Abstract

We report an experimental method to create optical lattices with real-time control of their periodicity. We demonstrate a continuous change of the lattice periodicity from 0.96 µm to 11.2 µm in one second, while the center fringe only moves less than 2.7 µm during the whole process. This provides a powerful tool for controlling ultracold atoms in optical lattices, where small spacing is essential for quantum tunneling, and large spacing enables single-site manipulation and spatially resolved detection.

© 2008 Optical Society of America

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  1. O. Morsch and M. Oberthaler, "Dynamics of Bose-Einstein condensates in optical lattices," Rev. Mod. Phys. 78, 179-215 (2006).
    [CrossRef]
  2. G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060-1063 (1999).
    [CrossRef]
  3. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Höansch, and I. Bloch, "Controlled collisions for multi-particle entanglement of optically trapped atoms," Nature 425, 937-940 (2003).
    [CrossRef] [PubMed]
  4. J. V. Porto, S. Rolston, B. Laburthe Tolra, C. J. Williams, and W. D. Phillips, "Quantum information with neutral atoms as qubits," Phil. Trans. R. Soc. Lond. A 361, 1417-1427 (2003).
    [CrossRef]
  5. F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843-846 (2001).
    [CrossRef] [PubMed]
  6. K. Henderson, H. Kelkar, B. Guti’errez-Medina, T. C. Li, and M. G. Raizen, "Experimental study of the role of atomic interactions on quantum transport," Phys. Rev. Lett. 96, 150401 (2006)
    [CrossRef] [PubMed]
  7. M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature 415, 39-44 (2002).
    [CrossRef] [PubMed]
  8. F. Gerbier, S. F¨olling, A. Widera, O. Mandel, and I. Bloch, "Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition," Phys. Rev. Lett. 96, 090401 (2006)
    [CrossRef] [PubMed]
  9. B. Paredes, A. Widera, V. Murg, O. Mandel, S. F¨olling, I. Cirac, G. V. Shlyapnikov, T. W. H¨ansch, and I. Bloch, "Tonks-Girardeau gas of ultracold atoms in an optical lattice," Nature 429, 277-281 (2004).
    [CrossRef] [PubMed]
  10. Q1. T. Kinoshita, T. Wenger, and D. S. Weiss, "Observation of a one-dimensional Tonks-Girardeau gas," Science 305, 1125-1128 (2004)
    [CrossRef]
  11. R. Scheunemann, F. S. Cataliotti, T. W. Hänsch, and M. Weitz, "Resolving and addressing atoms in individual sites of a CO2-laser optical lattice," Phys. Rev. A 62, 051801(R) (2000).
    [CrossRef]
  12. Q2. K. D. Nelson, X. Li, and D. S. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556-560 (2007).
    [CrossRef]
  13. S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, "Patterned loading of a Bose-Einstein condensate into an optical lattice," Phys. Rev. A 67, 051603(R) (2003).
    [CrossRef]
  14. J. H. Huckans, "Optical lattices and quantum degenerate 87Rb in reduced dimensions, " Ph.D. dissertation, University of Maryland, College Park (2006).
  15. L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, "Bose-Einstein condensate in an optical lattice with tunable spacing: transport and static properties," Opt. Express 13, 4303-4313 (2005).
    [CrossRef] [PubMed]
  16. Q3. K. Venkatakrishnan, N. R. Sivakumar, C. W. Hee, B. Tan, W. L. Liang, and G. K. Gan, "Direct fabrication of surface-relief grating by interferometric technique using femtosecond laser, " Appl. Phys. A 77, 959-963 (2003).
    [CrossRef]
  17. B. Tan, N. R. Sivakumar, and K. Venkatakrishnan, "Direct grating writing using femtosecond laser interference frings formed at the focal point," J. Opt. A: Pure Appl. Opt. 7, 169-174 (2005)
    [CrossRef]
  18. X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, "Phase manipulated multi-beam holographic lithography for tunable optical lattices," Opt. Express 15, 7032-7037 (2007).
    [CrossRef] [PubMed]
  19. M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
    [CrossRef] [PubMed]

2007 (2)

2006 (3)

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

K. Henderson, H. Kelkar, B. Guti’errez-Medina, T. C. Li, and M. G. Raizen, "Experimental study of the role of atomic interactions on quantum transport," Phys. Rev. Lett. 96, 150401 (2006)
[CrossRef] [PubMed]

F. Gerbier, S. F¨olling, A. Widera, O. Mandel, and I. Bloch, "Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition," Phys. Rev. Lett. 96, 090401 (2006)
[CrossRef] [PubMed]

2005 (2)

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

B. Tan, N. R. Sivakumar, and K. Venkatakrishnan, "Direct grating writing using femtosecond laser interference frings formed at the focal point," J. Opt. A: Pure Appl. Opt. 7, 169-174 (2005)
[CrossRef]

2004 (2)

B. Paredes, A. Widera, V. Murg, O. Mandel, S. F¨olling, I. Cirac, G. V. Shlyapnikov, T. W. H¨ansch, and I. Bloch, "Tonks-Girardeau gas of ultracold atoms in an optical lattice," Nature 429, 277-281 (2004).
[CrossRef] [PubMed]

Q1. T. Kinoshita, T. Wenger, and D. S. Weiss, "Observation of a one-dimensional Tonks-Girardeau gas," Science 305, 1125-1128 (2004)
[CrossRef]

2003 (4)

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Höansch, and I. Bloch, "Controlled collisions for multi-particle entanglement of optically trapped atoms," Nature 425, 937-940 (2003).
[CrossRef] [PubMed]

