Abstract

We demonstrate a method to create dynamic optical lattices with lattice constant tunable down to the optical wavelength limit. The periodicity of 1D lattice is to be adjusted by rotating the incoming direction of one of the two interfering laser beams with its fiber port. The relative phase between the stationary and rotating lasers are stabilized with a heterodyne phase-lock loop (Ma et al, Opt. Lett. 19, 1777, 1994), by reflecting part of the rotating laser beam back from a cylindrical mirror near the experiment. Our preliminary demonstration shows tuning of lattice constant λ2sinθ/2, limited by our imaging resolution, between θ = 3° and 20°, with stable and tunable phase. The results can be extended to achieve lattice constant tuning range from ∼ 10λ down to λ/2. We discuss extension of the demonstrated scheme for improved vibration suppression, and for lattice utilizing broadband lasers. Finally we propose a 2D accordion lattice design for quantum gas experiments.

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

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References

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2017 (2)

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

2016 (2)

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

2015 (5)

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
[Crossref]

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

2014 (1)

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

2013 (1)

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

2012 (2)

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8(4), 267–276 (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(7389), 302–305 (2012).
[Crossref] [PubMed]

2010 (2)

S. Al-Assam, R. A. Williams, and C. J. Foot, “Ultracold atoms in an optical lattice with dynamically variable periodicity,” Phys. Rev. A 82, 021604 (2010).
[Crossref]

T. Esslinger, “Fermi-Hubbard physics with atoms in an optical lattice,” Annu. Rev. Condens. Matter Phys. 1(1), 129–152 (2010).
[Crossref]

2008 (3)

2007 (3)

K. D Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3(8), 556–560 (2007).
[Crossref]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

2006 (2)

2004 (1)

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z.J Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51(14), 2235–2240 (2004).
[Crossref]

2002 (1)

W. Alt, “An objective lens for efficient fluorescence detection of single atoms,” Optik 113(3), 142–144 (2002).
[Crossref]

1994 (1)

Aidelsburger, M.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

Al-Assam, S.

Alberti, A.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Alt, W.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

W. Alt, “An objective lens for efficient fluorescence detection of single atoms,” Optik 113(3), 142–144 (2002).
[Crossref]

Altman, E.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Anderlini, M.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

Atala, M.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Bakr, W. S.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Barredo, D.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Barreiro, J. T.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

Béguin, L.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Bienaimé, T.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Blatt, S.

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Bloch, I.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8(4), 267–276 (2012).
[Crossref]

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

Bordia, P.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Boyer, V.

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z.J Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51(14), 2235–2240 (2004).
[Crossref]

Brakhane, S.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Browaeys, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Brown, B. L.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

Bruce, G. D.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
[Crossref]

Chandrashekar, C. M.

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z.J Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51(14), 2235–2240 (2004).
[Crossref]

Charrière, F.

Cheuk, L. W.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Chiu, C. S

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Chiu, C. S.

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Chomaz, L.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Chu, S.

N. Gemelke, E. Sarajlic, and S. Chu, “Rotating few-body atomic systems in the fractional quantum Hall regime,” ArXiv e-prints, arXiv:1007.2677 (2010).

Colomb, T.

Corman, L.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Cotta, D. A.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
[Crossref]

Cuche, E.

Dalibard, J.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8(4), 267–276 (2012).
[Crossref]

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

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Demler, E.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Depeursinge, C.

Duarte, P. M.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Esslinger, T.

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(7389), 302–305 (2012).
[Crossref] [PubMed]

T. Esslinger, “Fermi-Hubbard physics with atoms in an optical lattice,” Annu. Rev. Condens. Matter Phys. 1(1), 129–152 (2010).
[Crossref]

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Fischer, M. H.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
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Fletcher, B.

Foot, C. J.

