Abstract

Imaging and manipulating individual atoms with submicrometer separation can be instrumental for quantum simulation of condensed matter Hamiltonians and quantum computation with neutral atoms. Here we present an open-source design of a microscope objective for atomic strontium, consisting solely of off-the-shelf lenses, that is diffraction-limited for 461 nm light. A prototype built with a simple stacking design is measured to have a resolution of 0.63(4) µm, which is in agreement with the predicted value. This performance, together with the near diffraction-limited performance for 532 nm light, makes this design useful for both quantum gas microscopes and optical tweezer experiments with strontium. Our microscope can easily be adapted to experiments with other atomic species such as erbium, ytterbium, and dysprosium, as with rubidium Rydberg atoms.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2020 (1)

N. C. Jackson, R. K. Hanley, M. Hill, F. Leroux, C. S. Adams, and M. P. A. Jones, “Number-resolved imaging of 88Sr atoms in a long working distance optical tweezer,” SciPost Phys. 8(3), 038 (2020).
[Crossref]

2019 (4)

O. Onishchenko, S. Pyatchenkov, A. Urech, C.-C. Chen, S. Bennetts, G. A. Siviloglou, and F. Schreck, “Frequency of the ultranarrow 1S0 − 3P2 transition in 87Sr,” Phys. Rev. A 99(5), 052503 (2019).
[Crossref]

J. P. Covey, I. S. Madjarov, A. Cooper, and M. Endres, “2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays,” Phys. Rev. Lett. 122(17), 173201 (2019).
[Crossref]

M. Saffman, “Quantum computing with neutral atoms,” Natl. Sci. Rev. 6(1), 24–25 (2019).
[Crossref]

D. Ohl de Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, “Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems,” Phys. Rev. Lett. 122(20), 203601 (2019).
[Crossref]

2018 (4)

X. Li, F. Zhou, M. Ke, P. Xu, X.-D. He, J. Wang, and M.-S. Zhan, “High-resolution ex vacuo objective for cold atom experiments,” Appl. Opt. 57(26), 7584–7590 (2018).
[Crossref]

A. Cooper, J. P. Covey, I. S. Madjarov, S. G. Porsev, M. S. Safronova, and M. Endres, “Alkaline-earth atoms in optical tweezers,” Phys. Rev. X 8(4), 041055 (2018).
[Crossref]

M. A. Norcia, A. W. Young, and A. M. Kaufman, “Microscopic control and detection of ultracold strontium in optical-tweezer arrays,” Phys. Rev. X 8(4), 041054 (2018).
[Crossref]

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561(7721), 79–82 (2018).
[Crossref]

2017 (5)

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

D. S. Weiss and M. Saffman, “Quantum computing with neutral atoms,” Phys. Today 70(7), 44–50 (2017).
[Crossref]

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

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]

C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola, and A. Alberti, “High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms,” Opt. Lett. 42(6), 1043–1046 (2017).
[Crossref]

2016 (3)

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]

S. Kuhr, “Quantum-gas microscopes: a new tool for cold-atom quantum simulators,” Natl. Sci. Rev. 3(2), 170–172 (2016).
[Crossref]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (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(2), 637–701 (2015).
[Crossref]

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(19), 193001 (2015).
[Crossref]

2014 (2)

K. Shibata, R. Yamamoto, Y. Seki, and Y. Takahashi, “Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition,” Phys. Rev. A 89(3), 031601 (2014).
[Crossref]

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

2013 (2)

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

L. M. Bennie, P. T. Starkey, M. Jasperse, C. J. Billington, R. P. Anderson, and L. D. Turner, “A versatile high resolution objective for imaging quantum gases,” Opt. Express 21(7), 9011–9016 (2013).
[Crossref]

2012 (1)

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

2010 (2)

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329(5991), 547–550 (2010).
[Crossref]

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467(7311), 68–72 (2010).
[Crossref]

2009 (1)

S. Stellmer, M. K. Tey, B. Huang, R. Grimm, and F. Schreck, “Bose-Einstein condensation of strontium,” Phys. Rev. Lett. 103(20), 200401 (2009).
[Crossref]

2008 (1)

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and Strehl ratio of optical systems with variable numerical aperture,” J. Mod. Opt. 55(7), 1127–1157 (2008).
[Crossref]

