Abstract

We investigate the mutiphoton process between different Bloch states in an amplitude modulated optical lattice. In the experiment, we perform the modulation with more than one frequency components, which includes a high degree of freedom and provides a flexible way to coherently control quantum states. Based on the study of single frequency modulation, we investigate the collaborative effect of different frequency components in two aspects. Through double frequency modulations, the spectrums of excitation rates for different lattice depths are measured. Moreover, interference between two separated excitation paths is shown, emphasizing the influence of modulation phases when two modulation frequencies are commensurate. Finally, we demonstrate the application of the double frequency modulation to design a large-momentum-transfer beam splitter. The beam splitter is easy in practice and would not introduce phase shift between two arms.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
  2. P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
    [Crossref] [PubMed]
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    [Crossref]
  4. A. Alberti, V. V. Ivanov, G. M. Tino, and G. Ferrari, “Engineering the quantum transport of atomic wavefunctions over macroscopic distances,” Nature Phys. 5, 547–550 (2009).
    [Crossref]
  5. A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  16. M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
    [Crossref]
  23. T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
    [Crossref] [PubMed]
  24. D. Döring, J. E. Debs, N. P. Robins, C. Figl, P. A. Altin, and J. D. Close, “Ramsey interferometry with an atom laser,” Opt. Express 17, 20661–20668 (2009).
    [Crossref] [PubMed]
  25. W. Zheng and H. Zhai, “Floquet topological states in shaking optical lattices,” Phys. Rev. A 89, 061603 (2014).
    [Crossref]
  26. S.-L. Zhang and Q. Zhou, “Shaping topological properties of the band structures in a shaken optical lattice,” Phys. Rev. A 90, 051601 (2014).
    [Crossref]

2014 (3)

W. Zheng and H. Zhai, “Floquet topological states in shaking optical lattices,” Phys. Rev. A 89, 061603 (2014).
[Crossref]

S.-L. Zhang and Q. Zhou, “Shaping topological properties of the band structures in a shaken optical lattice,” Phys. Rev. A 90, 051601 (2014).
[Crossref]

K. Hai, Y. Luo, G. Lu, and W. Hai, “Phase-controlled localization and directed transport in an optical bipartite lattice,” Opt. Express 22, 4277–4289 (2014).
[Crossref] [PubMed]

2013 (6)

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

C. V. Parker, L. C. Ha, and C. Chin, “Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice,” Nat. Phys. 9, 769–774 (2013).
[Crossref]

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

A. Gómez-León and G. Platero, “Floquet-Bloch theory and topology in periodically driven lattices,” Phys. Rev. Lett. 110, 200403 (2013).
[Crossref] [PubMed]

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
[Crossref]

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

2012 (2)

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

2011 (2)

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

X. X. Liu, X. J. Zhou, W. Xiong, T. Vogt, and X. Z. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
[Crossref]

2010 (1)

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
[Crossref]

2009 (4)

P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “Large momentum beam splitter using Bloch oscillations,” Phys. Rev. Lett. 102, 240402 (2009).
[Crossref] [PubMed]

A. Alberti, V. V. Ivanov, G. M. Tino, and G. Ferrari, “Engineering the quantum transport of atomic wavefunctions over macroscopic distances,” Nature Phys. 5, 547–550 (2009).
[Crossref]

A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
[Crossref] [PubMed]

D. Döring, J. E. Debs, N. P. Robins, C. Figl, P. A. Altin, and J. D. Close, “Ramsey interferometry with an atom laser,” Opt. Express 17, 20661–20668 (2009).
[Crossref] [PubMed]

2004 (2)

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a strongly interacting 1D superfluid to a Mott insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[Crossref] [PubMed]

S.-I. Chu and D. A. Telnov, “Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields,” Phys. Rep. 390, 1–131 (2004).
[Crossref]

2002 (1)

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

2001 (3)

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274–278 (2001).
[Crossref] [PubMed]

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, “Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices,” Phys. Rev. Lett. 87, 140402 (2001).
[Crossref] [PubMed]

1999 (2)

D. Choi and Q. Niu, “Bose-Einstein condensates in an optical lattice,” Phys. Rev. Lett. 82, 2022 (1999).
[Crossref]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Alberti, A.

