Abstract

The precise calibration of optical lattice depth is an important step in the experiments of ultracold atoms in optical lattices. The Raman-Nath diffraction method, as the most commonly used method of calibrating optical lattice depth, has a limited range of validity and the calibration accuracy is not high enough. Based on multiple pulses Kapitza-Dirac diffraction, we propose and demonstrate a new calibration method by measuring the fully transfer fidelity of the first diffraction order. The high sensitivity of the transfer fidelity to the lattice depth ensures the highly precision calibration of the optical lattice depth. For each lattice depth measured, the calibration uncertainty is further reduced to less than 0.6% by applying the Back-Propagation Neural Network Algorithm. The accuracy of this method is almost one order of magnitude higher than that of the Raman-Nath diffraction method, and it has a wide range of validity applicable to both shallow lattices and deep lattices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
[Crossref] [PubMed]

2017 (4)

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
[Crossref]

C. Li, T. Zhou, Y. Zhai, J. Xiang, T. Luan, Q. Huang, S. Yang, W. Xiong, and X. Chen, “Deep cooling of optically trapped atoms implemented by magnetic levitation without transverse confinement,” Rev. Sci. Instruments 88, 053104 (2017).
[Crossref]

C. Gross and I. Bloch, “Quantum simulations with ultracold atoms in optical lattices,” Science. 357, 995–1001 (2017).
[Crossref] [PubMed]

F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
[Crossref]

2016 (2)

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
[Crossref] [PubMed]

N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12, 639 (2016).
[Crossref]

2015 (2)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
[Crossref]

2014 (2)

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

T. Maier, S. Kraemer, L. Ostermann, and H. Ritsch, “A superradiant clock laser on a magic wavelength optical lattice,” Opt. Express 22, 13269–13279 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267 (2012).
[Crossref]

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302 (2012).
[Crossref] [PubMed]

G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012).
[Crossref] [PubMed]

2011 (1)

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

2010 (1)

M. Edwards, B. Benton, J. Heward, and C. W. Clark, “Momentum-space engineering of gaseous Bose-Einstein condensates,” Phys. Rev. A 82, 063613 (2010).
[Crossref]

2009 (4)

B. Gadway, D. Pertot, R. Reimann, M. G. Cohen, and D. Schneble, “Analysis of Kapitza-Dirac diffraction patterns beyond the Raman-Nath regime,” Opt. Express 17, 19173–19180 (2009).
[Crossref]

R. E. Sapiro, R. Zhang, and G. Raithel, “Reversible loss of superfluidity of a Bose-Einstein condensate in a 1D optical lattice,” New J. Phys. 11, 013013 (2009).
[Crossref]

J. H. Huckans, I. B. Spielman, B. L. Tolra, W. D. Phillips, and J. V. Porto, “Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice,” Phys. Rev. A 80, 043609 (2009).
[Crossref]

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

2008 (2)

M. Greiner and S. Fölling, “Optical lattices,” Nature. 453, 736 (2008).
[Crossref] [PubMed]

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
[Crossref]

2006 (2)

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78, 179–215 (2006).
[Crossref]

A. K. Tuchman, W. Li, H. Chien, S. Dettmer, and M. A. Kasevich, “Localization and anomalous transport in a 1D soft boson optical lattice,” New J. Phys. 8, 311 (2006).
[Crossref]

2005 (4)

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature. 435, 321 (2005).
[Crossref] [PubMed]

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23 (2005).
[Crossref]

L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, “Bose-Einstein condensate in an optical lattice with tunable spacing: transport and static properties,” Opt. Express 13, 4303–4313 (2005).
[Crossref] [PubMed]

S. Wu, Y.-J. Wang, Q. Diot, and M. Prentiss, “Splitting matter waves using an optimized standing-wave light-pulse sequence,” Phys. Rev. A 71, 043602 (2005).
[Crossref]

2002 (2)

M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, “Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,” Phys. Rev. A 65, 063612 (2002).
[Crossref]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature. 415, 39 (2002).
[Crossref] [PubMed]

1999 (2)

Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
[Crossref]

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

1998 (2)

S. Friebel, C. D’Andrea, J. Walz, M. Weitz, and T. W. Hänsch, “CO2-laser optical lattice with cold rubidium atoms,” Phys. Rev. A 57, R20–R23 (1998).
[Crossref]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
[Crossref]

1986 (1)

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[Crossref] [PubMed]

Aidelsburger, M.

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

Akamatsu, D.

Arimondo, E.

M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, “Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,” Phys. Rev. A 65, 063612 (2002).
[Crossref]

Arnold, A. S.

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
[Crossref]

Atala, M.

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

Barreiro, J. T.

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

Benton, B.

