Abstract

We propose a new method of resonant enhancement of optical Kerr nonlinearity that uses multilevel atomic coherence. The enhancement is accompanied by suppression of the other linear and nonlinear susceptibility terms of the medium. We show that the effect results in a modification of the nonlinear Faraday rotation of light propagating in an Rb87 vapor cell by changing the ellipticity of the light.

© 2003 Optical Society of America

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  1. A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
    [CrossRef]
  2. A. Steane, Rep. Prog. Phys. 61, 117 (1998).
    [CrossRef]
  3. S. E. Harris, Phys. Today 52(6), 36 (1997).
    [CrossRef]
  4. J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
    [CrossRef]
  5. E. Arimondo, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1996), Vol. XXXV, p. 257.
    [CrossRef]
  6. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
    [CrossRef]
  7. S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef] [PubMed]
  8. H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
    [CrossRef] [PubMed]
  9. M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
    [CrossRef] [PubMed]
  10. S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
    [CrossRef]
  11. M. D. Lukin and A. Imamoglu, Phys. Rev. Lett. 84, 1419 (2000).
    [CrossRef] [PubMed]
  12. S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
    [CrossRef]
  13. B. S. Ham and P. R. Hemmer, Phys. Rev. Lett. 84, 4080 (2000).
    [CrossRef] [PubMed]
  14. M. Yan, E. G. Rickey, and Y. Zhu, Opt. Lett. 26, 548 (2001).
    [CrossRef]
  15. M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, R041801 (2001).
  16. M. S. Zubairy, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043804 (2002).
    [CrossRef]
  17. M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
    [CrossRef]
  18. I. Novikova, A. B. Matsko, and G. R. Welch, Opt. Lett. 26, 1016 (2001) and references therein.
    [CrossRef]
  19. A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
    [CrossRef]
  20. I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
    [CrossRef]
  21. See, for example, M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, Cambridge, 2000).
  22. A. Matsko, I. Novikova, M. S. Zubairy, and G. R. Welch, “Nonlinear magneto-optical rotation of elliptically polarized light,” October25, 2002, arXiv.org ePrint archive, physics/0210107.

2002 (2)

M. S. Zubairy, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043804 (2002).
[CrossRef]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

2001 (5)

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

I. Novikova, A. B. Matsko, and G. R. Welch, Opt. Lett. 26, 1016 (2001) and references therein.
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, Opt. Lett. 26, 548 (2001).
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, R041801 (2001).

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

2000 (3)

M. D. Lukin and A. Imamoglu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

B. S. Ham and P. R. Hemmer, Phys. Rev. Lett. 84, 4080 (2000).
[CrossRef] [PubMed]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

1999 (1)

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

1998 (3)

A. Steane, Rep. Prog. Phys. 61, 117 (1998).
[CrossRef]

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

1997 (1)

S. E. Harris, Phys. Today 52(6), 36 (1997).
[CrossRef]

1996 (2)

A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
[CrossRef]

H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
[CrossRef] [PubMed]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Arimondo, E.

E. Arimondo, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1996), Vol. XXXV, p. 257.
[CrossRef]

Chuang, I. L.

See, for example, M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, Cambridge, 2000).

Ekert, A.

A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
[CrossRef]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

Ham, B. S.

B. S. Ham and P. R. Hemmer, Phys. Rev. Lett. 84, 4080 (2000).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

S. E. Harris, Phys. Today 52(6), 36 (1997).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Hau, L. V.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Hemmer, P. R.

B. S. Ham and P. R. Hemmer, Phys. Rev. Lett. 84, 4080 (2000).
[CrossRef] [PubMed]

Imamoglu, A.

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamoglu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Javan, A.

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Jozsa, R.

A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
[CrossRef]

Kocharovskaya, O.

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Lee, H.

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamoglu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

Marangos, J. P.

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

Matsko, A.

A. Matsko, I. Novikova, M. S. Zubairy, and G. R. Welch, “Nonlinear magneto-optical rotation of elliptically polarized light,” October25, 2002, arXiv.org ePrint archive, physics/0210107.

Matsko, A. B.

M. S. Zubairy, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043804 (2002).
[CrossRef]

I. Novikova, A. B. Matsko, and G. R. Welch, Opt. Lett. 26, 1016 (2001) and references therein.
[CrossRef]

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

Nielsen, M. A.

See, for example, M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, Cambridge, 2000).

Novikova, I.

I. Novikova, A. B. Matsko, and G. R. Welch, Opt. Lett. 26, 1016 (2001) and references therein.
[CrossRef]

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

A. Matsko, I. Novikova, M. S. Zubairy, and G. R. Welch, “Nonlinear magneto-optical rotation of elliptically polarized light,” October25, 2002, arXiv.org ePrint archive, physics/0210107.