S. Al-Assam, R. A. Williams, and C. J. Foot, “Ultracold atoms in an optical lattice with dynamically variable periodicity,” Phys. Rev. A 82, 021604 (2010).
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R. A. Williams, J. D. Pillet, S. Al-Assam, B. Fletcher, M. Shotter, and C. J. Foot, “Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms,” Opt. Express 16(21), 16977–16983 (2008).
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V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z.J Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51(14), 2235–2240 (2004).
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Gemelke, N.

N. Gemelke, E. Sarajlic, and S. Chu, “Rotating few-body atomic systems in the fractional quantum Hall regime,” ArXiv e-prints, arXiv:1007.2677 (2010).

Gersdorf, T.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Greif, D.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

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(7389), 302–305 (2012).
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Greiner, M.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Grusdt, F.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Hall, J. L.

Haller, E.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
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Hart, R. A.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Hodgman, S. S.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Huber, F.

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
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Hudson, J.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
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Hulet, R. G.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Huse, D. A.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Ji, G.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Jotzu, G.

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(7389), 302–305 (2012).
[Crossref] [PubMed]

Jungner, P.

Kanász-Nagy, M.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Karski, M.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Kaufman, A. M.

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

Kelkar, H.

Kelly, A.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
[Crossref]

Khatami, E.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Kleinlein, K.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Kuehn, J.

Kuhr, S.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
[Crossref]

Labuhn, H.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Laczik, Z.J

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z.J Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51(14), 2235–2240 (2004).
[Crossref]

Lahaye, T.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Lee, P. J.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

Li, T. C.

Li, X.

K. D Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3(8), 556–560 (2007).
[Crossref]

Liu, X.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Lohse, M.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

Lompe, T.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Lukin, A.

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

Lüschen, H. P.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Ma, L. S.

Marian, A.

Marquet, P.

Mazurenko, A.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Medellin, D.

Meschede, D.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Montfort, F.

Morsch, O.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179 (2006).
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Nascimbene, S.

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8(4), 267–276 (2012).
[Crossref]

Nascimbène, S.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Nelson, K. D

K. D Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3(8), 556–560 (2007).
[Crossref]

Nichols, M. A.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Nogrette, F.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Oberthaler, M.

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78(1), 179 (2006).
[Crossref]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717 (2007).
[Crossref] [PubMed]

Okan, M.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Paiva, T.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Paredes, B.

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices,” Phys. Rev. Lett. 111(18), 185301 (2013).
[Crossref] [PubMed]

Parsons, M. F

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Parsons, M. F.

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Peaudecerf, B.

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11(9), 738–742 (2015).
[Crossref]

Perconte, D

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Phillips, W. D.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

Pillet, J. D.

Porto, J. V.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

Preiss, P. M.

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

Raizen, M. G.

Ramasesh, V. V.

L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).
[Crossref] [PubMed]

Ravets, S.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Reimann, R.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Rispoli, M.

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

Robens, C.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Saint-Jalm, R.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Sarajlic, E.

N. Gemelke, E. Sarajlic, and S. Chu, “Rotating few-body atomic systems in the fractional quantum Hall regime,” ArXiv e-prints, arXiv:1007.2677 (2010).

Scalettar, R. T.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Schittko, R.

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (2016).
[Crossref] [PubMed]

Schmidt, R.

A. Mazurenko, C. S Chiu, G. Ji, M. F Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature 545(7655), 462–466 (2017).
[Crossref] [PubMed]

Schneider, U.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Schreiber, M.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Sebby-Strabley, J.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice,” Nature 448(7152), 452–456 (2007).
[Crossref] [PubMed]

Setiawan, W.

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Shotter, M.

Tai, M. E.

A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353(6301), 794–800 (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(7389), 302–305 (2012).
[Crossref] [PubMed]

Trivedi, N.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Uehlinger, T.

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(7389), 302–305 (2012).
[Crossref] [PubMed]

Vernier, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).

Ville, J. L.