J. V. Porto, S. Rolston, B. Laburthe Tolra, C. J. Williams, and W. D. Phillips, "Quantum information with neutral atoms as qubits," Phil. Trans. R. Soc. Lond. A 361, 1417-1427 (2003).
[CrossRef]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Q3. K. Venkatakrishnan, N. R. Sivakumar, C. W. Hee, B. Tan, W. L. Liang, and G. K. Gan, "Direct fabrication of surface-relief grating by interferometric technique using femtosecond laser, " Appl. Phys. A 77, 959-963 (2003).
[CrossRef]

2002 (1)

M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature 415, 39-44 (2002).
[CrossRef] [PubMed]

2001 (1)

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843-846 (2001).
[CrossRef] [PubMed]

1999 (1)

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060-1063 (1999).
[CrossRef]

Appl. Phys. A (1)

Q3. K. Venkatakrishnan, N. R. Sivakumar, C. W. Hee, B. Tan, W. L. Liang, and G. K. Gan, "Direct fabrication of surface-relief grating by interferometric technique using femtosecond laser, " Appl. Phys. A 77, 959-963 (2003).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

B. Tan, N. R. Sivakumar, and K. Venkatakrishnan, "Direct grating writing using femtosecond laser interference frings formed at the focal point," J. Opt. A: Pure Appl. Opt. 7, 169-174 (2005)
[CrossRef]

Nat. Phys. (1)

Q2. K. D. Nelson, X. Li, and D. S. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556-560 (2007).
[CrossRef]

Nature (4)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Höansch, and I. Bloch, "Controlled collisions for multi-particle entanglement of optically trapped atoms," Nature 425, 937-940 (2003).
[CrossRef] [PubMed]

M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature 415, 39-44 (2002).
[CrossRef] [PubMed]

B. Paredes, A. Widera, V. Murg, O. Mandel, S. F¨olling, I. Cirac, G. V. Shlyapnikov, T. W. H¨ansch, and I. Bloch, "Tonks-Girardeau gas of ultracold atoms in an optical lattice," Nature 429, 277-281 (2004).
[CrossRef] [PubMed]

Opt. Express (2)

Phil. Trans. R. Soc. Lond. A (1)

J. V. Porto, S. Rolston, B. Laburthe Tolra, C. J. Williams, and W. D. Phillips, "Quantum information with neutral atoms as qubits," Phil. Trans. R. Soc. Lond. A 361, 1417-1427 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060-1063 (1999).
[CrossRef]

F. Gerbier, S. F¨olling, A. Widera, O. Mandel, and I. Bloch, "Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition," Phys. Rev. Lett. 96, 090401 (2006)
[CrossRef] [PubMed]

K. Henderson, H. Kelkar, B. Guti’errez-Medina, T. C. Li, and M. G. Raizen, "Experimental study of the role of atomic interactions on quantum transport," Phys. Rev. Lett. 96, 150401 (2006)
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Science (2)

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843-846 (2001).
[CrossRef] [PubMed]

Q1. T. Kinoshita, T. Wenger, and D. S. Weiss, "Observation of a one-dimensional Tonks-Girardeau gas," Science 305, 1125-1128 (2004)
[CrossRef]

Other (3)

R. Scheunemann, F. S. Cataliotti, T. W. Hänsch, and M. Weitz, "Resolving and addressing atoms in individual sites of a CO2-laser optical lattice," Phys. Rev. A 62, 051801(R) (2000).
[CrossRef]

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, "Patterned loading of a Bose-Einstein condensate into an optical lattice," Phys. Rev. A 67, 051603(R) (2003).
[CrossRef]

J. H. Huckans, "Optical lattices and quantum degenerate 87Rb in reduced dimensions, " Ph.D. dissertation, University of Maryland, College Park (2006).

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Figures (6)

Fig. 1.
Fig. 1.

Two parallel beams separated by a distance D, produce an optical lattice at the focal plane of the lens. We use an achromatic doublet lens to minimize the aberration of the off-axis beams. The highly curved surface faces the incident parallel beams.

Fig. 2.
Fig. 2.

Experimental set-up for creating and imaging the optical lattices with real-time control of periodicity. L1, L2 are singlet lenses; P1 is a pinhole; M1 and M2 are mirrors; BS1 and BS2 are polarizing cube beam splitters; and L3 is an achromatic doublet lens.

Fig. 3.
Fig. 3.

The distance between the two parallel beams can be changed by moving M1.

Fig. 4.
Fig. 4.

(a): An optical lattice with spacing of 0.81 µm, recorded by a CCD camera; (b): the lattice periodicity at the focus of a f=30 mm lens as a function of the distance between the two parallel beams. The statistical error of the data is smaller than the size of the squares.

Fig. 5.
Fig. 5.

Optical lattices with spacing of 0.98 µm and 6.20 µm.

Fig. 6.
Fig. 6.

Continuous change of the lattice periodicity from 0.96 µm to 11.2 µm, and back to 0.96 µm by moving M1 at different speed: 10 mm/s (a) and 20 mm/s (b). The center fringe (marked by a solid line) moved less than 2.7 µm during the whole process.

Equations (5)

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d λ ( D 2 4 + f 2 ) 1 2 D ,
U + D 2 ( x , y , f ) = exp ( j π D λ f x ) U 0 ( x , y , f ) ,
or U D 2 ( x , y , f ) = exp ( + j π D λ f x ) U 0 ( x , y , f ) .
I ( x , y , f ) = 2 ( cos 2 π D λ f x + 1 ) I 0 ( x , y , f ) ,
d = λ f D .

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