Abstract

We propose and investigate a technique for generating smooth two-dimensional potentials for ultra-cold atoms based on the rapid scanning of a far-detuned laser beam using a two-dimensional acousto-optical modulator (AOM). We demonstrate the implementation of a feed-forward mechanism for fast and accurate control of the spatial intensity of the laser beam, resulting in improved homogeneity for the atom trap. This technique could be used to generate a smooth toroidal trap that would be useful for static and dynamic experiments on superfluidity and persistent currents with ultra-cold atoms.

© 2008 Optical Society of America

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  1. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell. "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
    [CrossRef] [PubMed]
  2. P. Kapitza. "Viscosity of liquid helium below the ⌊ -point," Nature 141, 74-75 (1938).
    [CrossRef]
  3. C. Raman, M. K¨ohl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle. "Evidence for a critical velocity in a Bose-Einstein condensed gas," Phys. Rev. Lett. 83, 2502-2505 (1999).
    [CrossRef]
  4. Q1. O. M. Marag`o, S. A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, and C. J. Foot. "Observation of the scissors mode and evidence for superfluidity of a trapped Bose-Einstein condensed gas," Phys. Rev. Lett. 84, 2056-2059 (2000).
    [CrossRef] [PubMed]
  5. B.P. Anderson, P.C. Haljan, C. E. Wieman, and E. A. Cornell, "Vortex precession in Bose-Einstein condensates: observations with filled and empty cores," Phys. Rev. Lett. 85, 2857-2860 (2000).
    [CrossRef] [PubMed]
  6. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle. "Observation of vortex lattices in Bose-Einstein condensates," Science 292, 476-479 (2001).
    [CrossRef] [PubMed]
  7. J. D. Reppy, and D. Depatie. "Persistent currents in superfluid helium," Phys. Rev. Lett. 12, 187-189 (1964).
    [CrossRef]
  8. A.S. Arnold, C.S. Garvie, and E. Riis. "Large magnetic storage ring for Bose-Einstein condensates," Phys. Rev. A 73, 041606 (2006).
    [CrossRef]
  9. S. Gupta, K.W. Murch, K.L. Moore, T.P. Purdy, and D.M. Stamper-Kurn. "Bose-Einstein condensation in a circular waveguide," Phys. Rev. Lett. 95, 143201 (2005).
    [CrossRef] [PubMed]
  10. J.A. Sauer, M.D. Barrett, and M.S. Chapman. "Storage ring for neutral atoms," Phys. Rev. Lett. 87, 270401 (2001).
    [CrossRef]
  11. O. Morizot, Y. Colombe, V. Lorent, and H. Perrin. "Ring trap for ultracold atoms," Phys. Rev. A 74, 023617 (2006).
    [CrossRef]
  12. S. Franke-Arnold, J. Leach, M.J. Padgett, V.E. Lebessis, D. Ellinas, A.J. Wright, J.M. Girkin, P. O¨ hberg, and A.S. Arnold. "Optical ferris wheel for ultracold atoms," Opt. Express 15, 8619-8625 (2007).
    [CrossRef] [PubMed]
  13. C. Ryu, M. F. Andersen, P. Clade, Vasant Natarajan, K.  Helmerson, W. D. Phillips. "Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap," arXiv:0709.0012v1 (2007).
  14. W. Petrich, M.H. Anderson, J.R. Ensher, and E.A. Cornell. "Stable, tightly confining magnetic trap for evaporative cooling of neutral atoms," Phys. Rev. Lett. 74, 3352-3355 (1995).
    [CrossRef] [PubMed]
  15. P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N.P. Bigelow. "An optical dynamical dark trap for neutral atoms," Opt. Express 8, 159-165 (2001).
    [CrossRef] [PubMed]
  16. N. Friedman, L. Khaykovich, R. Ozeri, and N. Davidson. "Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap," Phys. Rev. A 61, 031403 (2000).
    [CrossRef]
  17. V. Milner, J.L. Hanssen, W.C. Campbell, and M.G. Raizen. "Optical billiards for atoms," Phys. Rev. Lett. 86, 1514-1517 (2001).
    [CrossRef] [PubMed]
  18. P. Ahmadi, B.P. Timmons, and G.S. Summy. "Geometric effects in the loading of an optical trap," Phys. Rev. A 72, 023411 (2005).
    [CrossRef]
  19. I. Lesanovsky, and W. von Klitzing. "Time-averaged adiabatic potentials: versatile matter-wave guides and atom traps," Phys. Rev. Lett. 99, 083001 (2007).
    [CrossRef] [PubMed]
  20. L. Allen, and J.H. Eberly. "Optical resonance and two-level atoms," Wiley (1975).
  21. T.A. Savard, K.M. O’Hara, and J.E. Thomas. "Laser-noise in far-off resonance optical traps," Phys. Rev. A,  56(2), 1095-1098 (1997).
    [CrossRef]
  22. E.M. Wright, J. Arlt, and K. Dholakia. "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2000).
    [CrossRef]
  23. C.J. Vale, B. Upcroft, M.J. Davis, N.R. Heckenberg, and H. Rubinsztein-Dunlop. "Foil-based atom chip for Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. 37, 2959-2967 (2004).
    [CrossRef]
  24. D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, S. Inouye, J. Stenger, andW. Ketterle. "Reversible formation of a Bose-Einstein condensate," Phys. Rev. Lett. 81, 2194-2197 (1998).
    [CrossRef]
  25. B.P. Anderson, K. Dholakia, and E.M. Wright. "Atomic-phase interference devices based on ring-shaped Bose- Einstein condensates: Two-ring case," Phys. Rev. A 67, 033601 (2003).
    [CrossRef]

