Abstract

A method of synthesizing localized optical fields with zeros on a periodic lattice is analyzed. The applicability to addressing atoms trapped in optical lattices with low cross talk is discussed.

© 2004 Optical Society of America

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References

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  1. I. H. Deutsch, G. K. Brennen, and P. S. Jessen, Fortschr. Phys. 48, 925 (2000).
    [CrossRef]
  2. T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
    [CrossRef]
  3. A. M. Steane, Nature 399, 124 (1999).
    [CrossRef]
  4. J. Preskill, in Introduction to Quantum Computation and Information, H.-K. Lo, T. Spiller, and S. Popescu, eds. (World Scientific, Singapore, 1998).
  5. R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
    [CrossRef]
  6. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
    [CrossRef] [PubMed]
  7. M. Saffman and T. G. Walker, Phys. Rev. A 66, 065403 (2002).
    [CrossRef]
  8. J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .
  9. S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
    [CrossRef]
  10. P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
    [CrossRef]
  11. M. Saffman, “Atomic lithography of two-dimensional nanostructures,” U.S. patent application filed April2003.

2003 (2)

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

2002 (3)

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

M. Saffman and T. G. Walker, Phys. Rev. A 66, 065403 (2002).
[CrossRef]

2000 (2)

I. H. Deutsch, G. K. Brennen, and P. S. Jessen, Fortschr. Phys. 48, 925 (2000).
[CrossRef]

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

1999 (1)

A. M. Steane, Nature 399, 124 (1999).
[CrossRef]

Birkl, G.

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Bloch, I.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

Brennen, G. K.

I. H. Deutsch, G. K. Brennen, and P. S. Jessen, Fortschr. Phys. 48, 925 (2000).
[CrossRef]

Briegel, H.-J.

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

Buchkremer, F. B. J.

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Calarco, T.

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

Cirac, J. I.

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

Daley, A. J.

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

Deutsch, I. H.

I. H. Deutsch, G. K. Brennen, and P. S. Jessen, Fortschr. Phys. 48, 925 (2000).
[CrossRef]

Dumke, R.

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Ertmer, W.

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Esslinger, T.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

Fedichev, P. O.

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

Greiner, M.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

Hänsch, T. W.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

Jaksch, D.

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

Jessen, P. S.

I. H. Deutsch, G. K. Brennen, and P. S. Jessen, Fortschr. Phys. 48, 925 (2000).
[CrossRef]

King, B. E.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Laburthe Tolra, B.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Mandel, O.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

Müther, T.

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Myrgren, S.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

Obrecht, J. M.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Peil, S.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Phillips, W. D.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Porto, J. V.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Preskill, J.

J. Preskill, in Introduction to Quantum Computation and Information, H.-K. Lo, T. Spiller, and S. Popescu, eds. (World Scientific, Singapore, 1998).

Rabl, P.

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

Rolston, S. L.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Saffman, M.

M. Saffman and T. G. Walker, Phys. Rev. A 66, 065403 (2002).
[CrossRef]

M. Saffman, “Atomic lithography of two-dimensional nanostructures,” U.S. patent application filed April2003.

Steane, A. M.

A. M. Steane, Nature 399, 124 (1999).
[CrossRef]

Subbotin, M.

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Thapliyal, A. V.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

Vala, J.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

Vazirani, U.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

Volk, M.

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Walker, T. G.

M. Saffman and T. G. Walker, Phys. Rev. A 66, 065403 (2002).
[CrossRef]

Weiss, D. S.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

Whaley, K. B.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

Zoller, P.

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

Fortschr. Phys. (2)

I. H. Deutsch, G. K. Brennen, and P. S. Jessen, Fortschr. Phys. 48, 925 (2000).
[CrossRef]

T. Calarco, H.-J. Briegel, D. Jaksch, J. I. Cirac, and P. Zoller, Fortschr. Phys. 48, 945 (2000).
[CrossRef]

Nature (2)

A. M. Steane, Nature 399, 124 (1999).
[CrossRef]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[CrossRef] [PubMed]

Phys. Rev. A (2)

M. Saffman and T. G. Walker, Phys. Rev. A 66, 065403 (2002).
[CrossRef]

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Phys. Rev. A 67, 051603 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

P. Rabl, A. J. Daley, P. O. Fedichev, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 91, 110403 (2003).
[CrossRef]

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef]

Other (3)

M. Saffman, “Atomic lithography of two-dimensional nanostructures,” U.S. patent application filed April2003.

J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani, D. S. Weiss, and K. B. Whaley, arXiv.org e-Print archive, , July10, 2003, http://arxiv.org/abs/quant-ph/0307085 .

J. Preskill, in Introduction to Quantum Computation and Information, H.-K. Lo, T. Spiller, and S. Popescu, eds. (World Scientific, Singapore, 1998).

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Figures (3)

Fig. 1
Fig. 1

Lens NA needed to focus a Gaussian beam to a waist w˜0 for λf/λ=1,2 and 10.

Fig. 2
Fig. 2

Optical system for producing a Bessel beam with a one-dimensional spatial light modulator that has N pixels. The additional beams of wavelength λf necessary for creating an optical lattice can in principle be combined with the imaging beams by use of dichroic mirrors not shown in the figure.

Fig. 3
Fig. 3

Intensity distribution calculated with N=100 and λ=0.78 µm. The central lobe was translated by Δx=4 µm and Δy=2 µm by adding phase offsets; see the text for details.

Tables (1)

Tables Icon

Table 1 Bessel Coefficients and Resulting Maximum Cross Talk at Site mmax away from the Origina

Equations (3)

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

NA=3/2πw˜0λ/λf1+3/2πw˜0λ/λf21/2.
Aρ,θ=J0kρ+n=1anJnkρexpinθ,
A˜q,ϕ=0dρρ02πdθAρ,θexpiρq cosθ-ϕ=2πkδq-k1+n=1anin expinϕ.

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