, D.-L.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 (Butterworth-Heinemann, 1980).

Latorre, J. I.

O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
[Crossref]

Le Hur, K.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Lee, H. S.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Lewenstein, M.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
[Crossref]

Li, L. H.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 (Butterworth-Heinemann, 1980).

Lin, Y. J.

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

Lipson, M.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

Livi, L.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Lo, G.-Q.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Lohse, M.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

Lu, H.-I.

B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).

Ludwig, M.

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14, 125005 (2012).
[Crossref]

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

Lukin, M. D.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

Lumer, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Mancini, M.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Marquardt, F.

M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical Dirac physics,” New J. Phys. 17, 023025 (2015).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14, 125005 (2012).
[Crossref]

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

G. Heinrich, J. G. E. Harris, and F. Marquardt, “Photon shuttle: Landau-Zener-Stückelberg dynamics in an optomechanical system,” Phys. Rev. A 81, 011801 (2010).
[Crossref]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” arXiv:1409.5375 (2014).

Massignan, P.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

McMillan, J. F.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Meaney, C. P.

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

Meenehan, S.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

Meystre, P.

M. Bhattacharya and P. Meystre, “Multiple membrane cavity optomechanics,” Phys. Rev. A 78, 041801 (2008).
[Crossref]

Migdall, A.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

Milburn, G. J.

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
[Crossref]

Mittal, S.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

Miyake, H.

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

Munro, W.

U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
[Crossref]

Nascimbène, S.

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

Nemoto, K.

U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
[Crossref]

Nolte, S.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Nussenzveig, P.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

Pagano, G.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Painter, O.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Paredes, B.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

Peano, V.

M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical Dirac physics,” New J. Phys. 17, 023025 (2015).
[Crossref]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” arXiv:1409.5375 (2014).

Pfeiffer, L. N.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Plotnik, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Plumhof, J. D.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Podolsky, D.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Porras, D.

A. Bermudez, T. Schaetz, and D. Porras, “Synthetic gauge fields for vibrational excitations of trapped ions,” Phys. Rev. Lett. 107, 150501 (2011).
[Crossref]

Porto, J. V.

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

Qian, J.

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

Rabl, P.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

M. Hafezi and P. Rabl, “Optomechanically induced non-reciprocity in microring resonators,” Opt. Express 20, 7672–7684 (2012).
[Crossref]

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

Rastelli, A.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Rechtsman, M. C.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Rider, M.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Robert-Philip, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Ruseckas, J.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
[Crossref]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

Sagnes, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

Schaetz, T.

A. Bermudez, T. Schaetz, and D. Porras, “Synthetic gauge fields for vibrational excitations of trapped ions,” Phys. Rev. Lett. 107, 150501 (2011).
[Crossref]

Schmidt, M.

M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical Dirac physics,” New J. Phys. 17, 023025 (2015).
[Crossref]

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14, 125005 (2012).
[Crossref]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” arXiv:1409.5375 (2014).

Schmidt, O. G.

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

Segev, M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Sias, C.

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Siviloglou, G. A.

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

Sols, F.

C. E. Creffield and F. Sols, “Comment on ‘Creating artificial magnetic fields for cold atoms by photon-assisted tunneling’ by Kolovsky A. R.,” Europhys. Lett. 101, 40001 (2013).
[Crossref]

Spielman, I. B.

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).

Stannigel, K.

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

Steinberg, H.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Stuhl, B. K.

B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).

Szameit, A.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Taylor, J. M.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

Tomadin, A.

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

Trotzky, S.

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

Tzuang, L. D.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

Umucalilar, R. O.

R. O. Umucalılar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
[Crossref]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Wang, H.

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

West, K. W.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Winger, M.

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

Wong, C. W.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Xuereb, A.

A. Xuereb, C. Genes, and A. Dantan, “Strong coupling and long-range collective interactions in optomechanical arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

Yacoby, A.

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Yu, M.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Yu, Z.

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6, 782–787 (2012).
[Crossref]

Zeuner, J. M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Zheng, J.

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Zoller, P.