2007 (2)

2006 (2)

O. Morizot, Y. Colombe, V. Lorent, and H. Perrin. "Ring trap for ultracold atoms," Phys. Rev. A 74, 023617 (2006).
[CrossRef]

A.S. Arnold, C.S. Garvie, and E. Riis. "Large magnetic storage ring for Bose-Einstein condensates," Phys. Rev. A 73, 041606 (2006).
[CrossRef]

2005 (2)

S. Gupta, K.W. Murch, K.L. Moore, T.P. Purdy, and D.M. Stamper-Kurn. "Bose-Einstein condensation in a circular waveguide," Phys. Rev. Lett. 95, 143201 (2005).
[CrossRef] [PubMed]

P. Ahmadi, B.P. Timmons, and G.S. Summy. "Geometric effects in the loading of an optical trap," Phys. Rev. A 72, 023411 (2005).
[CrossRef]

2004 (1)

C.J. Vale, B. Upcroft, M.J. Davis, N.R. Heckenberg, and H. Rubinsztein-Dunlop. "Foil-based atom chip for Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. 37, 2959-2967 (2004).
[CrossRef]

2003 (1)

B.P. Anderson, K. Dholakia, and E.M. Wright. "Atomic-phase interference devices based on ring-shaped Bose- Einstein condensates: Two-ring case," Phys. Rev. A 67, 033601 (2003).
[CrossRef]

2001 (4)

V. Milner, J.L. Hanssen, W.C. Campbell, and M.G. Raizen. "Optical billiards for atoms," Phys. Rev. Lett. 86, 1514-1517 (2001).
[CrossRef] [PubMed]

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N.P. Bigelow. "An optical dynamical dark trap for neutral atoms," Opt. Express 8, 159-165 (2001).
[CrossRef] [PubMed]

J.A. Sauer, M.D. Barrett, and M.S. Chapman. "Storage ring for neutral atoms," Phys. Rev. Lett. 87, 270401 (2001).
[CrossRef]

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle. "Observation of vortex lattices in Bose-Einstein condensates," Science 292, 476-479 (2001).
[CrossRef] [PubMed]

2000 (4)

Q1. O. M. Marag`o, S. A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, and C. J. Foot. "Observation of the scissors mode and evidence for superfluidity of a trapped Bose-Einstein condensed gas," Phys. Rev. Lett. 84, 2056-2059 (2000).
[CrossRef] [PubMed]

B.P. Anderson, P.C. Haljan, C. E. Wieman, and E. A. Cornell, "Vortex precession in Bose-Einstein condensates: observations with filled and empty cores," Phys. Rev. Lett. 85, 2857-2860 (2000).
[CrossRef] [PubMed]