Rickey, E. G.

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, R041801 (2001).

M. Yan, E. G. Rickey, and Y. Zhu, Opt. Lett. 26, 548 (2001).
[CrossRef]

Schmidt, H.

Scully, M. O.

M. S. Zubairy, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043804 (2002).
[CrossRef]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

Steane, A.

A. Steane, Rep. Prog. Phys. 61, 117 (1998).
[CrossRef]

Velichansky, V. L.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

Welch, G. R.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

I. Novikova, A. B. Matsko, and G. R. Welch, Opt. Lett. 26, 1016 (2001) and references therein.
[CrossRef]

A. Matsko, I. Novikova, M. S. Zubairy, and G. R. Welch, “Nonlinear magneto-optical rotation of elliptically polarized light,” October25, 2002, arXiv.org ePrint archive, physics/0210107.

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

Yan, M.

M. Yan, E. G. Rickey, and Y. Zhu, Opt. Lett. 26, 548 (2001).
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, R041801 (2001).

Zhu, Y.

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, R041801 (2001).

M. Yan, E. G. Rickey, and Y. Zhu, Opt. Lett. 26, 548 (2001).
[CrossRef]

Zubairy, M. S.

M. S. Zubairy, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043804 (2002).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

A. Matsko, I. Novikova, M. S. Zubairy, and G. R. Welch, “Nonlinear magneto-optical rotation of elliptically polarized light,” October25, 2002, arXiv.org ePrint archive, physics/0210107.

J. Mod. Opt. (1)

J. P. Marangos, J. Mod. Opt. 45, 471 (1998).
[CrossRef]

Nature (1)

M. D. Lukin and A. Imamoglu, Nature 413, 273 (2001).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (5)

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, Phys. Rev. A 63, 063802 (2001).
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, R041801 (2001).

M. S. Zubairy, A. B. Matsko, and M. O. Scully, Phys. Rev. A 65, 043804 (2002).
[CrossRef]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

M. D. Lukin and A. Imamoglu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

B. S. Ham and P. R. Hemmer, Phys. Rev. Lett. 84, 4080 (2000).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, Phys. Today 52(6), 36 (1997).
[CrossRef]

Rep. Prog. Phys. (1)

A. Steane, Rep. Prog. Phys. 61, 117 (1998).
[CrossRef]

Rev. Mod. Phys. (1)

A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
[CrossRef]

Other (4)

E. Arimondo, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1996), Vol. XXXV, p. 257.
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, 1997).
[CrossRef]

See, for example, M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, Cambridge, 2000).

A. Matsko, I. Novikova, M. S. Zubairy, and G. R. Welch, “Nonlinear magneto-optical rotation of elliptically polarized light,” October25, 2002, arXiv.org ePrint archive, physics/0210107.

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Figures (3)

Fig. 1
Fig. 1

Energy-level schemes for (a) Λ system, (b) N system, (c) M system.

Fig. 2
Fig. 2

(a) Energy-level scheme for Rb87 atoms. This scheme may be decomposed into a superposition of (b) a Λ system and (c) an M system.

Fig. 3
Fig. 3

Slope of nonlinear magneto-optic rotation as a function of the ellipticity of the incident light. The slope is normalized by the value of linearly polarized light (zero ellipticity). Experimental data are shown by squares (1-mW laser power) and by circles (2-mW laser power), and the results of the numerical simulations for the case of 2-mW laser power are shown by the solid curve. The laser beam has a 2-mm diameter. Inset, theoretical dependence of naturally broadened Rb vapor, from Eq. (10).

Equations (11)

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

HM=-δ|b3b3|+j=12(αj|ajbj+Ωjajbj+1|+H.c.),
|D=α1α2|b3-Ω2α1|b2+Ω1Ω2|b1α12α22+Ω22α12+Ω12Ω221/2.
|D˜ζ(|D-δα1*α22Ω12Ω22|a1+δα1α2Ω1Ω22|a2),
λD˜-δα12α22Ω12Ω22,
αˆi=2πPi2νiVi1/2aˆi=ξiaˆi,
HM=-δξ12ξ22Ω12Ω22aˆ1aˆ1aˆ2aˆ2.
HN=ξ12ξ22ΔΩ12aˆ1aˆ1aˆ2aˆ2.
R=δΔ/Ω22,
χM=-i38π2Nλα23γ2γ0+iδγ0+iδWd+Ω22α12Ω12.
χN=-i38π2Nλα23γ2Wd+iΔα12Ω12.
ϕBϕΛB12+2+q22-q22.

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