Abstract

We demonstrate the possibility of dynamic imaging of magnetic fields using electromagnetically induced transparency in an atomic gas. As an experimental demonstration we employ an atomic Rb gas confined in a glass cell to image the transverse magnetic field created by a long straight wire. In this arrangement, which clearly reveals the essential effect, the field of view is about 2×2mm2 and the field detection uncertainty is 0.14 mG per 10μm×10μm image pixel.

© 2009 Optical Society of America

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  1. D. Budker and M. V. Romalis, Nat. Phys. 3, 227 (2007).
    [CrossRef]
  2. C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
    [CrossRef]
  3. I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
    [CrossRef] [PubMed]
  4. S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
    [CrossRef]
  5. M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
    [CrossRef] [PubMed]
  6. H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
    [CrossRef]
  7. G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.
  8. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  9. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 133, 60 (1931).
    [CrossRef]
  10. D. Budker, V. Yashchuk, and M. Zolotorev, Phys. Rev. Lett. 81, 5788 (1998).
    [CrossRef]
  11. M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
    [CrossRef]
  12. H. Asahi, K. Motomura, K. Harada, and M. Mitsunaga, Opt. Lett. 28, 1153 (2003).
    [CrossRef] [PubMed]
  13. For arbitrary orientation of the laser polarization with respect of the magnetic field vector the analysis of relative amplitudes of EIT resonances at 0,+/-gmB and +/-2gmB two-photon detunings may allow measurements of both magnitude and direction of a magnetic field.
  14. S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).
  15. http://femm.foster-miller.net/wiki/HomePage.
  16. W. Happer, Rev. Mod. Phys. 44, 169 (1972).
    [CrossRef]
  17. S. Knappe, L. Hollberg, and J. Kitching, Opt. Lett. 29, 388 (2004).
    [CrossRef] [PubMed]
  18. A. G. Marshall and F. R. Verdun, Fourier Transforms in NMR, Optical, and Mass Spectrometry (Elsevier, 1990).
  19. J. Vanier, Appl. Phys. B 81, 421 (2005).
    [CrossRef]
  20. V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
    [CrossRef]

2009

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

2007

V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
[CrossRef]

D. Budker and M. V. Romalis, Nat. Phys. 3, 227 (2007).
[CrossRef]

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

2006

H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
[CrossRef]

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

2005

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

2004

2003

H. Asahi, K. Motomura, K. Harada, and M. Mitsunaga, Opt. Lett. 28, 1153 (2003).
[CrossRef] [PubMed]

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
[CrossRef] [PubMed]

2002

C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
[CrossRef]

2001

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

1998

D. Budker, V. Yashchuk, and M. Zolotorev, Phys. Rev. Lett. 81, 5788 (1998).
[CrossRef]

1972

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

1931

P. A. M. Dirac, Proc. R. Soc. London, Ser. A 133, 60 (1931).
[CrossRef]

Affolderbach, C.

C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
[CrossRef]

Allred, J. C.

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
[CrossRef] [PubMed]

Asahi, H.

Ben-Amar Baranga, A.

H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
[CrossRef]

Bison, G.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

Budker, D.

D. Budker and M. V. Romalis, Nat. Phys. 3, 227 (2007).
[CrossRef]

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

D. Budker, V. Yashchuk, and M. Zolotorev, Phys. Rev. Lett. 81, 5788 (1998).
[CrossRef]

Castagna, N.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

Dirac, P. A. M.

P. A. M. Dirac, Proc. R. Soc. London, Ser. A 133, 60 (1931).
[CrossRef]

Donaldson, M. H.

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

Erhard, M.

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Guzman, J.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

Happer, W.

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Harada, K.

Helm, H.

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

Higbie, J. M.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

Hofer, A.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

Hoffman, D.

H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
[CrossRef]

Hollberg, L.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Kitching, J.

V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
[CrossRef]

S. Knappe, L. Hollberg, and J. Kitching, Opt. Lett. 29, 388 (2004).
[CrossRef] [PubMed]

Knappe, S.

V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
[CrossRef]

S. Knappe, L. Hollberg, and J. Kitching, Opt. Lett. 29, 388 (2004).
[CrossRef] [PubMed]

C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
[CrossRef]

Knowles, P.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

Kominis, I. K.

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
[CrossRef] [PubMed]

Kornack, T. W.

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
[CrossRef] [PubMed]

Leslie, S. R.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Marshall, A. G.

A. G. Marshall and F. R. Verdun, Fourier Transforms in NMR, Optical, and Mass Spectrometry (Elsevier, 1990).

Mitsunaga, M.

Motomura, K.