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
[Crossref]

A. Alberti, V. V. Ivanov, G. M. Tino, and G. Ferrari, “Engineering the quantum transport of atomic wavefunctions over macroscopic distances,” Nature Phys. 5, 547–550 (2009).
[Crossref]

Altin, P. A.

Arimondo, E.

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, “Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices,” Phys. Rev. Lett. 87, 140402 (2001).
[Crossref] [PubMed]

Arimonodo, E.

A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
[Crossref] [PubMed]

Biraben, F.

P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “Large momentum beam splitter using Bloch oscillations,” Phys. Rev. Lett. 102, 240402 (2009).
[Crossref] [PubMed]

Browaeys, A.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Celi, A.

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

Cheiney, P.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Chen, X. Z.

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
[Crossref]

X. X. Liu, X. J. Zhou, W. Xiong, T. Vogt, and X. Z. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
[Crossref]

Chin, C.

C. V. Parker, L. C. Ha, and C. Chin, “Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice,” Nat. Phys. 9, 769–774 (2013).
[Crossref]

Chiofalo, M. L.

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
[Crossref]

Cho, D.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

Choi, D.

D. Choi and Q. Niu, “Bose-Einstein condensates in an optical lattice,” Phys. Rev. Lett. 82, 2022 (1999).
[Crossref]

Chu, S.-I.

S.-I. Chu and D. A. Telnov, “Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields,” Phys. Rep. 390, 1–131 (2004).
[Crossref]

Ciampini, D.

A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
[Crossref] [PubMed]

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, “Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices,” Phys. Rev. Lett. 87, 140402 (2001).
[Crossref] [PubMed]

Cladé, P.

P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “Large momentum beam splitter using Bloch oscillations,” Phys. Rev. Lett. 102, 240402 (2009).
[Crossref] [PubMed]

Close, J. D.

Cristiani, M.

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, “Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices,” Phys. Rev. Lett. 87, 140402 (2001).
[Crossref] [PubMed]

Debs, J. E.

Deng, L.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Denisov, S.

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

Denschlag, J. H.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

Döring, D.

Eckardt, A.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

Esslinger, T.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a strongly interacting 1D superfluid to a Mott insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[Crossref] [PubMed]

Fabre, C. M.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Ferrari, G.

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
[Crossref]

A. Alberti, V. V. Ivanov, G. M. Tino, and G. Ferrari, “Engineering the quantum transport of atomic wavefunctions over macroscopic distances,” Nature Phys. 5, 547–550 (2009).
[Crossref]

Figl, C.

Gattobigio, G. L.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Gómez-León, A.

A. Gómez-León and G. Platero, “Floquet-Bloch theory and topology in periodically driven lattices,” Phys. Rev. Lett. 110, 200403 (2013).
[Crossref] [PubMed]

Guellati-Khélifa, S.

P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “Large momentum beam splitter using Bloch oscillations,” Phys. Rev. Lett. 102, 240402 (2009).
[Crossref] [PubMed]

Guéry-Odelin, D.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Ha, L. C.

C. V. Parker, L. C. Ha, and C. Chin, “Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice,” Nat. Phys. 9, 769–774 (2013).
[Crossref]

Häffner, H.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Hagley, E. W.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Hai, K.

Hai, W.

Hänggi, P.

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

Hauke, P.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

Heckenberg, N. R.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Helmerson, K.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Hensinger, W. K.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Höppner, R.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

Ivanov, V. V.

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
[Crossref]

A. Alberti, V. V. Ivanov, G. M. Tino, and G. Ferrari, “Engineering the quantum transport of atomic wavefunctions over macroscopic distances,” Nature Phys. 5, 547–550 (2009).
[Crossref]

Kling, S.