M. Edwards, B. Benton, J. Heward, and C. W. Clark, “Momentum-space engineering of gaseous Bose-Einstein condensates,” Phys. Rev. A 82, 063613 (2010).
[Crossref]

Bidel, Y.

F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
[Crossref]

Bloch, I.

C. Gross and I. Bloch, “Quantum simulations with ultracold atoms in optical lattices,” Science. 357, 995–1001 (2017).
[Crossref] [PubMed]

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267 (2012).
[Crossref]

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
[Crossref]

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23 (2005).
[Crossref]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature. 415, 39 (2002).
[Crossref] [PubMed]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Bresson, A.

F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
[Crossref]

Bruder, C.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
[Crossref]

Budich, J. C.

N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12, 639 (2016).
[Crossref]

Cadoret, M.

F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
[Crossref]

Ceperley, D.

D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
[Crossref]

Chen, X.

C. Li, T. Zhou, Y. Zhai, J. Xiang, T. Luan, Q. Huang, S. Yang, W. Xiong, and X. Chen, “Deep cooling of optically trapped atoms implemented by magnetic levitation without transverse confinement,” Rev. Sci. Instruments 88, 053104 (2017).
[Crossref]

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

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

Chien, H.

A. K. Tuchman, W. Li, H. Chien, S. Dettmer, and M. A. Kasevich, “Localization and anomalous transport in a 1D soft boson optical lattice,” New J. Phys. 8, 311 (2006).
[Crossref]

Ciampini, D.

M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, “Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,” Phys. Rev. A 65, 063612 (2002).
[Crossref]

Cirac, J. I.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
[Crossref]

Clark, C. W.

M. Edwards, B. Benton, J. Heward, and C. W. Clark, “Momentum-space engineering of gaseous Bose-Einstein condensates,” Phys. Rev. A 82, 063613 (2010).
[Crossref]

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Cohen, M. G.

Cooper, N. R.

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

Cristiani, M.

M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, “Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,” Phys. Rev. A 65, 063612 (2002).
[Crossref]

Cronin, A. D.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

D’Andrea, C.

S. Friebel, C. D’Andrea, J. Walz, M. Weitz, and T. W. Hänsch, “CO2-laser optical lattice with cold rubidium atoms,” Phys. Rev. A 57, R20–R23 (1998).
[Crossref]

Dalibard, J.

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267 (2012).
[Crossref]

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
[Crossref]

DeMarco, B.

D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
[Crossref]

Deng, L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
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F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
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A. K. Tuchman, W. Li, H. Chien, S. Dettmer, and M. A. Kasevich, “Localization and anomalous transport in a 1D soft boson optical lattice,” New J. Phys. 8, 311 (2006).
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F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
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Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
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M. Edwards, B. Benton, J. Heward, and C. W. Clark, “Momentum-space engineering of gaseous Bose-Einstein condensates,” Phys. Rev. A 82, 063613 (2010).
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L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
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F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
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L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302 (2012).
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature. 415, 39 (2002).
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N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
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Gadway, B.

Gardiner, C. W.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
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N. Goldman, J. C. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nat. Phys. 12, 639 (2016).
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M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
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Görg, F.

F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
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P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
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L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302 (2012).
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature. 415, 39 (2002).
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B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
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B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
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Hagley, E. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
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Halket, J.

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature. 415, 39 (2002).
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S. Friebel, C. D’Andrea, J. Walz, M. Weitz, and T. W. Hänsch, “CO2-laser optical lattice with cold rubidium atoms,” Phys. Rev. A 57, R20–R23 (1998).
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Helmerson, K.

Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
[Crossref]

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
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Heward, J.

M. Edwards, B. Benton, J. Heward, and C. W. Clark, “Momentum-space engineering of gaseous Bose-Einstein condensates,” Phys. Rev. A 82, 063613 (2010).
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M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature. 435, 321 (2005).
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Hosaka, K.

Hosur, P.

G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012).
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C. Li, T. Zhou, Y. Zhai, J. Xiang, T. Luan, Q. Huang, S. Yang, W. Xiong, and X. Chen, “Deep cooling of optically trapped atoms implemented by magnetic levitation without transverse confinement,” Rev. Sci. Instruments 88, 053104 (2017).
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Huckans, J. H.

J. H. Huckans, I. B. Spielman, B. L. Tolra, W. D. Phillips, and J. V. Porto, “Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice,” Phys. Rev. A 80, 043609 (2009).
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Inguscio, M.

Iwakuni, K.

Jaksch, D.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).
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Jo, G.-B.

G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012).
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Jotzu, G.

F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
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L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302 (2012).
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Kasevich, M. A.

A. K. Tuchman, W. Li, H. Chien, S. Dettmer, and M. A. Kasevich, “Localization and anomalous transport in a 1D soft boson optical lattice,” New J. Phys. 8, 311 (2006).
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Katori, H.