J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D Perconte, S. Nascimbène, J. Dalibard, and et al., “Loading and compression of a single two-dimensional Bose gas in an optical accordion,” Phys. Rev. A 95(1), 013632 (2017).
[Crossref]

Vosk, R.

M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, “Observation of many-body localization of interacting fermions in a quasirandom optical lattice,” Science 349(6250), 842–845 (2015).
[Crossref] [PubMed]

Weiss, D. S.

K. D Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3(8), 556–560 (2007).
[Crossref]

Widera, A.

A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18(5), 053010 (2016).
[Crossref]

Williams, R. A.

Wooley-Brown, K.

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic Li 6 in an optical lattice,” Phys. Rev. Lett. 114(21), 213002 (2015).
[Crossref] [PubMed]

Yang, T.-L.

R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, “Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms,” Nature 519(7542), 211–214 (2015).
[Crossref] [PubMed]

Ye, J.

Zwerger, W.

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964, (2008).
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Figures (6)

Fig. 1
Fig. 1 Experimental setup of the optical accordion. (a) The schematic in the y-z plane (b) The schematic of the Michelson interferometer on the top layer in the x-y plane. PBS: polarization beam splitter; WP: Wave Plate. Notice AOM2 is vertically positioned so its 0th and 1st order diffractions are displaced along z. (c) The schematic of the rotating fiber port and the accordion lattice (inset) on the lower layer in the x-y plane.
Fig. 2
Fig. 2 Compression of the 1D lattice with the two-beam angle scan from 8° to 20°. The CCD camera is set with 30 frames per second. The image are generated by compiling a same line of pixels from image frames of a video record. The scale of intensity is individually adjusted for each frame. (a) Complied image without phase lock. (b) Complied image with phase lock loop closed. Here the drift of lattice phase is about 70 rad. The occasional sudden jump is likely due to the mechanical vibrations of M6, M4, M3 and C1 as in Fig. 1. The stage stops rotating after the 1130 frames in this measurement.
Fig. 3
Fig. 3 (a) Compiled image for compression of the 1D lattice from d = 11 µm to 2 µm with phase locked and phase drift compensated. Here θ is scanned from 3° to 20°. (b),(c) Original images of the 1D lattice with lattice constant d ≈ 8 µm and 2 µm respectively.
Fig. 4
Fig. 4 (a) The cosine function of the phase ϕ at location O during a 35 seconds θ scan. The green and red curves are respectively extracted from the video image for Fig. 2(a)(green) and 3(a)(red) via 2D Fourier transform. (b) The phase noise spectrum of the data in (a) and of the data with the stage kept stationary. In the red plot a few sharp peaks are likely due to mechanical resonances. (c) Plot of the lattice constant as a function of the stage readout θ according to λ/d = 2 sin θ/2. Blue: line plot of the lattice constant extracted from the video images for Fig. 3; Green: the theoretical curve of λ/d = 2 sin θ/2 with a fitted θ offset. Some experimental data are plotted with error bars to reflect the uncertainty of fringe periods due to digital noise and finite extension of the images.
Fig. 5
Fig. 5 A more symmetric scheme in which Beam A and B are treated on equal footing and can support optical accordion with a broadband laser.
Fig. 6
Fig. 6 Two schemes of 2D optical accordion. (a) Accordion by two laser beam pairs. Beam A and A′ are mounted on the same motorized rotation stage. The relative phase between the pair A, B and the pair A′, B′ are individually locked. The lattice constant is adjusted by scanning the equal angle θ between the A, B beams and A′, B′ beams simultaneously. Bottom: Typical calculated lattice intensity profiles during θ scan for B and B′ intersect at 90° (first line) and 120° (second line). (b) Accordion by three laser beams. The beams share the same linear polarization along z axis. With Beam B fixed, Beam A and A′ rotate oppositely by two rotation stages by angle θ and −θ. Bottom: Calculated lattice intensity profiles with θ = 60, 90, 120, 150°.

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