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

Köhl, M.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a strongly interacting 1D superfluid to a Mott insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[Crossref] [PubMed]

Kozuma, M.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Lahaye, T.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Lewenstein, M.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

Lignier, H.

A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
[Crossref] [PubMed]

Liu, X. X.

X. X. Liu, X. J. Zhou, W. Xiong, T. Vogt, and X. Z. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
[Crossref]

Lu, G.

Luo, Y.

Lutwak, R.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Mathevet, R.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Mathey, L.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

McKenzie, C.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Milburn, G. J.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Moritz, H.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a strongly interacting 1D superfluid to a Mott insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[Crossref] [PubMed]

Morsch, O.

A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
[Crossref] [PubMed]

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, “Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices,” Phys. Rev. Lett. 87, 140402 (2001).
[Crossref] [PubMed]

Müller, J. H.

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, “Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices,” Phys. Rev. Lett. 87, 140402 (2001).
[Crossref] [PubMed]

Nez, F.

P. Cladé, S. Guellati-Khélifa, F. Nez, and F. Biraben, “Large momentum beam splitter using Bloch oscillations,” Phys. Rev. Lett. 102, 240402 (2009).
[Crossref] [PubMed]

Niu, Q.

D. Choi and Q. Niu, “Bose-Einstein condensates in an optical lattice,” Phys. Rev. Lett. 82, 2022 (1999).
[Crossref]

Ölschläger, C.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

Oskay, W. H.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274–278 (2001).
[Crossref] [PubMed]

Parker, C. V.

C. V. Parker, L. C. Ha, and C. Chin, “Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice,” Nat. Phys. 9, 769–774 (2013).
[Crossref]

Phillips, W. D.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Platero, G.

A. Gómez-León and G. Platero, “Floquet-Bloch theory and topology in periodically driven lattices,” Phys. Rev. Lett. 110, 200403 (2013).
[Crossref] [PubMed]

Poli, N.

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

Ponomarev, A. V.

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

Prevedelli, M.

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

Raizen, M. G.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274–278 (2001).
[Crossref] [PubMed]

Robins, N. P.

Rolston, S. L.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Rubinsztein-Dunlop, H.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Salger, T.

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

Schori, C.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a strongly interacting 1D superfluid to a Mott insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[Crossref] [PubMed]

Sengstock, K.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

Simonet, J.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

Simsarian, J. E.

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
[Crossref]

Steck, D. A.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science 293, 274–278 (2001).
[Crossref] [PubMed]

Stöferle, T.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a strongly interacting 1D superfluid to a Mott insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[Crossref] [PubMed]

Struck, J.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

Tarallo, M. G.

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

Telnov, D. A.

S.-I. Chu and D. A. Telnov, “Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields,” Phys. Rep. 390, 1–131 (2004).
[Crossref]

Tieleman, O.

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

Tino, G. M.

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
[Crossref]

A. Alberti, V. V. Ivanov, G. M. Tino, and G. Ferrari, “Engineering the quantum transport of atomic wavefunctions over macroscopic distances,” Nature Phys. 5, 547–550 (2009).
[Crossref]

Upcroft, B.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
[Crossref] [PubMed]

Vermersch, F.

P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

Vogt, T.

X. X. Liu, X. J. Zhou, W. Xiong, T. Vogt, and X. Z. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
[Crossref]

Wang, F.-Y.

N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, “Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter,” Phys. Rev. Lett. 106, 038501 (2011).
[Crossref] [PubMed]

Weinberg, M.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

Weitz, M.

T. Salger, S. Kling, S. Denisov, A. V. Ponomarev, P. Hänggi, and M. Weitz, “Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands,” Phys. Rev. Lett. 110, 135302 (2013).
[Crossref] [PubMed]

Wen, J.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction,” Phys. Rev. Lett. 82, 871–875 (1999).
[Crossref]

Windpassinger, P.

