Abstract

We present an experimental method to create a single high frequency optical trap for atoms based on an elongated Hermite-Gaussian TEM01 mode beam. This trap results in confinement strength similar to that which may be obtained in an optical lattice. We discuss an optical setup to produce the trapping beam and then detail a method to load a Bose-Einstein Condensate (BEC) into a TEM01 trap. Using this method, we have succeeded in producing individual highly confined lower dimensional condensates.

© 2005 Optical Society of America

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References

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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 Atomics Vapor,� Science 269, 198-201 (1995)
    [CrossRef] [PubMed]
  2. K. B. Davis, M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, �Bose-Einstein Condensation in a Gas of Sodium Atoms,� Phys. Rev. Lett. 75, 3969 (1995)
    [CrossRef] [PubMed]
  3. Conventional magnetic traps refer to Ioffe-Prichard type or TOP traps, atom chip setups may also generate high strength traps because of the close proximity of the atoms to the chip surface [4].
  4. R. Folman, P. Kr�ger, J. Schmiedmayer, J. Denschlag, and C. Henkel, �Microscoptic Atom Optics: From Wires to an Atom Chip,� Adv. At. Mol. Opt. Phys. 48, 263 (2002).
    [CrossRef]
  5. P. S. Jessen and I. H. Deutsch, �Optical Lattices� Adv. At. Mol. Opt. Phys. 37, 95-138 (1996).
    [CrossRef]
  6. M. Greiner, O. Mandel, T. Esslinger, T.W. H�nsch, Immanuel Bloch, �Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,� Nature 415, 39 (2002).
    [CrossRef] [PubMed]
  7. B. Paredes, A. Widera, V. Murg, O. Mandel, S. F�lling, I. Cirac, G.V. Shlyapnikov, T.W. H�nsch, I. Bloch, �Tonks-Girardeau Gas of Ultracold Atoms in an Optical Lattice,� Nature 429, 277 (2004).
    [CrossRef] [PubMed]
  8. T. Kinoshita, T. Wenger, and D.S. Weiss, �Observation of a One-Dimensional Tonks-Girardeau Gas,� Science 305, 1125 (2004).
    [CrossRef] [PubMed]
  9. B. Laburthe Tolra, K. M. O�Hara, J. H. Huckans, W. D. Phillips, S. L. Rolston, and J. V. Porto, �Observation of Reduced Three-Body Recombination in a Correlated 1D Degenerate Bose Gas,� Phys. Rev. Lett. 92, 190401 (2004).
    [CrossRef] [PubMed]
  10. R.B. Diener, B. Wu, M.G. Raizen, and Q. Niu, �Quantum Tweezer for Atoms,� Phys. Rev. Lett. 89, 070401 (2002)
    [CrossRef] [PubMed]
  11. Saleh and Teich, Fundamentals of Photonics, (Wiley, New York, 1991)
    [CrossRef]
  12. The waist sizes depend on the propagation distance s as W2 q,p(s) = W2 q,p(0)+(?s/?Wq,p(0))2 [11]. This fact results in a weak anti-trap in this direction, see Eq. (8).
  13. R. Grimm, M. Weidem�ller, and Y.B. Ovchinnikov, �Optical Dipole Traps for Neutral Atoms,� Adv. At. Mol. Opt. Phys. 42, 95 (2000).
    [CrossRef]
  14. N. Freidman, A. Kaplan, N. Davidson, �Dark Optical Traps for Cold Atoms,� Adv. At. Mol. Opt. Phys. 48, 99 (2002).
    [CrossRef]
  15. MgF2 was chosen because it is a soft coating and more easily makes a sharp feature. This thickness is for a ? relative phase difference at wavelength ? = 532nm
  16. W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, �An Atom Faucet,� Eur. Phys. J. D 15, 237 (2001).
    [CrossRef]
  17. T. Esslinger, I. Bloch, and T.W. H�nsch, �Bose-Einstein condensation in a quadrupole-Ioffe-configuration trap,� Phys. Rev. A, Vol. 58, pp. R2664 No 4, (1998).
    [CrossRef]
  18. The TEM01 traps discussed here use laser wavelength ? = 532 nm and the infrared vertical trap uses ? = 1064 nm. These are blue and red relative to the strong transitions of rubidium near 780 nm. Blue traps result in a repulsive potential whereas red traps result in an attractive potential [13].
  19. Yariv and Yeh, Optical Waves in Crystals, (Wiley, New York, 1984).
  20. This is what it means to be lower dimensional, the motion in the strongly confined direction is frozen out and the wave function may be written as the ground state of a single particle harmonic oscillator in the direction in question. This occurs when the three-dimensional chemical potential ?3D is below the harmonic oscillator energy state splitting of the strong direction ?wq [21].
  21. D. S. Petrov, G. V. Shlyapnikov, and J. T. M.Walraven, �Regimes of Quantum Degeneracy in Trapped 1D Gases,� Phys. Rev. Lett. 85, 3745 (2000).
    [CrossRef] [PubMed]
  22. Y. Castin and R. Dum, �Bose-Einstein Condensates in Time Dependent Traps,� Phys. Rev. Lett. 77 5315 (1996).
    [CrossRef] [PubMed]
  23. We use values for the D2 line of rubidium 87: Is ~ 1.67mW/cm2, ? _= 2? ? 6.065MHz, w0 _= 2? ? 384.23THz, and m _= 1.443�10-25 kg. In Eq. (3), it is important not to use the common rotating wave approximation (which is to assume |w0 -w|�w0 +w and neglect the second term in parenthesis) because the detuning is too far for this to be valid. This is a larger effect than explicitly including the D1 line which is typically done for nearer detunings.
  24. This is a gradium index lens with f /# = 2.2.
  25. T.P. Meyrath, F. Schreck, J.L. Hanssen, C.-S. Chuu, and M.G. Raizen, �Bose Einstein Condensation in a Box,� Phys. Rev. A (to be published), preprint at cond-mat/0503590
  26. N. L. Smith, W. H. Heathcote, G. Hechenblaikner, E. Nugent, and C. J. Foot, �Quasi-2D Confinement of a BEC in a Combined Optical and Magnetic Potential,� J. Phys. B: At. Mol. Opt. Phys. 38 223-235 (2005).
    [CrossRef]