2007 (1)

2006 (1)

S. Fölling, A. Widera, T. Müller, F. Gerbier, and I. Bloch, “Formation of spatial shell structure in the superfluid to mott insulator transition,” Phys. Rev. Lett. 97(6), 060403 (2006).
[Crossref]

2002 (4)

2001 (2)

K. Van de Velde and P. Kiekens, “Thermoplastic polymers: overview of several properties and their consequences in flax fibre reinforced composites,” Polym. Test. 20(8), 885–893 (2001).
[Crossref]

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-Poissonian loading of single atoms in a microscopic dipole trap,” Nature 411(6841), 1024–1027 (2001).
[Crossref]

1986 (1)

1879 (1)

F. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Phil. Mag. 8(49), 261–274 (1879).
[Crossref]

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Phil. Mag. 4(9), 401 (1836).

Adams, C. S.

N. C. Jackson, R. K. Hanley, M. Hill, F. Leroux, C. S. Adams, and M. P. A. Jones, “Number-resolved imaging of 88Sr atoms in a long working distance optical tweezer,” SciPost Phys. 8(3), 038 (2020).
[Crossref]

Alberti, A.

C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola, and A. Alberti, “High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms,” Opt. Lett. 42(6), 1043–1046 (2017).
[Crossref]

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.

C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola, and A. Alberti, “High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms,” Opt. Lett. 42(6), 1043–1046 (2017).
[Crossref]

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]

Anderson, R. P.

Ashkin, A.

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(19), 193001 (2015).
[Crossref]

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329(5991), 547–550 (2010).
[Crossref]

Barredo, D.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561(7721), 79–82 (2018).
[Crossref]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

Benko, C.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

Bennetts, S.

O. Onishchenko, S. Pyatchenkov, A. Urech, C.-C. Chen, S. Bennetts, G. A. Siviloglou, and F. Schreck, “Frequency of the ultranarrow 1S0 − 3P2 transition in 87Sr,” Phys. Rev. A 99(5), 052503 (2019).
[Crossref]

Bennie, L. M.

Bernien, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Billington, C. J.

Birkl, G.

D. Ohl de Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, “Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems,” Phys. Rev. Lett. 122(20), 203601 (2019).
[Crossref]

Bishof, M.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

Bjorkholm, J. E.

Bloch, I.

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

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467(7311), 68–72 (2010).
[Crossref]

S. Fölling, A. Widera, T. Müller, F. Gerbier, and I. Bloch, “Formation of spatial shell structure in the superfluid to mott insulator transition,” Phys. Rev. Lett. 97(6), 060403 (2006).
[Crossref]

Bloom, B. J.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

Bonod, N.

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Braat, J.

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and Strehl ratio of optical systems with variable numerical aperture,” J. Mod. Opt. 55(7), 1127–1157 (2008).
[Crossref]

J. Braat, P. Dirksen, and A. J. E. M. Janssen, “Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A 19(5), 858–870 (2002).
[Crossref]

Brakhane, S.

C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola, and A. Alberti, “High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms,” Opt. Lett. 42(6), 1043–1046 (2017).
[Crossref]

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.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561(7721), 79–82 (2018).
[Crossref]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

Campbell, S. L.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

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[Crossref]

Reymond, G.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-Poissonian loading of single atoms in a microscopic dipole trap,” Nature 411(6841), 1024–1027 (2001).
[Crossref]

Rigneault, H.

Robens, C.

C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola, and A. Alberti, “High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms,” Opt. Lett. 42(6), 1043–1046 (2017).
[Crossref]

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]

Robinson, J. M.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

Rogers, E. T. F.

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

Roy, T.

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

Saffman, M.

M. Saffman, “Quantum computing with neutral atoms,” Natl. Sci. Rev. 6(1), 24–25 (2019).
[Crossref]

D. S. Weiss and M. Saffman, “Quantum computing with neutral atoms,” Phys. Today 70(7), 44–50 (2017).
[Crossref]

Safronova, M. S.

A. Cooper, J. P. Covey, I. S. Madjarov, S. G. Porsev, M. S. Safronova, and M. Endres, “Alkaline-earth atoms in optical tweezers,” Phys. Rev. X 8(4), 041055 (2018).
[Crossref]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2013).