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature. 435, 321 (2005).
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Kohno, T.

Kraemer, S.

Li, C.

C. Li, T. Zhou, Y. Zhai, J. Xiang, T. Luan, Q. Huang, S. Yang, W. Xiong, and X. Chen, “Deep cooling of optically trapped atoms implemented by magnetic levitation without transverse confinement,” Rev. Sci. Instruments 88, 053104 (2017).
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Li, W.

A. K. Tuchman, W. Li, H. Chien, S. Dettmer, and M. A. Kasevich, “Localization and anomalous transport in a 1D soft boson optical lattice,” New J. Phys. 8, 311 (2006).
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X. Liu, X. Zhou, W. Xiong, T. Vogt, and X. Chen, “Rapid nonadiabatic loading in an optical lattice,” Phys. Rev. A 83, 063402 (2011).
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M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
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Luan, T.

C. Li, T. Zhou, Y. Zhai, J. Xiang, T. Luan, Q. Huang, S. Yang, W. Xiong, and X. Chen, “Deep cooling of optically trapped atoms implemented by magnetic levitation without transverse confinement,” Rev. Sci. Instruments 88, 053104 (2017).
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A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
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Lühmann, D.-S.

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
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Lye, J. E.

MacKellar, A. R.

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
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Maier, T.

Mandel, O.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature. 415, 39 (2002).
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D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
[Crossref]

Messer, M.

F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
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M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, “Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,” Phys. Rev. A 65, 063612 (2002).
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M. Cristiani, O. Morsch, J. H. Müller, D. Ciampini, and E. Arimondo, “Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,” Phys. Rev. A 65, 063612 (2002).
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Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
[Crossref]

Nakajima, Y.

Nascimbène, S.

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
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I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267 (2012).
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D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
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O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78, 179–215 (2006).
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Okubo, S.

Onae, A.

Ostermann, L.

Ovchinnikov, Y. B.

Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
[Crossref]

Peik, E.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Pertot, D.

Phillips, W. D.

J. H. Huckans, I. B. Spielman, B. L. Tolra, W. D. Phillips, and J. V. Porto, “Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice,” Phys. Rev. A 80, 043609 (2009).
[Crossref]

Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
[Crossref]

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Porto, J. V.

J. H. Huckans, I. B. Spielman, B. L. Tolra, W. D. Phillips, and J. V. Porto, “Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice,” Phys. Rev. A 80, 043609 (2009).
[Crossref]

Prentiss, M.

S. Wu, Y.-J. Wang, Q. Diot, and M. Prentiss, “Splitting matter waves using an optimized standing-wave light-pulse sequence,” Phys. Rev. A 71, 043602 (2005).
[Crossref]

Pritchard, D. E.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[Crossref] [PubMed]

Pritchard, J. D.

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
[Crossref]

Raithel, G.

R. E. Sapiro, R. Zhang, and G. Raithel, “Reversible loss of superfluidity of a Bose-Einstein condensate in a 1D optical lattice,” New J. Phys. 11, 013013 (2009).
[Crossref]

Ray, U.

D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
[Crossref]

Reimann, R.

Rem, B. S.

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
[Crossref] [PubMed]

Riis, E.

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
[Crossref]

Ritsch, H.

Robertson, B. I.

B. I. Robertson, A. R. MacKellar, J. Halket, A. Gribbon, J. D. Pritchard, A. S. Arnold, E. Riis, and P. F. Griffin, “Detection of applied and ambient forces with a matter-wave magnetic gradiometer,” Phys. Rev. A 96, 053622 (2017).
[Crossref]

Rolston, S. L.

Y. B. Ovchinnikov, J. H. Müller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave,” Phys. Rev. Lett. 83, 284–287 (1999).
[Crossref]

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Ruff, G. A.

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[Crossref] [PubMed]

Russ, P.

D. McKay, U. Ray, S. Natu, P. Russ, D. Ceperley, and B. DeMarco, “Metastable Bose-Einstein condensation in a strongly correlated optical lattice,” Phys. Rev. A 91, 023625 (2015).
[Crossref]

Sandholzer, K.

F. Görg, M. Messer, K. Sandholzer, G. Jotzu, R. Desbuquois, and T. Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018).
[Crossref] [PubMed]

Sapiro, R. E.

R. E. Sapiro, R. Zhang, and G. Raithel, “Reversible loss of superfluidity of a Bose-Einstein condensate in a 1D optical lattice,” New J. Phys. 11, 013013 (2009).
[Crossref]

Schmidt, P. O.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Schmiedmayer, J.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

Schneble, D.

Schweizer, C.

M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms,” Nat. Phys. 11, 162 (2014).
[Crossref]

Sengstock, K.

