Abstract

Atomic media are important in optics research since they can be conveniently manipulated and controlled due to easy selection of atomic levels, laser fields, and the active adjustment of many system parameters. In this paper, we investigate optical Bloch oscillation, Zener tunneling, and Bloch–Zener oscillation in atomic media both theoretically and numerically. We use two coupling fields to prepare the dynamical optical lattice through interference. To induce a transverse force, we make the frequency difference between the two coupling fields increase linearly along the longitudinal coordinate. These phenomena have potential application for beam splitters and optical interconnects, and are helpful for investigating quantum analogies.

© 2017 Optical Society of America

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References

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  1. F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555–600 (1929).
    [Crossref]
  2. J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
    [Crossref]
  3. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
    [Crossref]
  4. R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
    [Crossref]
  5. P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
    [Crossref]
  6. G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
    [Crossref]
  7. U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703 (1998).
    [Crossref]
  8. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
    [Crossref]
  9. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
    [Crossref]
  10. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
    [Crossref]
  11. R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
    [Crossref]
  12. V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
    [Crossref]
  13. M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
    [Crossref]
  14. H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
    [Crossref]
  15. Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
    [Crossref]
  16. Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
    [Crossref]
  17. M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
    [Crossref]
  18. S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).
    [Crossref]
  19. Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
    [Crossref]
  20. C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. London Ser. A 145, 523–529 (1934).
    [Crossref]
  21. F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
    [Crossref]
  22. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
    [Crossref]
  23. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [Crossref]
  24. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
    [Crossref]
  25. I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
    [Crossref]
  26. X.-G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B 54, R5235–R5238 (1996).
    [Crossref]
  27. M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
    [Crossref]
  28. Y. V. Bludov, V. V. Konotop, and M. Salerno, “Rabi oscillations of matter-wave solitons in optical lattices,” Phys. Rev. A 80, 023623 (2009).
    [Crossref]
  29. Y. V. Bludov, V. V. Konotop, and M. Salerno, “Matter waves and quantum tunneling engineered by time-dependent interactions,” Phys. Rev. A 81, 053614 (2010).
    [Crossref]
  30. X. Zhang, F. Ye, Y. V. Kartashov, and X. Chen, “Rabi oscillations and stimulated mode conversion on the subwavelength scale,” Opt. Express 23, 6731–6737 (2015).
    [Crossref]
  31. P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (2013).
    [Crossref]
  32. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [Crossref]
  33. Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
    [Crossref]
  34. H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
    [Crossref]
  35. Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
    [Crossref]
  36. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
    [Crossref]
  37. Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
    [Crossref]
  38. D.-W. Wang, H. Cai, L. Yuan, S.-Y. Zhu, and R.-B. Liu, “Topological phase transitions in superradiance lattices,” Optica 2, 712–715 (2015).
    [Crossref]
  39. C. Hang, G. Huang, and V. V. Konotop, “PT symmetry with a system of three-level atoms,” Phys. Rev. Lett. 110, 083604 (2013).
    [Crossref]
  40. P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
    [Crossref]
  41. Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
    [Crossref]
  42. D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
    [Crossref]
  43. J.-H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
    [Crossref]
  44. C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
    [Crossref]
  45. J.-H. Wu, M. Artoni, and G. C. L. Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
    [Crossref]
  46. J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
    [Crossref]
  47. M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
    [Crossref]
  48. S. Longhi, “Self-imaging and modulational instability in an array of periodically curved waveguides,” Opt. Lett. 30, 2137–2139 (2005).
    [Crossref]
  49. F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
    [Crossref]
  50. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
    [Crossref]
  51. Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

2016 (4)

Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
[Crossref]

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

2015 (4)

X. Zhang, F. Ye, Y. V. Kartashov, and X. Chen, “Rabi oscillations and stimulated mode conversion on the subwavelength scale,” Opt. Express 23, 6731–6737 (2015).
[Crossref]

D.-W. Wang, H. Cai, L. Yuan, S.-Y. Zhu, and R.-B. Liu, “Topological phase transitions in superradiance lattices,” Optica 2, 712–715 (2015).
[Crossref]

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

2014 (2)

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref]

2013 (4)

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

C. Hang, G. Huang, and V. V. Konotop, “PT symmetry with a system of three-level atoms,” Phys. Rev. Lett. 110, 083604 (2013).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (2013).
[Crossref]

2012 (1)

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

2011 (2)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[Crossref]

2010 (3)

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[Crossref]

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Matter waves and quantum tunneling engineered by time-dependent interactions,” Phys. Rev. A 81, 053614 (2010).
[Crossref]

2009 (4)

