Abstract

We present a laser beam shaping method using acousto-optic deflection of light and discuss its application to dipole trapping of ultracold atoms. By driving the acousto-optic deflector with multiple frequencies, we generate an array of overlapping diffraction-limited beams that combine to form an arbitrary-shaped smooth and continuous trapping potential. Confinement of atoms in a flat-bottomed potential formed by a laser beam with uniform intensity over its central region confers numerous advantages over the harmonic confinement intrinsic to Gaussian beam dipole traps and many other trapping schemes. We demonstrate the versatility of this beam shaping method by generating potentials with large flat-topped regions as well as intensity patterns that compensate for residual external potentials to create a uniform background to which the trapping potential of experimental interest can be added.

© 2013 OSA

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  1. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
    [CrossRef]
  4. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett.81, 3108 (1998).
    [CrossRef]
  5. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
    [CrossRef] [PubMed]
  6. M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
    [CrossRef] [PubMed]
  7. R. N. Palmer and D. Jaksch, “High-field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett.96, 180407 (2006).
    [CrossRef] [PubMed]
  8. C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
    [CrossRef]
  14. N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B41, 211001 (2008).
    [CrossRef]
  15. 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. Express16, 16977–16983 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  21. P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser. Eng.43, 43–56 (2005).
    [CrossRef]
  22. J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
    [CrossRef]
  23. A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep.2, 721 (2012).
    [CrossRef] [PubMed]
  24. T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
    [CrossRef]
  25. S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
    [CrossRef]
  26. G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
    [CrossRef]

2013 (1)

S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
[CrossRef]

2012 (1)

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep.2, 721 (2012).
[CrossRef] [PubMed]

2011 (3)

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[CrossRef]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
[CrossRef]

2010 (3)

H. Xiong and B. Wu, “Atomic quantum corrals for Bose-Einstein condensates,” Phys. Rev. A82, 053634 (2010).
[CrossRef]

S. Al-Assam, R. A. Williams, and C. J. Foot, “Ultracold atoms in an optical lattice with dynamically variable periodicity,” Phys. Rev. A82, 021604 (2010).
[CrossRef]

J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
[CrossRef]

2009 (1)

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
[CrossRef]

2008 (4)

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B41, 211001 (2008).
[CrossRef]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

M. Pasienski and B. DeMarco, “A high-accuracy algorithm for designing arbitrary holographic atom traps,” Opt. Express16, 2176–2190 (2008).
[CrossRef] [PubMed]

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. Express16, 16977–16983 (2008).
[CrossRef] [PubMed]

2007 (3)

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express15, 8619–8625 (2007).
[CrossRef] [PubMed]

V. L. Campo, K. Capelle, J. Quintanilla, and C. Hooley, “Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,” Phys. Rev. Lett.99, 240403 (2007).
[CrossRef]

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

2006 (1)

R. N. Palmer and D. Jaksch, “High-field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett.96, 180407 (2006).
[CrossRef] [PubMed]

2005 (3)

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett.95, 063201 (2005).
[CrossRef] [PubMed]

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser. Eng.43, 43–56 (2005).
[CrossRef]

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[CrossRef]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light - linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

2002 (1)

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

2001 (1)

M. D. Barrett, J. A. Sauer, and M. S. Chapman, “All-optical formation of an atomic Bose-Einstein condensate,” Phys. Rev. Lett.87, 010404 (2001).
[CrossRef] [PubMed]

1998 (1)

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

1997 (1)

1916 (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J.44, 76–86 (1916).
[CrossRef]

Ahufinger, V.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

Al-Assam, S.

Amico, L.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett.95, 063201 (2005).
[CrossRef] [PubMed]

Arnold, A. S.

Aspect, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Barrett, M. D.

M. D. Barrett, J. A. Sauer, and M. S. Chapman, “All-optical formation of an atomic Bose-Einstein condensate,” Phys. Rev. Lett.87, 010404 (2001).
[CrossRef] [PubMed]

Becker, M. F.

J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
[CrossRef]

Bernard, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Billy, J.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Bloch, I.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

Boshier, M. G.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
[CrossRef]

Bouyer, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Bromley, S. L.

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

Bruce, G. D.

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[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 (1998).
[CrossRef]

Buchleitner, A.

S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
[CrossRef]

Campo, V. L.

V. L. Campo, K. Capelle, J. Quintanilla, and C. Hooley, “Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,” Phys. Rev. Lett.99, 240403 (2007).
[CrossRef]

Capelle, K.