J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, and L. Mathey, “Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields,” Nature Phys. 9, 738–743 (2013).
[Crossref]

J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, “Tunable gauge potential for neutral and spinless particles in driven optical lattices,” Phys. Rev. Lett. 108, 225304 (2012).
[Crossref] [PubMed]

P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, “Non-Abelian gauge fields and topological insulators in shaken optical lattices,” Phys. Rev. Lett. 109, 145301 (2012).
[Crossref] [PubMed]

Wu, Y. J.

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
[Crossref]

Xiong, W.

X. X. Liu, X. J. Zhou, W. Xiong, T. Vogt, and X. Z. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
[Crossref]

Yue, X. G.

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
[Crossref]

Zenesini, A.

A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimonodo, “Coherent control of dressed matter waves,” Phys. Rev. Lett. 102, 100403 (2009).
[Crossref] [PubMed]

Zhai, H.

W. Zheng and H. Zhai, “Floquet topological states in shaking optical lattices,” Phys. Rev. A 89, 061603 (2014).
[Crossref]

Zhai, Y. Y.

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
[Crossref]

Zhang, P.

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
[Crossref]

Zhang, S.-L.

S.-L. Zhang and Q. Zhou, “Shaping topological properties of the band structures in a shaken optical lattice,” Phys. Rev. A 90, 051601 (2014).
[Crossref]

Zheng, W.

W. Zheng and H. Zhai, “Floquet topological states in shaking optical lattices,” Phys. Rev. A 89, 061603 (2014).
[Crossref]

Zhou, Q.

S.-L. Zhang and Q. Zhou, “Shaping topological properties of the band structures in a shaken optical lattice,” Phys. Rev. A 90, 051601 (2014).
[Crossref]

Zhou, X. J.

Y. Y. Zhai, X. G. Yue, Y. J. Wu, X. Z. Chen, P. Zhang, and X. J. Zhou, “Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice,” Phys. Rev. A 87, 063638 (2013).
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X. X. Liu, X. J. Zhou, W. Xiong, T. Vogt, and X. Z. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
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J. Phys. B (1)

J. H. Denschlag, J. E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A Bose-Einstein condensate in an optical lattice,” J. Phys. B 35, 3095–3110 (2002).
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Nat. Phys. (1)

C. V. Parker, L. C. Ha, and C. Chin, “Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice,” Nat. Phys. 9, 769–774 (2013).
[Crossref]

Nature (1)

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunnelling of ultracold atoms,” Nature 412, 52–55 (2001).
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Nature Phys. (2)

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New J. Phys. (1)

A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo, and G. M. Tino, “Atomic wave packets in amplitude-modulated vertical optical lattices,” New J. Phys. 12, 065037 (2010).
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Opt. Express (2)

Phys. Rep. (1)

S.-I. Chu and D. A. Telnov, “Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields,” Phys. Rep. 390, 1–131 (2004).
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P. Cheiney, C. M. Fabre, F. Vermersch, G. L. Gattobigio, R. Mathevet, T. Lahaye, and D. Guéry-Odelin, “Matter-wave scattering on an amplitude-modulated optical lattice,” Phys. Rev. A 87, 013623 (2013).
[Crossref]

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[Crossref]

W. Zheng and H. Zhai, “Floquet topological states in shaking optical lattices,” Phys. Rev. A 89, 061603 (2014).
[Crossref]

S.-L. Zhang and Q. Zhou, “Shaping topological properties of the band structures in a shaken optical lattice,” Phys. Rev. A 90, 051601 (2014).
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Figures (7)