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Rabi oscillations of matter-wave solitons in optical lattices,” Phys. Rev. A 80, 023623 (2009).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[Crossref]

S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).
[Crossref]

2008 (4)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

J.-H. Wu, M. Artoni, and G. C. L. Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
[Crossref]

2007 (1)

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[Crossref]

2006 (6)

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[Crossref]

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref]

2005 (3)

S. Longhi, “Self-imaging and modulational instability in an array of periodically curved waveguides,” Opt. Lett. 30, 2137–2139 (2005).
[Crossref]

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

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

2004 (2)

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

2003 (1)

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

1999 (2)

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

1998 (2)

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
[Crossref]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703 (1998).
[Crossref]

1996 (2)

X.-G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B 54, R5235–R5238 (1996).
[Crossref]

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

1992 (1)

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

1934 (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. London Ser. A 145, 523–529 (1934).
[Crossref]

1929 (1)

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555–600 (1929).
[Crossref]

Agarwal, V.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Artoni, M.

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref]

J.-H. Wu, M. Artoni, and G. C. L. Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
[Crossref]

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[Crossref]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Battesti, R.

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Belic, M. R.

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Ben Dahan, M.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

Biraben, F.

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Biraben, F. M. C.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

Bloch, F.

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555–600 (1929).
[Crossref]

Bludov, Y. V.

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Matter waves and quantum tunneling engineered by time-dependent interactions,” Phys. Rev. A 81, 053614 (2010).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Rabi oscillations of matter-wave solitons in optical lattices,” Phys. Rev. A 80, 023623 (2009).
[Crossref]

Bräuer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

Bromberg, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[Crossref]

Brown, A. W.

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[Crossref]

Cadoret, M.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

Cai, H.

Cao, W.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Castin, Y.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

Chen, X.

Chen, Y.-F.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Christodoulides, D. N.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Cladé, P.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Coquillat, D.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Costantino, P.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

Cunningham, J. E.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

de Mirandes, E.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

del Río, J. A.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Desbuquois, R.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Desyatnikov, A. S.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

Döring, S.

Dreisow, F.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Esslinger, T.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Evers, J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

Fahr, S.

Fegadolli, W. S.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Feldmann, J.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Ferrari, G.

G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref]

Fischer, M. C.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
[Crossref]

Fleischhauer, M.

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

Gaburro, Z.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

Gan, L.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

Georgakis, G. A.

X.-G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B 54, R5235–R5238 (1996).
[Crossref]

Ghulinyan, M.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

Gil, B.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Gräfe, M.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

Greif, D.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Grémaud, B.

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Guellati-Khélifa, S.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Guo, M.-J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

Hang, C.

C. Hang, G. Huang, and V. V. Konotop, “PT symmetry with a system of three-level atoms,” Phys. Rev. Lett. 110, 083604 (2013).
[Crossref]

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[Crossref]

He, B.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Heilmann, R.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

Heinrich, M.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

Huang, G.

C. Hang, G. Huang, and V. V. Konotop, “PT symmetry with a system of three-level atoms,” Phys. Rev. Lett. 110, 083604 (2013).
[Crossref]

Imamoglu, A.

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

Jiang, L.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Jotzu, G.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Julien, L.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Kartashov, Y. V.

Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
[Crossref]

X. Zhang, F. Ye, Y. V. Kartashov, and X. Chen, “Rabi oscillations and stimulated mode conversion on the subwavelength scale,” Opt. Express 23, 6731–6737 (2015).
[Crossref]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Kavokin, A.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

Konotop, V. V.

Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
[Crossref]

C. Hang, G. Huang, and V. V. Konotop, “PT symmetry with a system of three-level atoms,” Phys. Rev. Lett. 110, 083604 (2013).
[Crossref]

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Matter waves and quantum tunneling engineered by time-dependent interactions,” Phys. Rev. A 81, 053614 (2010).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Rabi oscillations of matter-wave solitons in optical lattices,” Phys. Rev. A 80, 023623 (2009).
[Crossref]

Krolikowski, W.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

La Rocca, G. C.

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref]

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[Crossref]

Lahini, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[Crossref]

Lebrat, M.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Lebugle, M.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703 (1998).
[Crossref]

Leo, K.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Li, Z.-Y.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Liu, R.-B.

Liu, X.

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Liu, X.-P.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[Crossref]

S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).
[Crossref]

S. Longhi, “Self-imaging and modulational instability in an array of periodically curved waveguides,” Opt. Lett. 30, 2137–2139 (2005).
[Crossref]

Lu, M.-H.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Madison, K. W.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
[Crossref]

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Malpuech, G.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Marangos, J. P.

