Abstract

We report a measurement of the 5P32 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to 1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to 0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3F=4 transition in Rb85 or the F=2F=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.

© 2007 Optical Society of America

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  1. D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
    [CrossRef]
  2. M. S. Safronova, C. J. Williams, and C. W. Clark, "Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium," Phys. Rev. A 69, 022509 (2004).
    [CrossRef]
  3. S. A. Blundell, W. R. Johnson, and J. Sapirstein, "Relativistic all-order calculations of energies and matrix elements in cesium," Phys. Rev. A 43, 3407-3418 (1991).
    [CrossRef] [PubMed]
  4. V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
    [CrossRef]
  5. C. W. Oates, K. R. Vogel, and J. L. Hall, "High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p 2P3/2 lifetime discrepancy," Phys. Rev. Lett. 76, 2866-2869 (1996).
    [CrossRef] [PubMed]
  6. J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
    [CrossRef]
  7. W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, "Radiative lifetime of the 2P state of lithium," Phys. Rev. A 54, R5-R8 (1996).
    [CrossRef] [PubMed]
  8. U. Volz and H. Schmoranzer, "Precision lifetime measurements on alkali atoms and on helium by beam-gas-laser spectroscopy," Phys. Scr., T T65, 48-56 (1996).
    [CrossRef]
  9. L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
    [CrossRef] [PubMed]
  10. C. K. N. Patel and R. E. Slusher, "Photon echoes in gases," Phys. Rev. Lett. 20, 1087-1089 (1968).
    [CrossRef]
  11. A. Flusber, T. Mossberg, and S. R. Hartman, "Excited-state photon-echo relaxation in Na vapor," Opt. Commun. 24, 207-210 (1978).
    [CrossRef]
  12. R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
    [CrossRef]
  13. Y. C. Chen, K. Chiang, and S. R. Hartmann, "Spectroscopic and relaxation character of the 3P4-3H4 transition in LaF3:Pr3+ measured by photon echoes," Phys. Rev. B 21, 40-47 (1980).
    [CrossRef]
  14. R. M. Macfarlane and R. M. Shelby, "Sub-kilohertz optical linewidths of the 7F0<->5D0 transition in Y2O3:Eu3+," Opt. Commun. 39, 169-171 (1981).
    [CrossRef]
  15. P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
    [CrossRef] [PubMed]
  16. E. L. Hahn, "Spin echoes," Phys. Rev. 80, 580-594 (1950).
    [CrossRef]
  17. I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391-406 (1965).
    [CrossRef]
  18. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).
  19. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley-Interscience, 1997).
    [CrossRef]
  20. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1998).
  21. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
    [CrossRef]
  22. A. E. Siegman, Lasers (University Science Books, 1986).
  23. A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
    [CrossRef]
  24. A. Gallagher and E. L. Lewis, "Resonance broadening of Hanle-effect signals in rubidium," Phys. Rev. A 10, 231-241 (1974).
    [CrossRef]
  25. N. Allard and J. Kielkopf, "The effect of neutral nonresonant collisions on atomic spectral lines," Rev. Mod. Phys. 54, 1103-1182 (1982).
    [CrossRef]

2006 (1)

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

2004 (1)

M. S. Safronova, C. J. Williams, and C. W. Clark, "Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium," Phys. Rev. A 69, 022509 (2004).
[CrossRef]

1998 (2)

J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
[CrossRef]

A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
[CrossRef]

1996 (3)

W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, "Radiative lifetime of the 2P state of lithium," Phys. Rev. A 54, R5-R8 (1996).
[CrossRef] [PubMed]

U. Volz and H. Schmoranzer, "Precision lifetime measurements on alkali atoms and on helium by beam-gas-laser spectroscopy," Phys. Scr., T T65, 48-56 (1996).
[CrossRef]

C. W. Oates, K. R. Vogel, and J. L. Hall, "High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p 2P3/2 lifetime discrepancy," Phys. Rev. Lett. 76, 2866-2869 (1996).
[CrossRef] [PubMed]

1994 (1)

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

1991 (1)

S. A. Blundell, W. R. Johnson, and J. Sapirstein, "Relativistic all-order calculations of energies and matrix elements in cesium," Phys. Rev. A 43, 3407-3418 (1991).
[CrossRef] [PubMed]

1990 (1)

R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
[CrossRef]

1989 (1)

V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
[CrossRef]

1988 (1)

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

1982 (1)

N. Allard and J. Kielkopf, "The effect of neutral nonresonant collisions on atomic spectral lines," Rev. Mod. Phys. 54, 1103-1182 (1982).
[CrossRef]

1981 (1)

R. M. Macfarlane and R. M. Shelby, "Sub-kilohertz optical linewidths of the 7F0<->5D0 transition in Y2O3:Eu3+," Opt. Commun. 39, 169-171 (1981).
[CrossRef]

1980 (1)

Y. C. Chen, K. Chiang, and S. R. Hartmann, "Spectroscopic and relaxation character of the 3P4-3H4 transition in LaF3:Pr3+ measured by photon echoes," Phys. Rev. B 21, 40-47 (1980).
[CrossRef]

1978 (1)

A. Flusber, T. Mossberg, and S. R. Hartman, "Excited-state photon-echo relaxation in Na vapor," Opt. Commun. 24, 207-210 (1978).
[CrossRef]

1974 (1)

A. Gallagher and E. L. Lewis, "Resonance broadening of Hanle-effect signals in rubidium," Phys. Rev. A 10, 231-241 (1974).
[CrossRef]

1969 (1)

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

1968 (1)

C. K. N. Patel and R. E. Slusher, "Photon echoes in gases," Phys. Rev. Lett. 20, 1087-1089 (1968).
[CrossRef]

1965 (1)

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391-406 (1965).
[CrossRef]

1950 (1)

E. L. Hahn, "Spin echoes," Phys. Rev. 80, 580-594 (1950).
[CrossRef]

Abella, I. D.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391-406 (1965).
[CrossRef]

Abraham, E. R. I.