Fig. 1
Fig. 1 A sketch of lattice depth modulation in our system. The depth of lattice potential V0 cos2(kLx) is driven by a polychromatic modulation ∑iVi cos(ωit +ϕi).
Fig. 2
Fig. 2 Left side is the calculated Floquet spectra of a single frequency driven system, with parameters V0 = 5Er, V1 = 0.5Er, h ¯ ω 1 = 5 E r. In the figure the first seven bands are presented. The heavy lines depict states maximally overlapping with the s(blue), p (green) and d (red) Bloch bands respectively. Right side shows the details of two Floquet bands most overlapping with s and d bands. The two bands are separated by a band gap EF at q = 0.
Fig. 3
Fig. 3 Time evolution of nl measured from the experiments with initial modulation phase (a1) ϕ = −π/2 and (a2) ϕ = π/2. Time averaged fraction 〈nl〉 are also shown for (b1) ϕ = −π/2 and (b2) ϕ = π/2 respectively. n0 is shown with black dots comparing to the numerical simulation in solid lines. n1 and n1 are shown in average with red circles the corresponding numerical result is shown in dashed lines. Each point is averaged by three experiments and the error bars indicate the standard deviation.
Fig. 4
Fig. 4 (a) Two special cases in detecting the transfer population spectrum. In case 1, absorption of photons with ω1(orange) or ω2(red) is resonant with d band. In case 2, two frequencies are equal. (b) For s-g coupling ω1 provides a two-photon process while ω2 = 2ω1 provides a one-photon process. Phases of two paths are controlled independently by modulation phases of ω1 and ω2.
Fig. 5
Fig. 5 Spectrum for the population on ± 4 h ¯ k L states with increasing of modulation frequency ω1. Population detected on ± 4 h ¯ k L after a double frequency modulation for (a) V0 = 5Er(black) with V1 = 1.4Er, ±V2 = 1.6Er t = 300μs, (b) V0 = 10Er(blue) with V1 = 2.8Er, V2 = 2.2Er and t = 200μs, (c) V0 = 14Er(red) with V1 = V2 = 2.5Er and t = 150μs are shown in rectangles with error bars. Solid lines are corresponding numerical simulation.
Fig. 6
Fig. 6 The excited population on g band shows the interference between two paths. (a) Population transferred to n±2 is shown in black dots with error bars. The dashed line shows theoretical simulation for comparison. (b1)-(b4) VL for different phases.
Fig. 7
Fig. 7 A LMT beam splitter with a separation of 12 h ¯ k L. (a) TOF image of the LMT beam splitter. (b) Experimentally measured population of atom on momentum states | ± 6 h ¯ k L are shown in black dots with error bars.

Equations (7)

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H ( t ) = p x 2 2 M + V 0 cos 2 ( k L x ) + i V i cos ( ω i t + ϕ i ) cos 2 ( k L x ) .
| ψ q , α ( t + T ) = U ^ ( T ) | ψ q , α ( t ) = e i ε q , α T | ψ q , α ( t ) ,
( H ( t ) i t ) | u q , α = H 0 | u q , α = ε q , α | u q , α .
A l m , l m = 1 T 0 T | v l m H 0 v l m | d t .
H R = ( H R V 1 e i ϕ 1 Ω α β * V 1 e i ϕ 1 Ω α β * E β h ¯ ω ) ,
H s g = ( E s e i ϕ 1 V 1 Ω s d e i ϕ 2 V 2 Ω s d 0 0 0 e i ϕ 1 V 1 Ω s d * E d h ¯ ω 1 0 e i ϕ 2 V 2 Ω d g e i ϕ 1 V 1 Ω d g 0 e i ϕ 2 V 2 Ω s d * 0 E d h ¯ ω 2 e i ϕ 1 V 1 Ω d g 0 e i ϕ 2 V 2 Ω d g 0 e i ϕ 2 V 2 Ω d g * e i ϕ 1 V 1 Ω d g * E g h ¯ ( ω 1 + ω 2 ) 0 0 0 e i ϕ 1 V 1 Ω d g * 0 0 E g 2 h ¯ ω 1 0 0 0 e i ϕ 2 V 2 Ω d g * 0 0 E g 2 h ¯ ω 2 ) ,
i h ¯ ψ t = [ h ¯ 2 2 m 2 x 2 + V L ( x , t ) + 1 2 m ω x 2 x 2 + g | ψ | 2 ] ψ ,

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