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
[Crossref] [PubMed]

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Spielman, I. B.

J. H. Huckans, I. B. Spielman, B. L. Tolra, W. D. Phillips, and J. V. Porto, “Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice,” Phys. Rev. A 80, 043609 (2009).
[Crossref]

Stamper-Kurn, D. M.

G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012).
[Crossref] [PubMed]

Takamoto, M.

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature. 435, 321 (2005).
[Crossref] [PubMed]

Tarnowski, M.

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
[Crossref] [PubMed]

Tarruell, L.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302 (2012).
[Crossref] [PubMed]

Theron, F.

F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
[Crossref]

Thomas, C. K.

G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012).
[Crossref] [PubMed]

Tolra, B. L.

J. H. Huckans, I. B. Spielman, B. L. Tolra, W. D. Phillips, and J. V. Porto, “Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice,” Phys. Rev. A 80, 043609 (2009).
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N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
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Nature (2)

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302 (2012).
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A. K. Tuchman, W. Li, H. Chien, S. Dettmer, and M. A. Kasevich, “Localization and anomalous transport in a 1D soft boson optical lattice,” New J. Phys. 8, 311 (2006).
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F. Theron, Y. Bidel, E. Dieu, N. Zahzam, M. Cadoret, and A. Bresson, “Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices,” Opt. Commun. 393, 152–155 (2017).
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Opt. Express (4)

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[Crossref]

Y. Zhai, X. Yue, Y. Wu, X. Chen, P. Zhang, and X. 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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G.-B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012).
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Rev. Mod. Phys. (4)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
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I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).
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C. Li, T. Zhou, Y. Zhai, J. Xiang, T. Luan, Q. Huang, S. Yang, W. Xiong, and X. Chen, “Deep cooling of optically trapped atoms implemented by magnetic levitation without transverse confinement,” Rev. Sci. Instruments 88, 053104 (2017).
[Crossref]

Science (1)

N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, “Experimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science.  352, 1091–1094 (2016).
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Figures (5)

Fig. 1
Fig. 1 Theoretical calculations reflect the variation of transfer fidelity with lattice depth. The solid lines in AF correspond to the calculated standing-wave laser pulse sequences (A–F) for different lattice depths in Table 1. The dash lines are the theoretical curves of Raman-Nath method and the fidelity for the dash line means transferring a BEC into the high diffraction orders not just the first order. The change of the transfer fidelity near the highest point of the MPKD diffraction method are clearly more significant than that of the Raman-Nath diffraction method.
Fig. 2
Fig. 2 Structure of the BPNN algorithm.
Fig. 3
Fig. 3 Data fitting process for the lattice depth of 9.97 Er using BPNN algorithm. The blue, green and red dots are the experimental data used for training, validation and test in turn. The black line is the final fit to the data. The errors of the fitting are also shown. The three insets ac are the corresponding integrated density profiles for the selected data to reveal the transfer fidelity variation of the MPKD diffraction method. The slight asymmetry of ±2ħkL peaks is mainly due to the imperfect overlap of the retroreflected lattice laser beam. The lattice depth values (up horizontal axis) put here as a reference come from the final conversion of lattice depth to detection voltage in Eq. (6).
Fig. 4
Fig. 4 The probability distribution of corresponding voltage values of the peak fidelity points from 10, 000 reasonable fittings for the lattice depth of 9.97 Er. The expectation value of the distribution is taken as the calibrated voltage value for the lattice depth. The corresponding calibration uncertainty is determined by the 95% confidence bounds of the distribution. The inset shows how the 95% confidence interval scales with the number of fittings.
Fig. 5
Fig. 5 Lattice depth calibration results. The error bars reflect the 95% confidence bounds of each calibrated value. a, Calibration results of the MPKD diffraction method for different lattice depths. The black solid line is a linear fit to the calibration results. b and c, Comparison of the Raman-Nath diffraction method (blue square with error bar) and the MPKD diffraction method (green circle with error bar) around 20 Er and 50 Er respectively. The corresponding color shaded areas indicate the uncertainty of the linear fitting of the calibration results. The calibration uncertainty of the MPKD diffraction method is much smaller than that of the Raman-Nath diffraction method.

Tables (1)

Tables Icon

Table 1 Calculated standing-wave laser pulse sequences

Equations (6)

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

P n ( V L , Δ t ) | J n ( V L Δ t 2 ) | 2 .
H ^ = 2 2 2 m + V L cos 2 ( k L x ) ,
| n , q = c | 2 k L + q .
| ψ f = j = 1 M U ^ j | ψ i ,
F = | ψ t | ψ f | 2 .
U D = ( 25.61 ± 0.11 ) × V L ( 10.40 ± 4.27 ) .

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