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

[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. 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]

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

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]

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]

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]

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]

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).

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]

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]

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]

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]

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

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

[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]

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]

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

[Crossref]

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

[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]

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

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

[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).

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

[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).

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]

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]

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]

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.

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

[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]

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

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. 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).

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

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]

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

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

[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]

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).

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]

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]

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]

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]

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

[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]

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]

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

[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).

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]

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]

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]

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, 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. 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]

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]

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]

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]

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]

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]

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

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]

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]

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]

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]

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]

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]

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).

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]

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]

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]

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. 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]

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]

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]

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

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

[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]

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

[Crossref]

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.

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

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

[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]

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]

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]

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]

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

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]

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]

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).

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.

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]

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).

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]

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]

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. 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).

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).

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]

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.

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. 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]

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

[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]

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]

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]

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]

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]

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

[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]

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

[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]

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]

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).

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]

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. 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).

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]

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]

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]

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]

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

[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]

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

[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. 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]

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]

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. 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).

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]

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]

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]

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]

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

[Crossref]

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).

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]

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. 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).

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]

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]

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).

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]

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]

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).

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]

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]

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. 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]

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]

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

[Crossref]

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

[Crossref]

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

[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]

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. 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.

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

[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]

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.

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. 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]

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.

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).

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]

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]

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]

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]

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]

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]

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]

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]

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

[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]

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]

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

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]

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]

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

[Crossref]

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

[Crossref]

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.