Novikova, I.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Phillips, D. F.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Rochester, S. M.

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

Romalis, M. V.

D. Budker and M. V. Romalis, Nat. Phys. 3, 227 (2007).
[CrossRef]

H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
[CrossRef]

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
[CrossRef] [PubMed]

Sadler, L. E.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

Schenker, J. -L.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

Schwindt, P. D. D.

V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
[CrossRef]

Shah, V.

V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
[CrossRef]

Stähler, M.

C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
[CrossRef]

Stamper-Kern, D. M.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

Taichenachev, A. V.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Vanier, J.

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

Velichansky, V. L.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Vengalattore, M.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

Verdun, F. R.

A. G. Marshall and F. R. Verdun, Fourier Transforms in NMR, Optical, and Mass Spectrometry (Elsevier, 1990).

Walsworth, R. L.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Weis, A.

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

Wynands, R.

C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
[CrossRef]

Xia, H.

H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
[CrossRef]

Xu, S.

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

Yashchuk, V.

D. Budker, V. Yashchuk, and M. Zolotorev, Phys. Rev. Lett. 81, 5788 (1998).
[CrossRef]

Yashchuk, V. V.

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

Yudin, V. I.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Zibrov, A. S.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Zibrov, S. A.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

Zolotorev, M.

D. Budker, V. Yashchuk, and M. Zolotorev, Phys. Rev. Lett. 81, 5788 (1998).
[CrossRef]

Appl. Phys. B

C. Affolderbach, M. Stähler, S. Knappe, and R. Wynands, Appl. Phys. B 75, 605 (2002).
[CrossRef]

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

Appl. Phys. Lett.

H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V. Romalis, Appl. Phys. Lett. 89, 211104 (2006).
[CrossRef]

Nat. Photonics

V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, Nat. Photonics 1, 649 (2007).
[CrossRef]

Nat. Phys.

D. Budker and M. V. Romalis, Nat. Phys. 3, 227 (2007).
[CrossRef]

Nature

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

Phys. Rev. Lett.

M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kern, Phys. Rev. Lett. 98, 200801 (2007).
[CrossRef] [PubMed]

D. Budker, V. Yashchuk, and M. Zolotorev, Phys. Rev. Lett. 81, 5788 (1998).
[CrossRef]

Proc. R. Soc. London, Ser. A

P. A. M. Dirac, Proc. R. Soc. London, Ser. A 133, 60 (1931).
[CrossRef]

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Rev. Sci. Instrum.

S. Xu, S. M. Rochester, V. V. Yashchuk, M. H. Donaldson, and D. Budker, Rev. Sci. Instrum. 77, 083106 (2006).
[CrossRef]

Other

G. Bison, N. Castagna, A. Hofer, P. Knowles, J.-L. Schenker, and A. Weis, arXiv:0906.4869.

For arbitrary orientation of the laser polarization with respect of the magnetic field vector the analysis of relative amplitudes of EIT resonances at 0,+/-gmB and +/-2gmB two-photon detunings may allow measurements of both magnitude and direction of a magnetic field.

S. A. Zibrov, I. Novikova, D. F. Phillips, R. L. Walsworth, A. S. Zibrov, V. L. Velichansky, A. V. Taichenachev, and V. I. Yudin, arXiv:0910.4703 (2009).

http://femm.foster-miller.net/wiki/HomePage.

A. G. Marshall and F. R. Verdun, Fourier Transforms in NMR, Optical, and Mass Spectrometry (Elsevier, 1990).

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Figures (2)

Fig. 1
Fig. 1

(a) A schematic diagram of the experiment. (b) Energy level diagram showing two EIT Λ schemes formed by the carrier E 0 and the first modulation sideband E + 1 .

Fig. 2
Fig. 2

(a) Transmission through the cell detected at three different camera pixels [marked in (b)] as functions of the two-photon detuning. Solid lines show low-pass filtered data used to determine the maximum transmission frequency. (b) Map of the magnetic field strength. Dashed lines mark the 75% and 50% levels of the maximum laser beam intensity. (c) Experimentally measured magnetic field slice of the map (b) along y = 0 as a function of x position, and the theoretically calculated magnetic fields using the Biot–Savart law and a finite element analysis. The error bars in the FEM curve represent the variation in the calculated magnetic field due to ±1 mm uncertainty in the magnetic shielding position with respect to the wire and the laser beam.

Equations (2)

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

B ( ρ ) = μ o I 2 π ( ρ + δ x ) μ o I 2 π ρ 0 ( 1 δ x ρ 0 ) ,
Δ B 1 2 g m γ S / N n .

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