Adv. At. Mol. Opt. Phys.

R. Folman, P. Kr�ger, J. Schmiedmayer, J. Denschlag, and C. Henkel, �Microscoptic Atom Optics: From Wires to an Atom Chip,� Adv. At. Mol. Opt. Phys. 48, 263 (2002).
[CrossRef]

P. S. Jessen and I. H. Deutsch, �Optical Lattices� Adv. At. Mol. Opt. Phys. 37, 95-138 (1996).
[CrossRef]

R. Grimm, M. Weidem�ller, and Y.B. Ovchinnikov, �Optical Dipole Traps for Neutral Atoms,� Adv. At. Mol. Opt. Phys. 42, 95 (2000).
[CrossRef]

N. Freidman, A. Kaplan, N. Davidson, �Dark Optical Traps for Cold Atoms,� Adv. At. Mol. Opt. Phys. 48, 99 (2002).
[CrossRef]

Eur. Phys. J. D

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, �An Atom Faucet,� Eur. Phys. J. D 15, 237 (2001).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys.

N. L. Smith, W. H. Heathcote, G. Hechenblaikner, E. Nugent, and C. J. Foot, �Quasi-2D Confinement of a BEC in a Combined Optical and Magnetic Potential,� J. Phys. B: At. Mol. Opt. Phys. 38 223-235 (2005).
[CrossRef]

Nature

M. Greiner, O. Mandel, T. Esslinger, T.W. H�nsch, Immanuel Bloch, �Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,� Nature 415, 39 (2002).
[CrossRef] [PubMed]

B. Paredes, A. Widera, V. Murg, O. Mandel, S. F�lling, I. Cirac, G.V. Shlyapnikov, T.W. H�nsch, I. Bloch, �Tonks-Girardeau Gas of Ultracold Atoms in an Optical Lattice,� Nature 429, 277 (2004).
[CrossRef] [PubMed]