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

Appl. Phys. B (1)

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, “Experimental realization of strong effective magnetic fields in optical superlattice potentials,” Appl. Phys. B 113, 1–11 (2013).
[Crossref]

Appl. Phys. Lett. (3)

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97, 181106 (2010).
[Crossref]

H. S. Lee, S. Kiravittaya, S. Kumar, J. D. Plumhof, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, A. Rastelli, and O. G. Schmidt, “Local tuning of photonic crystal nanocavity modes by laser-assisted oxidation,” Appl. Phys. Lett. 95, 191109 (2009).
[Crossref]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[Crossref]

Europhys. Lett. (2)

A. R. Kolovsky, “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling,” Europhys. Lett. 93, 20003 (2011).
[Crossref]

C. E. Creffield and F. Sols, “Comment on ‘Creating artificial magnetic fields for cold atoms by photon-assisted tunneling’ by Kolovsky A. R.,” Europhys. Lett. 101, 40001 (2013).
[Crossref]

Nat. Commun. (1)

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity-optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

Nat. Photonics (3)

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8, 701–705 (2014).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6, 782–787 (2012).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

Nat. Phys. (2)

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. Le Hur, “Charge fractionalization in quantum wires,” Nat. Phys. 4, 116–119 (2008).
[Crossref]

Nature (4)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Y. J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto, and I. B. Spielman, “Synthetic magnetic fields for ultracold neutral atoms,” Nature 462, 628–632 (2009).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

New J. Phys. (4)

M. Schmidt, M. Ludwig, and F. Marquardt, “Optomechanical circuits for nanomechanical continuous variable quantum state processing,” New J. Phys. 14, 125005 (2012).
[Crossref]

D. E. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

M. Schmidt, V. Peano, and F. Marquardt, “Optomechanical Dirac physics,” New J. Phys. 17, 023025 (2015).
[Crossref]

S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, “Continuous mode cooling and phonon routers for phononic quantum networks,” New J. Phys. 14, 115004 (2012).
[Crossref]

Opt. Express (2)

Phys. Rev. (1)

Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485–491 (1959).
[Crossref]

Phys. Rev. A (7)

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED-based photon lattices,” Phys. Rev. A 82, 043811 (2010).
[Crossref]

W. Chen and A. A. Clerk, “Photon propagation in a one-dimensional optomechanical lattice,” Phys. Rev. A 89, 033854 (2014).
[Crossref]

U. Akram, W. Munro, K. Nemoto, and G. J. Milburn, “Photon-phonon entanglement in coupled optomechanical arrays,” Phys. Rev. A 86, 042306 (2012).
[Crossref]

A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, “Reservoir engineering and dynamical phase transitions in optomechanical arrays,” Phys. Rev. A 86, 033821 (2012).
[Crossref]

M. Bhattacharya and P. Meystre, “Multiple membrane cavity optomechanics,” Phys. Rev. A 78, 041801 (2008).
[Crossref]

R. O. Umucalılar and I. Carusotto, “Artificial gauge field for photons in coupled cavity arrays,” Phys. Rev. A 84, 043804 (2011).
[Crossref]

G. Heinrich, J. G. E. Harris, and F. Marquardt, “Photon shuttle: Landau-Zener-Stückelberg dynamics in an optomechanical system,” Phys. Rev. A 81, 011801 (2010).
[Crossref]

Phys. Rev. B (1)

D. R. Hofstadter, “Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,” Phys. Rev. B 14, 2239–2249 (1976).

Phys. Rev. E (1)

C. A. Holmes, C. P. Meaney, and G. J. Milburn, “Synchronization of many nanomechanical resonators coupled via a common cavity field,” Phys. Rev. E 85, 066203 (2012).
[Crossref]

Phys. Rev. Lett. (11)

M. Ludwig and F. Marquardt, “Quantum many-body dynamics in optomechanical arrays,” Phys. Rev. Lett. 111, 073603 (2013).
[Crossref]

A. Xuereb, C. Genes, and A. Dantan, “Strong coupling and long-range collective interactions in optomechanical arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112, 153603 (2014).
[Crossref]

G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett. 107, 043603 (2011).
[Crossref]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[Crossref]

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113, 087403 (2014).
[Crossref]

A. Bermudez, T. Schaetz, and D. Porras, “Synthetic gauge fields for vibrational excitations of trapped ions,” Phys. Rev. Lett. 107, 150501 (2011).
[Crossref]

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013).
[Crossref]

H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, “Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices,” Phys. Rev. Lett. 111, 185302 (2013).
[Crossref]

O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, “Quantum simulation of an extra dimension,” Phys. Rev. Lett. 108, 133001 (2012).
[Crossref]

A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliunas, and M. Lewenstein, “Synthetic gauge fields in synthetic dimensions,” Phys. Rev. Lett. 112, 043001 (2014).
[Crossref]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Science (1)

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

Other (5)

L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 (Butterworth-Heinemann, 1980).

M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,” arXiv:1502.02495 (2015).

B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, “Visualizing edge states with an atomic Bose gas in the quantum Hall regime,” arXiv:1502.02496 (2015).