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

Meier, T.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Messer, M.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

Michinel, H.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[Crossref]

Miller, D. A. B.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Miri, M.-A.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Morandotti, R.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Neshev, D. N.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

Nez, F.

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Nez, F. M. C.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

Niu, Q.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
[Crossref]

X.-G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B 54, R5235–R5238 (1996).
[Crossref]

Nolte, S.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

Oton, C. J.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

Pavesi, L.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

Paz-Alonso, M. J.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[Crossref]

Peik, E.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

Peng, P.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Pérez-García, V. M.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[Crossref]

Perez-Leija, A.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

Pertsch, T.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703 (1998).
[Crossref]

Peschel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703 (1998).
[Crossref]

Poli, N.

G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref]

Qu, W.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Raizen, M. G.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
[Crossref]

Reichel, J.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

Rocca, G. C. L.

Salerno, M.

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Matter waves and quantum tunneling engineered by time-dependent interactions,” Phys. Rev. A 81, 053614 (2010).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Rabi oscillations of matter-wave solitons in optical lattices,” Phys. Rev. A 80, 023623 (2009).
[Crossref]

Salomon, C.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

Sapienza, R.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

Scalbert, D.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Scherer, A.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Schmitt-Rink, S.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Schulze, A.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Schwob, C.

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Sengstock, K.

P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (2013).
[Crossref]

Shah, J.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Shen, C.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Sheng, J.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[Crossref]

Sheng, J. T.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Silberberg, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[Crossref]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Sorrentino, F.

G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

Szameit, A.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

Thomas, P.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Tino, G. M.

G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref]

Toninelli, C.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

Torner, L.

Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
[Crossref]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Trompeter, H.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

Tünnermann, A.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

Uehlinger, T.

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Vladimirova, M.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

von Plessen, G.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Wang, D.-W.

D.-W. Wang, H. Cai, L. Yuan, S.-Y. Zhu, and R.-B. Liu, “Topological phase transitions in superradiance lattices,” Optica 2, 712–715 (2015).
[Crossref]

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

Wang, Z. G.

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Wen, F.

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

Wen, J.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Wiersma, D.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

Wiersma, D. S.

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

Windpassinger, P.

P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (2013).
[Crossref]

Wu, H.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[Crossref]

Wu, J.-H.

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref]

J.-H. Wu, M. Artoni, and G. C. L. Rocca, “Controlling the photonic band structure of optically driven cold atoms,” J. Opt. Soc. Am. B 25, 1840–1849 (2008).
[Crossref]

Wu, Z. K.

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

Xiao, M.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[Crossref]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[Crossref]

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Xiao, Y.

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Xu, Y.-L.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Yang, L.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Yang, X.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[Crossref]

Ye, F.

Yuan, C. Z.

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

Yuan, L.

Zamfirescu, M.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

Zener, C.

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. London Ser. A 145, 523–529 (1934).
[Crossref]

Zezyulin, D. A.

Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
[Crossref]

Zhang, D.

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Zhang, J.-X.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

Zhang, X.

Zhang, Y. P.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[Crossref]

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Zhang, Y. Q.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Zhang, Z. Y.

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

Zhao, X.-G.

X.-G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B 54, R5235–R5238 (1996).
[Crossref]

Zheng, H. B.

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

Zhou, H.-T.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

Zhu, S.-Y.

D.-W. Wang, H. Cai, L. Yuan, S.-Y. Zhu, and R.-B. Liu, “Topological phase transitions in superradiance lattices,” Optica 2, 712–715 (2015).
[Crossref]

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (2)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[Crossref]

Y. Q. Zhang, Z. K. Wu, M. R. Belić, H. B. Zheng, Z. G. Wang, M. Xiao, and Y. P. Zhang, “Photonic Floquet topological insulators in atomic ensembles,” Laser Photon. Rev. 9, 331–338 (2015).
[Crossref]

Nat. Commun. (2)

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7, 11319 (2016).
[Crossref]

Nat. Phys. (1)

P. Peng, W. Cao, C. Shen, W. Qu, J. Wen, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).
[Crossref]

Nature (1)

G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimental realization of the topological Haldane model,” Nature 515, 237–240 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Optica (1)

Phys. Rep. (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[Crossref]

Phys. Rev. A (6)

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58, R2648–R2651 (1998).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Rabi oscillations of matter-wave solitons in optical lattices,” Phys. Rev. A 80, 023623 (2009).
[Crossref]

Y. V. Bludov, V. V. Konotop, and M. Salerno, “Matter waves and quantum tunneling engineered by time-dependent interactions,” Phys. Rev. A 81, 053614 (2010).
[Crossref]