V. L. Campo, K. Capelle, J. Quintanilla, and C. Hooley, “Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,” Phys. Rev. Lett.99, 240403 (2007).
[CrossRef]

Cassettari, D.

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[CrossRef]

Cataliotti, F.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett.95, 063201 (2005).
[CrossRef] [PubMed]

Chapman, M. S.

M. D. Barrett, J. A. Sauer, and M. S. Chapman, “All-optical formation of an atomic Bose-Einstein condensate,” Phys. Rev. Lett.87, 010404 (2001).
[CrossRef] [PubMed]

Chuu, C.

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[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 (1998).
[CrossRef]

Clément, D.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Damski, B.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

DeMarco, B.

den Dekker, A. J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light - linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

Ellinas, D.

Esslinger, T.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

Fletcher, B.

Foot, C. J.

Franke-Arnold, S.

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 (1998).
[CrossRef]

Gaunt, A. L.

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep.2, 721 (2012).
[CrossRef] [PubMed]

Girkin, J. M.

Greiner, M.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

Hadzibabic, Z.

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep.2, 721 (2012).
[CrossRef] [PubMed]

Hambrecht, B.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Hansch, T. W.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

Hanssen, J. L.

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[CrossRef]

Heinzen, D. J.

J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
[CrossRef]

Henderson, K.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
[CrossRef]

Hiller, M.

S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
[CrossRef]

Hooley, C.

V. L. Campo, K. Capelle, J. Quintanilla, and C. Hooley, “Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,” Phys. Rev. Lett.99, 240403 (2007).
[CrossRef]

Houston, N.

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B41, 211001 (2008).
[CrossRef]

Hunn, S.

S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
[CrossRef]

Jaksch, D.

R. N. Palmer and D. Jaksch, “High-field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett.96, 180407 (2006).
[CrossRef] [PubMed]

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

Josse, V.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Kohn, J.

J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
[CrossRef]

Kuhr, S.

C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
[CrossRef]

Leach, J.

Lembessis, V. E.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light - linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

Lewenstein, M.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

Liang, J.

J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
[CrossRef]

Lugan, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

MacCormick, C.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
[CrossRef]

Mandel, O.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

Mayoh, J.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[CrossRef]

Meyrath, T. P.

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[CrossRef]

Mølmer, K.

C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
[CrossRef]

Ohberg, P.

Osterloh, A.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett.95, 063201 (2005).
[CrossRef] [PubMed]

Padgett, M. J.

Palmer, R. N.

R. N. Palmer and D. Jaksch, “High-field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett.96, 180407 (2006).
[CrossRef] [PubMed]

Pasienski, M.

Pillet, J. D.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light - linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

Quintanilla, J.

V. L. Campo, K. Capelle, J. Quintanilla, and C. Hooley, “Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,” Phys. Rev. Lett.99, 240403 (2007).
[CrossRef]

Raizen, M. G.

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[CrossRef]

Riis, E.

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B41, 211001 (2008).
[CrossRef]

Ryu, C.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
[CrossRef]

Sanchez-Palencia, L.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Sanpera, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

Sauer, J. A.

M. D. Barrett, J. A. Sauer, and M. S. Chapman, “All-optical formation of an atomic Bose-Einstein condensate,” Phys. Rev. Lett.87, 010404 (2001).
[CrossRef] [PubMed]

Schimmel, H.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser. Eng.43, 43–56 (2005).
[CrossRef]

Schreck, F.

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[CrossRef]

Sen, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

Sen, U.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

Senthilkumaran, P.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser. Eng.43, 43–56 (2005).
[CrossRef]

Sherson, J. F.

C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
[CrossRef]

Shotter, M.

Smirne, G.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[CrossRef]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

Sparrow, C. M.

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J.44, 76–86 (1916).
[CrossRef]

Torralbo-Campo, L.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[CrossRef]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

van den Bos, A.

Weitenberg, C.

C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
[CrossRef]

Williams, R. A.

Wright, A. J.

Wu, B.

H. Xiong and B. Wu, “Atomic quantum corrals for Bose-Einstein condensates,” Phys. Rev. A82, 053634 (2010).
[CrossRef]

Wyrowski, F.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser. Eng.43, 43–56 (2005).
[CrossRef]

Xiong, H.

H. Xiong and B. Wu, “Atomic quantum corrals for Bose-Einstein condensates,” Phys. Rev. A82, 053634 (2010).
[CrossRef]

Zimmermann, K.

S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
[CrossRef]

Zoller, P.