N. Friedman, L. Khaykovich, R. Ozeri, and N. Davidson. "Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap," Phys. Rev. A 61, 031403 (2000).
[CrossRef]

E.M. Wright, J. Arlt, and K. Dholakia. "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2000).
[CrossRef]

1999 (1)

C. Raman, M. K¨ohl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle. "Evidence for a critical velocity in a Bose-Einstein condensed gas," Phys. Rev. Lett. 83, 2502-2505 (1999).
[CrossRef]

1998 (1)

D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, S. Inouye, J. Stenger, andW. Ketterle. "Reversible formation of a Bose-Einstein condensate," Phys. Rev. Lett. 81, 2194-2197 (1998).
[CrossRef]

1997 (1)

T.A. Savard, K.M. O’Hara, and J.E. Thomas. "Laser-noise in far-off resonance optical traps," Phys. Rev. A,  56(2), 1095-1098 (1997).
[CrossRef]

1995 (2)

W. Petrich, M.H. Anderson, J.R. Ensher, and E.A. Cornell. "Stable, tightly confining magnetic trap for evaporative cooling of neutral atoms," Phys. Rev. Lett. 74, 3352-3355 (1995).
[CrossRef] [PubMed]

M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell. "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

1964 (1)

J. D. Reppy, and D. Depatie. "Persistent currents in superfluid helium," Phys. Rev. Lett. 12, 187-189 (1964).
[CrossRef]

1938 (1)

P. Kapitza. "Viscosity of liquid helium below the ⌊ -point," Nature 141, 74-75 (1938).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

C.J. Vale, B. Upcroft, M.J. Davis, N.R. Heckenberg, and H. Rubinsztein-Dunlop. "Foil-based atom chip for Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. 37, 2959-2967 (2004).
[CrossRef]

Nature (1)

P. Kapitza. "Viscosity of liquid helium below the ⌊ -point," Nature 141, 74-75 (1938).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (7)

N. Friedman, L. Khaykovich, R. Ozeri, and N. Davidson. "Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap," Phys. Rev. A 61, 031403 (2000).
[CrossRef]

P. Ahmadi, B.P. Timmons, and G.S. Summy. "Geometric effects in the loading of an optical trap," Phys. Rev. A 72, 023411 (2005).
[CrossRef]

O. Morizot, Y. Colombe, V. Lorent, and H. Perrin. "Ring trap for ultracold atoms," Phys. Rev. A 74, 023617 (2006).
[CrossRef]

A.S. Arnold, C.S. Garvie, and E. Riis. "Large magnetic storage ring for Bose-Einstein condensates," Phys. Rev. A 73, 041606 (2006).
[CrossRef]

T.A. Savard, K.M. O’Hara, and J.E. Thomas. "Laser-noise in far-off resonance optical traps," Phys. Rev. A,  56(2), 1095-1098 (1997).
[CrossRef]

E.M. Wright, J. Arlt, and K. Dholakia. "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2000).
[CrossRef]

B.P. Anderson, K. Dholakia, and E.M. Wright. "Atomic-phase interference devices based on ring-shaped Bose- Einstein condensates: Two-ring case," Phys. Rev. A 67, 033601 (2003).
[CrossRef]

Phys. Rev. Lett. (10)

D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, S. Inouye, J. Stenger, andW. Ketterle. "Reversible formation of a Bose-Einstein condensate," Phys. Rev. Lett. 81, 2194-2197 (1998).
[CrossRef]

S. Gupta, K.W. Murch, K.L. Moore, T.P. Purdy, and D.M. Stamper-Kurn. "Bose-Einstein condensation in a circular waveguide," Phys. Rev. Lett. 95, 143201 (2005).
[CrossRef] [PubMed]

J.A. Sauer, M.D. Barrett, and M.S. Chapman. "Storage ring for neutral atoms," Phys. Rev. Lett. 87, 270401 (2001).
[CrossRef]

J. D. Reppy, and D. Depatie. "Persistent currents in superfluid helium," Phys. Rev. Lett. 12, 187-189 (1964).
[CrossRef]

C. Raman, M. K¨ohl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle. "Evidence for a critical velocity in a Bose-Einstein condensed gas," Phys. Rev. Lett. 83, 2502-2505 (1999).
[CrossRef]

