Abstract

Quantum interference in the rate of two-photon excitation of the 6S1/2 → 6P3/26D5/2 transition in atomic cesium is exploited to demonstrate phase-sensitive frequency demodulation for an optical interval of ± 12.5 THz. By thus using atoms as ultrafast nonlinear mixing elements, we suggest and analyze a new avenue for absolute comparisons of a dense set of frequencies over the range of 200–2000 nm.

© 1996 Optical Society of America

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References

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  1. L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
    [CrossRef]
  2. D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
    [CrossRef] [PubMed]
  3. M. W. Noel, C. R. Stroud, Phys. Rev. Lett. 75, 1252 (1995).
    [CrossRef] [PubMed]
  4. N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, “Quantum interference in two-photon excitation,” Phys. Rev. B (to be published).
  5. B. R. Morrow, Phys. Rev. 175, 1555 (1968).
    [CrossRef]
  6. N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
    [CrossRef]
  7. N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, Opt. Lett. 19, 1474 (1994).
    [CrossRef]
  8. K. Libbrecht, J. L. Hall, Rev. Sci. Instrum. 64, 2133 (1993).
    [CrossRef]
  9. In principle V and Λ two-photon transitions will also exhibit QI. We could likewise include atoms other than the alkalis.
  10. Our database of possible triangles was constructed from atomic energy levels for Li, Rb, and Cs Vols. I–III [C. E. Moore, Atomic Energy Levels, Nat. Bur. Stand. (U.S.) Circ. 467 (National Bureau of Standards, Washington, D.C., 1949)] and from data on the Internet at http://aeldata.phy.nist.gov/archive/el.html by NIST for Na and K.
  11. H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
    [CrossRef] [PubMed]
  12. H. R. Telle, D. Meschede, T. W. Hänsch, Opt. Lett. 15, 532 (1990).
    [CrossRef] [PubMed]
  13. D. Lee, N. C. Wong, Opt. Lett. 17, 13 (1992).
    [CrossRef] [PubMed]
  14. D. A. Van Baak, L. Hollberg, Opt. Lett. 19, 1586 (1994).
    [CrossRef] [PubMed]
  15. V. M. Klementyev, Yu. A. Matyugin, V. P. Chebotayev, Zh. Eksp. Teor. Fiz. Pis’ma Red. 24, 8 (1976); D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, H. P. Layer, Opt. Lett. 8, 136 (1983).
    [CrossRef] [PubMed]
  16. Details will appear on the Internet at http://www.cco.caltech.edu/~qoptics .
  17. D. J. E. Knight, Laser Phys. 4, 345 (1994).

1996 (1)

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

1995 (3)

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

M. W. Noel, C. R. Stroud, Phys. Rev. Lett. 75, 1252 (1995).
[CrossRef] [PubMed]

1994 (4)

D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

D. J. E. Knight, Laser Phys. 4, 345 (1994).

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef]

D. A. Van Baak, L. Hollberg, Opt. Lett. 19, 1586 (1994).
[CrossRef] [PubMed]

1993 (1)

K. Libbrecht, J. L. Hall, Rev. Sci. Instrum. 64, 2133 (1993).
[CrossRef]

1992 (1)

1990 (1)

1976 (1)

V. M. Klementyev, Yu. A. Matyugin, V. P. Chebotayev, Zh. Eksp. Teor. Fiz. Pis’ma Red. 24, 8 (1976); D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, H. P. Layer, Opt. Lett. 8, 136 (1983).
[CrossRef] [PubMed]

1968 (1)

B. R. Morrow, Phys. Rev. 175, 1555 (1968).
[CrossRef]

Bucksbaum, P. H.

D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

Chebotayev, V. P.

V. M. Klementyev, Yu. A. Matyugin, V. P. Chebotayev, Zh. Eksp. Teor. Fiz. Pis’ma Red. 24, 8 (1976); D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, H. P. Layer, Opt. Lett. 8, 136 (1983).
[CrossRef] [PubMed]

Edamatsu, K.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

Gordon, R. J.

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Hall, J. L.

K. Libbrecht, J. L. Hall, Rev. Sci. Instrum. 64, 2133 (1993).
[CrossRef]

Hänsch, T. W.

Helmcke, J.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

Hollberg, L.

Kimble, H. J.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, “Quantum interference in two-photon excitation,” Phys. Rev. B (to be published).

Kleman, V.

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Klementyev, V. M.

V. M. Klementyev, Yu. A. Matyugin, V. P. Chebotayev, Zh. Eksp. Teor. Fiz. Pis’ma Red. 24, 8 (1976); D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, H. P. Layer, Opt. Lett. 8, 136 (1983).
[CrossRef] [PubMed]

Knight, D. J. E.