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” arXiv:1409.5375 (2014).

J. Zheng, C. J. Chen, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Selective tuning of silicon photonic crystal cavities via laser-assisted local oxidation,” in Conference on Lasers and Electro-Optics (CLEO), May 1–6, 2011, pp. 1–2.

Supplementary Material (1)

NameDescription
» Supplement 1: PDF (542 KB)      Supplemental Document

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Proposed schemes to create a photonic gauge field in optomechanical arrays by engineering photon hopping phases. (a) Modulated-link scheme. (b) Corresponding optical spectrum of a row with relevant sidebands (dashed). Driven vibrational modes (yellow) optomechanically modulate the frequency of optical link modes. Tunneling photons are thus upconverted to the first sideband and pick up the phase of the modulation. Arrows in (b) indicate the resonant photon transmission process in a row. (c) Wavelength-conversion scheme and (d) corresponding optical spectrum: neighboring modes in a row couple to a vibrational mode (yellow) optomechanically (red lines, denoting the linearized optomechanical interaction). Two lasers, driving the optical modes close to the red sidebands [wiggly arrows in (d)], give rise to resonant photon–phonon–photon conversion with the phase set by the lasers. Different rows are connected via simple photon hopping (blue lines), without a phase, in both schemes (a),(c). The indicated phase configuration corresponds to a constant magnetic field.
Fig. 2.
Fig. 2. Comparison between (a) experimentally accessible optical spectrum (LDOS) of the ideal effective Hofstadter model and (b)–(d) actual results from the proposed modulated-link scheme, for different optical decay rates and magnetic fluxes. The simulation results indicate that the scheme works even beyond the perturbative regime. The resulting Hofstadter butterfly could be observed by a local tapered fiber probe. Modulation of links produces higher sidebands (d). The phase configuration corresponds to a constant magnetic flux Φ per plaquette; see Fig. 1. [Parameters: grid (a) 10×10, (b)–(d) 12×12; (a)–(d) Jeff=0.108Ω0; (a),(c),(d) κ=0.01Ω0, (b) κ=0.05Ω0; (b)–(d) J=0.3Ω0; (b)–(d) g0|β|=0.3Ω0; optical eigenfrequencies (relative to first mode) in a row (left to right) including interface modes: (b)–(d) (0,0.5,1,1.5,)Ω0.]
Fig. 3.
Fig. 3. Microscopic simulation of the wavelength-conversion scheme, Eq. (4), indicating its feasibility: spatial distribution of light intensity upon local injection of a probe laser (a) in the bulk and (b) at the edge, for a constant artificial magnetic field. Bulk transport (a) is governed by Landau levels and can be understood as a superposition of classical cyclotron orbits (yellow circles) for different momentum directions. (b) At the edges robust edge channels exist. (c) Optical Aharonov–Bohm effect in minimal symmetric setup. (d) The interference pattern (normalized probe laser transmission intensity) is shifted by the magnetic flux through the ring. [Parameters: (a),(b) 22×22 grid; (a),(b) δ=0.3Ω0, (d) δ=0.1Ω0; (a),(b) g=0.2Ω0, (d) g=0.01Ω0; (a),(b) κ=0.01Ω0; Γ=κ/10; (a),(b) Φ=2π/8; (a),(b) J=0.13Ω0, (d) J=0.001Ω0, (a) Δp=1.278Ω0, (b) Δp=1.260Ω0, (d) Δp=1.103Ω0.]
Fig. 4.
Fig. 4. Optomechanical gauge fields within the concept of synthetic dimensions. (a) The optomechanical coupling, g, can be viewed as connecting sites along a synthetic dimension (photons versus phonons). A phase for the photon hopping, engineered using the schemes from above, creates a flux in the optical plaquette (blue, top) and in the adjacent synthetic plaquette (gray). Hence, the magnetic field (black lines) in the full space is divergence-free. (b) Engineering exclusively the phases of g allows us to create magnetic fields/fluxes, but only perpendicular to the synthetic dimension. Shining a single tilted laser on a 1D chain yields a synthetic optomechanical ladder system with constant synthetic magnetic flux. (c) 2D array, with the field inside the (physical) plane generated by an arbitrary laser phase pattern.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

H^hop=Jijeiϕija^ja^i+h.c.,
H^int=g0a^a^(b^+b^).
H^/=i=A,Bωia^ia^i+ωI(t)a^Ia^IJ(a^Ia^A+a^Ba^I+h.c.).
H^/=Ωi=A,Ba^ia^i+Ω0b^b^(gA*a^Ab^+gBa^Bb^+h.c.).

Metrics