Schäffner, D.

D. Ohl de Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, “Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems,” Phys. Rev. Lett. 122(20), 203601 (2019).
[Crossref]

Schlosser, M.

D. Ohl de Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, “Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems,” Phys. Rev. Lett. 122(20), 203601 (2019).
[Crossref]

Schlosser, N.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-Poissonian loading of single atoms in a microscopic dipole trap,” Nature 411(6841), 1024–1027 (2001).
[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(2), 637–701 (2015).
[Crossref]

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]

Schreck, F.

O. Onishchenko, S. Pyatchenkov, A. Urech, C.-C. Chen, S. Bennetts, G. A. Siviloglou, and F. Schreck, “Frequency of the ultranarrow 1S0 − 3P2 transition in 87Sr,” Phys. Rev. A 99(5), 052503 (2019).
[Crossref]

S. Stellmer, M. K. Tey, B. Huang, R. Grimm, and F. Schreck, “Bose-Einstein condensation of strontium,” Phys. Rev. Lett. 103(20), 200401 (2009).
[Crossref]

Schwartz, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Seki, Y.

K. Shibata, R. Yamamoto, Y. Seki, and Y. Takahashi, “Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition,” Phys. Rev. A 89(3), 031601 (2014).
[Crossref]

Sentenac, A.

Sherson, J. F.

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467(7311), 68–72 (2010).
[Crossref]

Shibata, K.

K. Shibata, R. Yamamoto, Y. Seki, and Y. Takahashi, “Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition,” Phys. Rev. A 89(3), 031601 (2014).
[Crossref]

Shillaber, C. P.

C. P. Shillaber, Photomicrography In Theory and Practice (John Wiley and Sons, 1944).

Simon, J.

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329(5991), 547–550 (2010).
[Crossref]

Siviloglou, G. A.

O. Onishchenko, S. Pyatchenkov, A. Urech, C.-C. Chen, S. Bennetts, G. A. Siviloglou, and F. Schreck, “Frequency of the ultranarrow 1S0 − 3P2 transition in 87Sr,” Phys. Rev. A 99(5), 052503 (2019).
[Crossref]

Sonderhouse, L.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

Starkey, P. T.

Stellmer, S.

S. Stellmer, M. K. Tey, B. Huang, R. Grimm, and F. Schreck, “Bose-Einstein condensation of strontium,” Phys. Rev. Lett. 103(20), 200401 (2009).
[Crossref]

Swallows, M. D.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

Tai, M. E.

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329(5991), 547–550 (2010).
[Crossref]

Takahashi, Y.

K. Shibata, R. Yamamoto, Y. Seki, and Y. Takahashi, “Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition,” Phys. Rev. A 89(3), 031601 (2014).
[Crossref]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Phil. Mag. 4(9), 401 (1836).

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2013).

Tey, M. K.

S. Stellmer, M. K. Tey, B. Huang, R. Grimm, and F. Schreck, “Bose-Einstein condensation of strontium,” Phys. Rev. Lett. 103(20), 200401 (2009).
[Crossref]

Turner, L. D.

Urech, A.

O. Onishchenko, S. Pyatchenkov, A. Urech, C.-C. Chen, S. Bennetts, G. A. Siviloglou, and F. Schreck, “Frequency of the ultranarrow 1S0 − 3P2 transition in 87Sr,” Phys. Rev. A 99(5), 052503 (2019).
[Crossref]

Van de Velde, K.

K. Van de Velde and P. Kiekens, “Thermoplastic polymers: overview of several properties and their consequences in flax fibre reinforced composites,” Polym. Test. 20(8), 885–893 (2001).
[Crossref]

van Haver, S.

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and Strehl ratio of optical systems with variable numerical aperture,” J. Mod. Opt. 55(7), 1127–1157 (2008).
[Crossref]

S. van Haver, “The extended Nijboer–Zernike diffraction theory and its applications,” Ph.D. thesis, Delft University of Technology (2010).

von Stecher, J.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

Vuletic, V.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Wang, J.

Weiss, D. S.

D. S. Weiss and M. Saffman, “Quantum computing with neutral atoms,” Phys. Today 70(7), 44–50 (2017).
[Crossref]

Weitenberg, C.

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467(7311), 68–72 (2010).
[Crossref]

Wenger, J.