Phys. Rev. A

T. Esslinger, I. Bloch, and T.W. H�nsch, �Bose-Einstein condensation in a quadrupole-Ioffe-configuration trap,� Phys. Rev. A, Vol. 58, pp. R2664 No 4, (1998).
[CrossRef]

T.P. Meyrath, F. Schreck, J.L. Hanssen, C.-S. Chuu, and M.G. Raizen, �Bose Einstein Condensation in a Box,� Phys. Rev. A (to be published), preprint at cond-mat/0503590

Phys. Rev. Lett.

D. S. Petrov, G. V. Shlyapnikov, and J. T. M.Walraven, �Regimes of Quantum Degeneracy in Trapped 1D Gases,� Phys. Rev. Lett. 85, 3745 (2000).
[CrossRef] [PubMed]

Y. Castin and R. Dum, �Bose-Einstein Condensates in Time Dependent Traps,� Phys. Rev. Lett. 77 5315 (1996).
[CrossRef] [PubMed]

K. B. Davis, M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, �Bose-Einstein Condensation in a Gas of Sodium Atoms,� Phys. Rev. Lett. 75, 3969 (1995)
[CrossRef] [PubMed]

B. Laburthe Tolra, K. M. O�Hara, J. H. Huckans, W. D. Phillips, S. L. Rolston, and J. V. Porto, �Observation of Reduced Three-Body Recombination in a Correlated 1D Degenerate Bose Gas,� Phys. Rev. Lett. 92, 190401 (2004).
[CrossRef] [PubMed]

R.B. Diener, B. Wu, M.G. Raizen, and Q. Niu, �Quantum Tweezer for Atoms,� Phys. Rev. Lett. 89, 070401 (2002)
[CrossRef] [PubMed]

Science

T. Kinoshita, T. Wenger, and D.S. Weiss, �Observation of a One-Dimensional Tonks-Girardeau Gas,� Science 305, 1125 (2004).
[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 Atomics Vapor,� Science 269, 198-201 (1995)
[CrossRef] [PubMed]

Other

We use values for the D2 line of rubidium 87: Is ~ 1.67mW/cm2, ? _= 2? ? 6.065MHz, w0 _= 2? ? 384.23THz, and m _= 1.443�10-25 kg. In Eq. (3), it is important not to use the common rotating wave approximation (which is to assume |w0 -w|�w0 +w and neglect the second term in parenthesis) because the detuning is too far for this to be valid. This is a larger effect than explicitly including the D1 line which is typically done for nearer detunings.

This is a gradium index lens with f /# = 2.2.

Saleh and Teich, Fundamentals of Photonics, (Wiley, New York, 1991)
[CrossRef]

The waist sizes depend on the propagation distance s as W2 q,p(s) = W2 q,p(0)+(?s/?Wq,p(0))2 [11]. This fact results in a weak anti-trap in this direction, see Eq. (8).

Conventional magnetic traps refer to Ioffe-Prichard type or TOP traps, atom chip setups may also generate high strength traps because of the close proximity of the atoms to the chip surface [4].

MgF2 was chosen because it is a soft coating and more easily makes a sharp feature. This thickness is for a ? relative phase difference at wavelength ? = 532nm

The TEM01 traps discussed here use laser wavelength ? = 532 nm and the infrared vertical trap uses ? = 1064 nm. These are blue and red relative to the strong transitions of rubidium near 780 nm. Blue traps result in a repulsive potential whereas red traps result in an attractive potential [13].

Yariv and Yeh, Optical Waves in Crystals, (Wiley, New York, 1984).

This is what it means to be lower dimensional, the motion in the strongly confined direction is frozen out and the wave function may be written as the ground state of a single particle harmonic oscillator in the direction in question. This occurs when the three-dimensional chemical potential ?3D is below the harmonic oscillator energy state splitting of the strong direction ?wq [21].