Z. K. Wu, Y. Q. Zhang, C. Z. Yuan, F. Wen, H. B. Zheng, Y. P. Zhang, and M. Xiao, “Cubic-quintic condensate solitons in four-wave mixing,” Phys. Rev. A 88, 063828 (2013).
[Crossref]

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[Crossref]

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[Crossref]

Phys. Rev. B (2)

X.-G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B 54, R5235–R5238 (1996).
[Crossref]

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[Crossref]

Phys. Rev. Lett. (23)

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[Crossref]

R. Battesti, P. Cladé, S. Guellati-Khélifa, C. Schwob, B. Grémaud, F. Nez, L. Julien, and F. Biraben, “Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mrb,” Phys. Rev. Lett. 92, 253001 (2004).
[Crossref]

P. Cladé, E. de Mirandes, M. Cadoret, S. Guellati-Khélifa, C. Schwob, F. M. C. Nez, L. Julien, and F. M. C. Biraben, “Determination of the fine structure constant based on Bloch oscillations of ultracold atoms in a vertical optical lattice,” Phys. Rev. Lett. 96, 033001 (2006).
[Crossref]

G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref]

S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[Crossref]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[Crossref]

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92, 097401 (2004).
[Crossref]

M. Ghulinyan, C. J. Oton, Z. Gaburro, L. Pavesi, C. Toninelli, and D. S. Wiersma, “Zener tunneling of light waves in an optical superlattice,” Phys. Rev. Lett. 94, 127401 (2005).
[Crossref]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006).
[Crossref]

Y. V. Kartashov, V. V. Konotop, D. A. Zezyulin, and L. Torner, “Bloch oscillations in optical and Zeeman lattices in the presence of spin-orbit coupling,” Phys. Rev. Lett. 117, 215301 (2016).
[Crossref]

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[Crossref]

C. Hang, G. Huang, and V. V. Konotop, “PT symmetry with a system of three-level atoms,” Phys. Rev. Lett. 110, 083604 (2013).
[Crossref]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[Crossref]

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[Crossref]

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[Crossref]

Z. Y. Zhang, Y. Q. Zhang, J. T. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. P. Zhang, and M. Xiao, “Observation of parity-time symmetry in optically induced atomic lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref]

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref]

J.-H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref]

Proc. R. Soc. London Ser. A (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. London Ser. A 145, 523–529 (1934).
[Crossref]

Rep. Prog. Phys. (1)

P. Windpassinger and K. Sengstock, “Engineering novel optical lattices,” Rep. Prog. Phys. 76, 086401 (2013).
[Crossref]

Rev. Mod. Phys. (2)

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

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Z. Phys. (1)

F. Bloch, “Über die Quantenmechanik der Elektronen in Kristallgittern,” Z. Phys. 52, 555–600 (1929).
[Crossref]

Other (1)

Z. Y. Zhang, X. Liu, D. Zhang, J. T. Sheng, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Observation of electromagnetically induced Talbot effect in an atomic system,” arXiv:1608.00298 (2016).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Λ-type energy system in a rubidium atomic system. (b) Geometry of the beams in (a). (c) Rabi frequency of the two interfering coupling fields for (c1) δ=0, (c2) δ being a constant, and (c3) δ increasing linearly with t.

Fig. 2.
Fig. 2.

Discrete diffraction. (a) δ=0. (b) δ=10  MHz. Inset shows the band structure. From top to bottom are the first, second, third, and fourth bands, respectively. Other parameters are: μ10=3×1029  C·m, N=2×1013  cm3, G12=30  MHz, G12=25  MHz, λ10=770.792  nm, λ12=770.778  nm, Γ10=1  MHz, Γ20=2  kHz, Δ12=0, and Δ10=1  MHz.

Fig. 3.
Fig. 3.

Optical Bloch oscillation and Zener tunneling when only one lattice waveguide is excited. (a) According to Eq. (1). (b) According to Eq. (3). (c) Same as (b), but in the momentum space, which is normalized with k12. We set a=1  MHz2; other parameters are the same as those in Fig. 2. To see the evolution dynamics explicitly, we show the amplitudes rather than the intensity in (a) and (b).

Fig. 4.
Fig. 4.

Same as Fig. 3, but with many lattice waveguides excited.

Fig. 5.
Fig. 5.

Projection coefficients of the beam during evolution. Amplitude is normalized by max{|A14|}.

Equations (3)

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

iE10z+12k102E10x2+12k10χ(1)E10=0,
iE10τ+idζdτE10ξ+12k102E10ξ2+12k10χ(1)E10=0.
iψτ+12k102ψξ2+12k10χ(1)ψ+k10d2ζdτ2ξψ=0.

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