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

Zuo, Z.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

Adv. Phys. (1)

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys.56, 243 (2007).
[CrossRef]

Appl. Optics (1)

J. Liang, J. Kohn, M. F. Becker, and D. J. Heinzen, “High-precision laser beam shaping using a binary-amplitude spatial light modulator,” Appl. Optics49, 1323–1330 (2010).
[CrossRef]

Astrophys. J. (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J.44, 76–86 (1916).
[CrossRef]

J. Mod. Opt. (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light - linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt.50, 1917–1926 (2003).

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

J. Phys. B (1)

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B41, 211001 (2008).
[CrossRef]

Nature (2)

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008).
[CrossRef] [PubMed]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002).
[CrossRef] [PubMed]

New J. Phys. (1)

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys.11, 043030 (2009).
[CrossRef]

Opt. Express (3)

Opt. Laser. Eng. (1)

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser. Eng.43, 43–56 (2005).
[CrossRef]

Phys. Rev. A (6)

S. Al-Assam, R. A. Williams, and C. J. Foot, “Ultracold atoms in an optical lattice with dynamically variable periodicity,” Phys. Rev. A82, 021604 (2010).
[CrossRef]

H. Xiong and B. Wu, “Atomic quantum corrals for Bose-Einstein condensates,” Phys. Rev. A82, 053634 (2010).
[CrossRef]

C. Weitenberg, S. Kuhr, K. Mølmer, and J. F. Sherson, “Quantum computation architecture using optical tweezers,” Phys. Rev. A84, 032322 (2011).
[CrossRef]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A84, 053410 (2011).
[CrossRef]

T. P. Meyrath, F. Schreck, J. L. Hanssen, C. Chuu, and M. G. Raizen, “Bose-Einstein condensate in a box,” Phys. Rev. A71, 041604 (2005).
[CrossRef]

S. Hunn, K. Zimmermann, M. Hiller, and A. Buchleitner, “Tunneling decay of two interacting bosons in an asymmetric double-well potential: A spectral approach,” Phys. Rev. A87, 043626 (2013).
[CrossRef]

Phys. Rev. Lett. (5)

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

M. D. Barrett, J. A. Sauer, and M. S. Chapman, “All-optical formation of an atomic Bose-Einstein condensate,” Phys. Rev. Lett.87, 010404 (2001).
[CrossRef] [PubMed]

V. L. Campo, K. Capelle, J. Quintanilla, and C. Hooley, “Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,” Phys. Rev. Lett.99, 240403 (2007).
[CrossRef]

R. N. Palmer and D. Jaksch, “High-field fractional quantum Hall effect in optical lattices,” Phys. Rev. Lett.96, 180407 (2006).
[CrossRef] [PubMed]

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett.95, 063201 (2005).
[CrossRef] [PubMed]

Phys. Scripta (1)

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. ScriptaT143, 014008 (2011).
[CrossRef]

Sci. Rep. (1)

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep.2, 721 (2012).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Intensity distribution measured using a CCD camera (top) for a flat-topped beam comprising 10 individual Gaussians of identical amplitude, with a line profile (bottom, solid line). Superposition of the dash-dot Gaussians yields the calculated target intensity distribution (dashed line).

Fig. 2
Fig. 2

Intensity distribution measured using a CCD camera (top) and the corresponding line profile (bottom, solid line) for a harmonic compensation potential, with the target intensity distribution (dashed line) the sum of the dash-dot Gaussians.

Fig. 3
Fig. 3

Intensity distribution measured using a CCD camera (top) and corresponding line profile (bottom, solid line) for an extension of the flat-topped beam creating a broad reservoir connected to a single well, with applications to studying decoherence in quantum systems. The target intensity (dashed line) is the sum of the dash-dot Gaussians.

Equations (10)

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

= J i , j a i a j + U 2 i n ^ i ( n ^ i 1 ) + i ε i n ^ i
d d x { f ( x ) + f ( x + a ) } = 0 and d 2 d x 2 { f ( x ) + f ( x + a ) } = 0
f ( x ) = n N A n e 2 ( x x n ) 2 / w 2
I ( x ) = n A n x n
V tot ( x ) = n = 0 n max V tot ( n ) ( x 0 ) n ! ( x x 0 ) n + 𝒪 ( n max + 1 )
V dip ( x ) = n = 1 N a i V beam ( x s i )
Δ θ = Δ f λ u s
f out = i = 1 N a i f i
f = ( n number of elements ) × f clock
S in = i a i sin ( 2 π n i L )

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