Werkmann, J.

D. Ohl de Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, “Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems,” Phys. Rev. Lett. 122(20), 203601 (2019).
[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]

S. Fölling, A. Widera, T. Müller, F. Gerbier, and I. Bloch, “Formation of spatial shell structure in the superfluid to mott insulator transition,” Phys. Rev. Lett. 97(6), 060403 (2006).
[Crossref]

Xu, P.

Yamamoto, R.

K. Shibata, R. Yamamoto, Y. Seki, and Y. Takahashi, “Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition,” Phys. Rev. A 89(3), 031601 (2014).
[Crossref]

Ye, J.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

Young, A. W.

M. A. Norcia, A. W. Young, and A. M. Kaufman, “Microscopic control and detection of ultracold strontium in optical-tweezer arrays,” Phys. Rev. X 8(4), 041054 (2018).
[Crossref]

Yuan, G.

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

Zhan, M.-S.

Zhang, W.

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

Zhang, X.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

Zheludev, N. I.

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

Zhou, F.

Zibrov, A. S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Zwierlein, M. 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(19), 193001 (2015).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Roy, E. T. F. Rogers, G. Yuan, and N. I. Zheludev, “Point spread function of the optical needle super-oscillatory lens,” Appl. Phys. Lett. 104(23), 231109 (2014).
[Crossref]

J. Mod. Opt. (1)

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and Strehl ratio of optical systems with variable numerical aperture,” J. Mod. Opt. 55(7), 1127–1157 (2008).
[Crossref]

J. Opt. Soc. Am. A (3)

Nat. Phys. (1)

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

Natl. Sci. Rev. (2)

M. Saffman, “Quantum computing with neutral atoms,” Natl. Sci. Rev. 6(1), 24–25 (2019).
[Crossref]

S. Kuhr, “Quantum-gas microscopes: a new tool for cold-atom quantum simulators,” Natl. Sci. Rev. 3(2), 170–172 (2016).
[Crossref]

Nature (5)

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]

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467(7311), 68–72 (2010).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-Poissonian loading of single atoms in a microscopic dipole trap,” Nature 411(6841), 1024–1027 (2001).
[Crossref]

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561(7721), 79–82 (2018).
[Crossref]

New J. Phys. (1)

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]

Opt. Express (2)

Opt. Lett. (2)

Optik (1)

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

Phil. Mag. (2)

F. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Phil. Mag. 8(49), 261–274 (1879).
[Crossref]

H. F. Talbot, “Facts relating to optical science,” Phil. Mag. 4(9), 401 (1836).

Phys. Rev. A (2)

O. Onishchenko, S. Pyatchenkov, A. Urech, C.-C. Chen, S. Bennetts, G. A. Siviloglou, and F. Schreck, “Frequency of the ultranarrow 1S0 − 3P2 transition in 87Sr,” Phys. Rev. A 99(5), 052503 (2019).
[Crossref]

K. Shibata, R. Yamamoto, Y. Seki, and Y. Takahashi, “Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition,” Phys. Rev. A 89(3), 031601 (2014).
[Crossref]

Phys. Rev. Lett. (5)

S. Fölling, A. Widera, T. Müller, F. Gerbier, and I. Bloch, “Formation of spatial shell structure in the superfluid to mott insulator transition,” Phys. Rev. Lett. 97(6), 060403 (2006).
[Crossref]

J. P. Covey, I. S. Madjarov, A. Cooper, and M. Endres, “2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays,” Phys. Rev. Lett. 122(17), 173201 (2019).
[Crossref]

S. Stellmer, M. K. Tey, B. Huang, R. Grimm, and F. Schreck, “Bose-Einstein condensation of strontium,” Phys. Rev. Lett. 103(20), 200401 (2009).
[Crossref]

D. Ohl de Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, “Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems,” Phys. Rev. Lett. 122(20), 203601 (2019).
[Crossref]

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(19), 193001 (2015).
[Crossref]

Phys. Rev. X (2)

A. Cooper, J. P. Covey, I. S. Madjarov, S. G. Porsev, M. S. Safronova, and M. Endres, “Alkaline-earth atoms in optical tweezers,” Phys. Rev. X 8(4), 041055 (2018).
[Crossref]