Q1. O. M. Marag`o, S. A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, and C. J. Foot. "Observation of the scissors mode and evidence for superfluidity of a trapped Bose-Einstein condensed gas," Phys. Rev. Lett. 84, 2056-2059 (2000).
[CrossRef] [PubMed]

B.P. Anderson, P.C. Haljan, C. E. Wieman, and E. A. Cornell, "Vortex precession in Bose-Einstein condensates: observations with filled and empty cores," Phys. Rev. Lett. 85, 2857-2860 (2000).
[CrossRef] [PubMed]

W. Petrich, M.H. Anderson, J.R. Ensher, and E.A. Cornell. "Stable, tightly confining magnetic trap for evaporative cooling of neutral atoms," Phys. Rev. Lett. 74, 3352-3355 (1995).
[CrossRef] [PubMed]

I. Lesanovsky, and W. von Klitzing. "Time-averaged adiabatic potentials: versatile matter-wave guides and atom traps," Phys. Rev. Lett. 99, 083001 (2007).
[CrossRef] [PubMed]

V. Milner, J.L. Hanssen, W.C. Campbell, and M.G. Raizen. "Optical billiards for atoms," Phys. Rev. Lett. 86, 1514-1517 (2001).
[CrossRef] [PubMed]

Science (2)

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle. "Observation of vortex lattices in Bose-Einstein condensates," Science 292, 476-479 (2001).
[CrossRef] [PubMed]

M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell. "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Other (2)

L. Allen, and J.H. Eberly. "Optical resonance and two-level atoms," Wiley (1975).

C. Ryu, M. F. Andersen, P. Clade, Vasant Natarajan, K.  Helmerson, W. D. Phillips. "Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap," arXiv:0709.0012v1 (2007).

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Figures (5)

Fig. 1.
Fig. 1.

Trapping frequencies as a function of ring size for a beam waist of 25µm. The minimum in this plot shows the regime where the radius a of the ring is of the same size as the focus of the laser focus and the minimum of the potential in the center of the trap <0.

Fig. 2.
Fig. 2.

Feed-forward technique to cancel the effect of different diffraction efficiencies depending on the angle of deflection. When the intensity locked laser beam is scanned it is imaged on a CCD camera and some part of it is deflected onto a photo diode. The photo diode gives an intensity profile that is then inverted and mixed with the rf signal that drives the AOM. Extra modulations of the intensity over the ring can be accomplished with an additional signal to the intensity lock.

Fig. 3.
Fig. 3.

Intensity profiles of the rings without (top curve) and with (bottom curve) feed-forward. Corresponding CCD images are shown in figure 5, where the first image shows the uncorrected and the second image the corrected ring.

Fig. 4.
Fig. 4.

Condensate fraction of a BEC in a magnetic trap with an optical dipole trap super-imposed run with a 20% on/off duty cycle. Initial condensate fraction without dipole trap was 15.3% and is indicated in gray. The line through the data points acts only as a guide to the eye.

Fig. 5.
Fig. 5.

Different possible waveforms for the function generator controlling the feed-forward technique and the function generator controlling the PID circuit and the resulting patterns. The top pattern shows a uniform distribution for both function generators resulting in a ring with non-uniform light distribution. For all the other cases the first generator is used to cancel the effects of different diffraction efficiencies and the second generator to create patterns of laser power leading to a uniform ring, horse shoe and ring lattice, respectively. The size of the images is 330×330µm.

Equations (4)

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

U ( r ) 3 π c 2 2 ω A 3 Γ Δ I ( r )
I ( r ) = 4 P w 2 exp ( 2 ( r 2 + a 2 ) w 2 ) 𝓘 0 ( ζ ) ,
ω r = 2 κ m P exp ( 4 a 2 w 2 ) [ 64 a 2 w 6 ( 𝓘 0 ( ζ ) 𝓘 1 ( ζ ) ) 8 w 4 ( 𝓘 0 ( ζ ) 𝓘 1 ( ζ ) ) ] ,
μ = h ¯ ω r ω z 3 N a s 4 a ,

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