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Figures (5)

Fig. 1.
Fig. 1.

Optics pictorial showing production of a TEM01 from an input Gaussian. (a) An input Gaussian passes the phase plate (PP) giving a relative π phase shift between the halves of the beam. (b) The aperture (A) is in the far field of the output beam from PP. This produces the Fourier transform at A. (c) Higher spatial modes are truncated by A. (d) Lens L1 produces the Fourier transform of the output of A resulting in a near TEM01 mode profile. (e) A true TEM01 beam, the profile in (d) only deviates in small fringes outside the main lobes. The images are numerically calculated beam profiles shown as I ( q , p ) .

Fig. 2.
Fig. 2.

Profile of TEM01 mode beam. (a) A CCD picture of a TEM01 trapping beam imaged as seen by the atoms. The image extends only 100µm in the z direction. (b) The profile along the narrow axis, the boxes are points integrated along the z axis for the center 10µm and the solid line is a fit to an ideal TEM01 mode profile in Equation 1, giving a waist size of Wx =1.8µm.

Fig. 3.
Fig. 3.

Optical trap beam input ports and imaging ports in the science chamber are shown in this schematic. The setup has the capacity to accept vertical and horizontal visible beams as well as a vertical infrared beam. There are 780 nm absorption imaging beams for both vertical and horizontal diagnostics. L1 and L2 are the final lenses in the vertical and horizontal beam paths, DM1 and DM2 are dichroic mirrors, AgM is a silver mirror. Gravity in the figure is in the -y direction.

Fig. 4.
Fig. 4.

Loading sequence of hTEM01 trap. The pair of lobes for each hTEM01 beam are represented in gray; the lower hTEM01 is the ligher shade. The vertical infrared beam is not shown, but present in all (b) to (d). (a) Combined optical and magnetic trap. (b) Combined gravito-optical trap where the lower hTEM01 beam acts as a sheet supporting against gravity. This trap has vertical trap frequency ωy ≅850Hz. (c) Transfer step into hTEM01 beam. (d) Final optical trap inside hTEM01 beam. This trap has vertical trap frequency ωy ≅21kHz.

Fig. 5.
Fig. 5.

BEC Expansion from hTEM01 trap. The black squares give data points for σ y as a function of time for condensates released at time zero. The data is consistent with the 21 kHz expected trap frequency for this TEM01 trap. The images to the right are absorption images of one of the shots of the indicated data point. The upper picture is of a condensate released from the inside the TEM01 trap, and the lower was released from above the sheet (the gravito-optical trap) as in Figure 4(b). This is the red circle data point on the plot. The lower picture is a 3-D condenstate and does not obey Equation 6.

Equations (10)

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I ( q , p ) = P π W q W p 8 q 2 W q 2 exp ( 2 q 2 W q 2 2 p 2 W p 2 ) ,
U ( q , p ) = U 0 2 e q 2 W q 2 exp ( 2 q 2 W q 2 2 p 2 W p 2 ) ,
U 0 = Γ 2 8 I s ( 1 ω 0 ω + 1 ω 0 + ω ) 4 P π e W q W p ,
ω q 2 π = e U 0 π 2 m W q 2 ,
R ( q , p ) = Γ 3 8 I s ( ω ω 0 ) 3 ( 1 ω 0 ω + 1 ω 0 + ω ) 2 I ( q , p ) .
σ y ( t ) = 2 m ω y ( 1 + t 2 ω y 2 ) 1 2 .
ω p 2 π = i 2 π 1 W p W q 1 2 ( e 2 U 0 m 3 ) 1 4 ,
ω s 2 π = 3 2 i 2 π 2 λ W q 5 2 ( e 2 U 0 m 3 ) 1 4 ,
ω q 2 π = 1 e 3 4 e U 0 π 2 m W q 2 ,
ω p ( 1 ) 2 π = i 2 e 3 4 e U 0 π 2 m W p 2 and ω p ( 2 ) 2 π = i 2 π e 3 8 1 W p W q 1 2 ( e 2 U 0 m 3 ) 1 4 ,

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