M. A. Norcia, A. W. Young, and A. M. Kaufman, “Microscopic control and detection of ultracold strontium in optical-tweezer arrays,” Phys. Rev. X 8(4), 041054 (2018).
[Crossref]

Phys. Today (1)

D. S. Weiss and M. Saffman, “Quantum computing with neutral atoms,” Phys. Today 70(7), 44–50 (2017).
[Crossref]

Polym. Test. (1)

K. Van de Velde and P. Kiekens, “Thermoplastic polymers: overview of several properties and their consequences in flax fibre reinforced composites,” Polym. Test. 20(8), 885–893 (2001).
[Crossref]

Rev. Mod. Phys. (1)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Science (4)

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329(5991), 547–550 (2010).
[Crossref]

S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, and J. Ye, “A Fermi-degenerate three-dimensional optical lattice clock,” Science 358(6359), 90–94 (2017).
[Crossref]

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, “A quantum many-body spin system in an optical lattice clock,” Science 341(6146), 632–636 (2013).
[Crossref]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

SciPost Phys. (1)

N. C. Jackson, R. K. Hanley, M. Hill, F. Leroux, C. S. Adams, and M. P. A. Jones, “Number-resolved imaging of 88Sr atoms in a long working distance optical tweezer,” SciPost Phys. 8(3), 038 (2020).
[Crossref]

Other (4)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2013).

C. P. Shillaber, Photomicrography In Theory and Practice (John Wiley and Sons, 1944).

B. D. Guenther, Modern Optics (Oxford University, 2015).

S. van Haver, “The extended Nijboer–Zernike diffraction theory and its applications,” Ph.D. thesis, Delft University of Technology (2010).

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Figures (5)

Fig. 1.
Fig. 1. The stacking design of the objective with modeled rays. Each lens is held in place with high precision spacing rings (orange). The assembly of lenses and spacing rings is fixed inside the tube with a locking ring (red). The first lens is mounted on a separate piece (yellow). The glass plate on the right depicts the viewport. All pieces are made out of PEEK.
Fig. 2.
Fig. 2. Setup for characterizing the objective. (a) Overview of the setup. The target consists of a glass plate with a metal coating that has six 200 nm diameter holes. The target, objective and the 500 mm lens are mounted on translation stages. Drawing is not to scale. (b) Scanning electron microscope image of holes similar to those used in the target. (c) Schematic drawing of the locations of the nanoholes on the test target.
Fig. 3.
Fig. 3. Analysis of the objective’s resolution. (a) Using a Laplacian of Gaussian algorithm each spot center is detected and marked at the center of the three red dots. (b) A typical image of the observed PSF without background subtraction. (c) An azimuthal average of the intensity of a single point. The red line shows a Gaussian fit through the data resulting in $\sigma _{\textrm {fit}} = 0.22$ µm, which corresponds to a resolution of 0.639 µm for 461 nm light.
Fig. 4.
Fig. 4. Through-focus PSF of the objective. The radial profile of the PSF is plotted for a range of $z$-values around the focus. (a) Experimental data with normalization to the maximum of intensity at each location. The blue solid line denotes the standard deviation, $\sigma _{\textrm {fit}}$, for each Gaussian fit. The black dashed line denotes the diffraction limit for 461 nm light of 639 nm ($\sigma _{\textrm {fit}} =$ 0.22 µm). (b) The corresponding radial profile simulated using the Extended Nijboer-Zernike diffraction theory with the same normalization as in (a). (c) The same as (b) but with the values normalized to the global maximum of the PSF. For (b) and (c) the black dashed line stops at the point where the theoretical Strehl ratio drops below 0.8. The colormap is identical with the one in Fig. 3. The objective is predicted to be diffraction-limited from around −1.0 µm to 1.3 µm.
Fig. 5.
Fig. 5. Radial profiles of target hole images in dependence of (a) displacement $\Delta y$ of the target hole perpendicularly to the optical axis (for the determination of the FOV) or (b) wavelength. Solid lines depict Gaussian fits to the data.

Tables (2)

Tables Icon

Table 1. The lenses used to create the objective. All these lenses are commercial lenses with anti-reflection coating in the range of 350 nm to 700 nm. The last column is the shortest distance of each lens to the air-side facet of the viewport.

Tables Icon

Table 2. Technical characteristics of the microscope objective at 461 nm.

Metrics