D. J. E. Knight, Laser Phys. 4, 345 (1994).

Lee, D.

Li, X.

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Libbrecht, K.

K. Libbrecht, J. L. Hall, Rev. Sci. Instrum. 64, 2133 (1993).
[CrossRef]

Lipphardt, B.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

Lu, S. P.

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Matyugin, Yu. A.

V. M. Klementyev, Yu. A. Matyugin, V. P. Chebotayev, Zh. Eksp. Teor. Fiz. Pis’ma Red. 24, 8 (1976); D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, H. P. Layer, Opt. Lett. 8, 136 (1983).
[CrossRef] [PubMed]

Meschede, D.

Morrow, B. R.

B. R. Morrow, Phys. Rev. 175, 1555 (1968).
[CrossRef]

Muller, H. Q.

D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

Noel, M. W.

M. W. Noel, C. R. Stroud, Phys. Rev. Lett. 75, 1252 (1995).
[CrossRef] [PubMed]

Parkins, A. S.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

Ph. Georgiades, N.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, “Quantum interference in two-photon excitation,” Phys. Rev. B (to be published).

Polzik, E. S.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, “Quantum interference in two-photon excitation,” Phys. Rev. B (to be published).

Riehle, F.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

Schnatz, H.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

Schumacher, D. W.

D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

Stroud, C. R.

M. W. Noel, C. R. Stroud, Phys. Rev. Lett. 75, 1252 (1995).
[CrossRef] [PubMed]

Telle, H. R.

Trentelman, K.

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Van Baak, D. A.

Weihe, F.

D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

Wong, N. C.

Zhu, L.

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Zinner, G.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

Laser Phys. (1)

D. J. E. Knight, Laser Phys. 4, 345 (1994).

Opt. Lett. (4)

Phys. Rev. (1)

B. R. Morrow, Phys. Rev. 175, 1555 (1968).
[CrossRef]

Phys. Rev. Lett. (4)

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, H. J. Kimble, A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

D. W. Schumacher, F. Weihe, H. Q. Muller, P. H. Bucksbaum, Phys. Rev. Lett. 73, 1344 (1994).
[CrossRef] [PubMed]

M. W. Noel, C. R. Stroud, Phys. Rev. Lett. 75, 1252 (1995).
[CrossRef] [PubMed]

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, G. Zinner, Phys. Rev. Lett. 76, 18 (1996).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

K. Libbrecht, J. L. Hall, Rev. Sci. Instrum. 64, 2133 (1993).
[CrossRef]

Science (1)

L. Zhu, V. Kleman, X. Li, S. P. Lu, K. Trentelman, R. J. Gordon, Science 270, 77 (1995).
[CrossRef]

Zh. Eksp. Teor. Fiz. Pis’ma Red. (1)

V. M. Klementyev, Yu. A. Matyugin, V. P. Chebotayev, Zh. Eksp. Teor. Fiz. Pis’ma Red. 24, 8 (1976); D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, H. P. Layer, Opt. Lett. 8, 136 (1983).
[CrossRef] [PubMed]

Other (4)

Details will appear on the Internet at http://www.cco.caltech.edu/~qoptics .

N. Ph. Georgiades, E. S. Polzik, H. J. Kimble, “Quantum interference in two-photon excitation,” Phys. Rev. B (to be published).

In principle V and Λ two-photon transitions will also exhibit QI. We could likewise include atoms other than the alkalis.

Our database of possible triangles was constructed from atomic energy levels for Li, Rb, and Cs Vols. I–III [C. E. Moore, Atomic Energy Levels, Nat. Bur. Stand. (U.S.) Circ. 467 (National Bureau of Standards, Washington, D.C., 1949)] and from data on the Internet at http://aeldata.phy.nist.gov/archive/el.html by NIST for Na and K.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup: PZT, piezoelectric transducer; OPO, optical parametric oscillator; MOT, magneto-optical trap.

Fig. 2
Fig. 2

Fluorescence from the 3 → 2 transition at as a function of time for illumination of the MOT optical trap with three fields at λa, b, c = (852, 917, 884) nm. Here the relative phase ϕ(t) = 2ϕ884(t) − ϕ852ϕ917, where ϕ884(t) = ωmt and ωm/2π = 11 Hz. The solid curve is a fit of a constant plus a sinusoidal variation with visibility ν ≈ 0.3.

Fig. 3
Fig. 3

Nonlinear mixer characteristics for the sideband-to-carrier separation Δν versus carrier wavelength λc from our database of 6800 transitions in the alkali elements. The circled point corresponds to the current experiment, for which λc = 884 nm and Δν = 12.5 THz.

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