Abstract

We analyze a cross-phase modulation (XPM) scheme that exhibits a giant, resonantly enhanced nonlinearity, along with vanishing linear susceptibilities. The proposed atomic system uses an electromagnetically induced transparency and is limited only by two-photon absorption. We predict dramatic improvement by several orders of magnitude for conditional phase shifts in XPM, and the system has possible applications in quantum nondemolition measurements and for quantum logic gates.

© 1996 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  2. J. P. Poizat, P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
    [CrossRef] [PubMed]
  3. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
    [CrossRef] [PubMed]
  4. S. P. Tewari, G. S. Agarwal, Phys. Rev. Lett. 56, 1811 (1986).
  5. S. E. Harris, J. E. Field, A. Imamoǧlu, Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef] [PubMed]
  6. K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
    [CrossRef] [PubMed]
  7. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. Shahriar, P. Kumar, Opt. Lett. 20, 982 (1995).
    [CrossRef] [PubMed]
  8. A. Imamoǧlu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, San Diego, Calif., 1989), Chap. 7, p. 175.
  10. N. B. Delone, V. P. Krainov, Fundamentals of Nonlinear Optics of Atomic Gases, 1st ed. (Wiley, New York, 1988), Chap. 3, p. 201.
  11. R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press., Berkeley, Calif., 1981), Appendix D, p. 640.
  12. S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
    [CrossRef] [PubMed]

1995

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. Shahriar, P. Kumar, Opt. Lett. 20, 982 (1995).
[CrossRef] [PubMed]

1993

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
[CrossRef] [PubMed]

J. P. Poizat, P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

1991

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

1990

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

1989

1986

S. P. Tewari, G. S. Agarwal, Phys. Rev. Lett. 56, 1811 (1986).

Agarwal, G. S.

S. P. Tewari, G. S. Agarwal, Phys. Rev. Lett. 56, 1811 (1986).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, San Diego, Calif., 1989), Chap. 7, p. 175.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Cowan, R. D.

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press., Berkeley, Calif., 1981), Appendix D, p. 640.

Cronin-Golomb, M.

Delone, N. B.

N. B. Delone, V. P. Krainov, Fundamentals of Nonlinear Optics of Atomic Gases, 1st ed. (Wiley, New York, 1988), Chap. 3, p. 201.

Donoghue, J.

Field, J. E.

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

Grangier, P.

J. P. Poizat, P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Hakuta, K.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
[CrossRef] [PubMed]

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

A. Imamoǧlu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
[CrossRef]

Hemmer, P. R.

Hood, C. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Imamoglu, A.

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

A. Imamoǧlu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
[CrossRef]

Katz, D. P.

Kimble, H. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Krainov, V. P.

N. B. Delone, V. P. Krainov, Fundamentals of Nonlinear Optics of Atomic Gases, 1st ed. (Wiley, New York, 1988), Chap. 3, p. 201.

Kumar, P.

Lange, W.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Marmet, L.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Poizat, J. P.

J. P. Poizat, P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Shahriar, M.

Stoicheff, B. P.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Tewari, S. P.

S. P. Tewari, G. S. Agarwal, Phys. Rev. Lett. 56, 1811 (1986).

Turchette, Q. A.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

J. P. Poizat, P. Grangier, Phys. Rev. Lett. 70, 271 (1993).
[CrossRef] [PubMed]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

S. P. Tewari, G. S. Agarwal, Phys. Rev. Lett. 56, 1811 (1986).

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

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993).
[CrossRef] [PubMed]

Other

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, San Diego, Calif., 1989), Chap. 7, p. 175.

N. B. Delone, V. P. Krainov, Fundamentals of Nonlinear Optics of Atomic Gases, 1st ed. (Wiley, New York, 1988), Chap. 3, p. 201.

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press., Berkeley, Calif., 1981), Appendix D, p. 640.

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Figures (2)

Fig. 1
Fig. 1

Conventional XPM scheme: ωa, ωb are the frequencies of the incident light fields. Δωa, Δωb are the frequency detunings from level |i〉 and |u〉, and Γi, Γu are the decay rates of states |i〉 and |u〉.

Fig. 2
Fig. 2

Four-level scheme for highly efficient XPM. ωa, ωb are the frequencies involved in the nonlinear process. Δωb is the frequency detuning from level |4〉 (Δωa = ω31ωa = 0). Γ3, Γ4 are the decay rates. Levels |2〉 and |3〉 are coherently coupled with Rabi frequency Ωc. The |1〉–|3〉 transition exhibits EIT. Inset, EIT scheme in the dressed-state basis.

Tables (2)

Tables Icon

Table 1 Values for Dissipative Susceptibility (Third Order for EIT Scheme and Linear for Three-Level Scheme), XPM Susceptibility, and the Ratio of XPM Phase Shift and Total Absorption for the Proposed EIT Scheme and the Three-Level System of Fig. 1

Tables Icon

Table 2 Required Detuning, Resulting Nonlinearity, and Pump Field Intensity for a 10° Conditional Phase Shift in a 1-cm-Long Na Cell

Equations (6)

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

b ˙ 1 = i 2 Ω 13 b 3 ,
b ˙ 2 = - i Δ ω 21 b 2 + i 2 Ω c b 3 + i 2 Ω 24 b 4 ,
b ˙ 3 = i 2 Ω 13 b 1 + i 2 Ω c b 2 - i ( Δ ω a - i 2 Γ 3 ) b 3 ,
b ˙ 4 = i 2 Ω 24 b 2 - i ( Δ ω b - i 2 Γ 4 ) b 4 .
Φ XPM = ( 3 π L / 2 λ n ) Re [ χ ( 3 ) ] E b 2
α = ( 8 π 2 / λ ) Im [ χ ( 3 ) ] E b 2 .

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