W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, "Radiative lifetime of the 2P state of lithium," Phys. Rev. A 54, R5-R8 (1996).
[CrossRef] [PubMed]

Allard, N.

N. Allard and J. Kielkopf, "The effect of neutral nonresonant collisions on atomic spectral lines," Rev. Mod. Phys. 54, 1103-1182 (1982).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).

Becker, P. C.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Blinov, B. B.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Blundell, S. A.

S. A. Blundell, W. R. Johnson, and J. Sapirstein, "Relativistic all-order calculations of energies and matrix elements in cesium," Phys. Rev. A 43, 3407-3418 (1991).
[CrossRef] [PubMed]

Brito Cruz, C. H.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Cahn, S. B.

A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
[CrossRef]

Chen, Y. C.

Y. C. Chen, K. Chiang, and S. R. Hartmann, "Spectroscopic and relaxation character of the 3P4-3H4 transition in LaF3:Pr3+ measured by photon echoes," Phys. Rev. B 21, 40-47 (1980).
[CrossRef]

Chiang, K.

Y. C. Chen, K. Chiang, and S. R. Hartmann, "Spectroscopic and relaxation character of the 3P4-3H4 transition in LaF3:Pr3+ measured by photon echoes," Phys. Rev. B 21, 40-47 (1980).
[CrossRef]

Clark, C. W.

M. S. Safronova, C. J. Williams, and C. W. Clark, "Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium," Phys. Rev. A 69, 022509 (2004).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley-Interscience, 1997).
[CrossRef]

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1998).

Cunningham, J. E.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1998).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley-Interscience, 1997).
[CrossRef]

Dzuba, V. A.

V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
[CrossRef]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).

Feld, M. S.

R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
[CrossRef]

Flambaum, V. V.

V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
[CrossRef]

Flusber, A.

A. Flusber, T. Mossberg, and S. R. Hartman, "Excited-state photon-echo relaxation in Na vapor," Opt. Commun. 24, 207-210 (1978).
[CrossRef]

Forber, R. A.

R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
[CrossRef]

Fork, R. L.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Fragnito, H. L.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Gallagher, A.

A. Gallagher and E. L. Lewis, "Resonance broadening of Hanle-effect signals in rubidium," Phys. Rev. A 10, 231-241 (1974).
[CrossRef]

Gidley, D. W.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1998).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley-Interscience, 1997).
[CrossRef]

Hahn, E. L.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

E. L. Hahn, "Spin echoes," Phys. Rev. 80, 580-594 (1950).
[CrossRef]

Hall, J. L.

C. W. Oates, K. R. Vogel, and J. L. Hall, "High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p 2P3/2 lifetime discrepancy," Phys. Rev. Lett. 76, 2866-2869 (1996).
[CrossRef] [PubMed]

Hartman, S. R.

A. Flusber, T. Mossberg, and S. R. Hartman, "Excited-state photon-echo relaxation in Na vapor," Opt. Commun. 24, 207-210 (1978).
[CrossRef]

Hartmann, S. R.

Y. C. Chen, K. Chiang, and S. R. Hartmann, "Spectroscopic and relaxation character of the 3P4-3H4 transition in LaF3:Pr3+ measured by photon echoes," Phys. Rev. B 21, 40-47 (1980).
[CrossRef]

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391-406 (1965).
[CrossRef]

Henry, J. E.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Hill, W. T.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Hulet, R. G.

W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, "Radiative lifetime of the 2P state of lithium," Phys. Rev. A 54, R5-R8 (1996).
[CrossRef] [PubMed]

Johnson, W. R.

S. A. Blundell, W. R. Johnson, and J. Sapirstein, "Relativistic all-order calculations of energies and matrix elements in cesium," Phys. Rev. A 43, 3407-3418 (1991).
[CrossRef] [PubMed]

Kielkopf, J.

N. Allard and J. Kielkopf, "The effect of neutral nonresonant collisions on atomic spectral lines," Rev. Mod. Phys. 54, 1103-1182 (1982).
[CrossRef]

Kohn, R. N.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Krafmakher, A. Y.

V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
[CrossRef]

Kumarakrishnan, A.

A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
[CrossRef]

Kurnit, N. A.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391-406 (1965).
[CrossRef]

Leone, S. R.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Lewis, E. L.

A. Gallagher and E. L. Lewis, "Resonance broadening of Hanle-effect signals in rubidium," Phys. Rev. A 10, 231-241 (1974).
[CrossRef]

Macfarlane, R. M.

R. M. Macfarlane and R. M. Shelby, "Sub-kilohertz optical linewidths of the 7F0<->5D0 transition in Y2O3:Eu3+," Opt. Commun. 39, 169-171 (1981).
[CrossRef]

Madsen, M. J.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

McAlexander, W. I.

W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, "Radiative lifetime of the 2P state of lithium," Phys. Rev. A 54, R5-R8 (1996).
[CrossRef] [PubMed]

McCall, S. L.

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

Moehring, D. L.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Monroe, C.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Mossberg, T.

A. Flusber, T. Mossberg, and S. R. Hartman, "Excited-state photon-echo relaxation in Na vapor," Opt. Commun. 24, 207-210 (1978).
[CrossRef]

Oates, C. W.

C. W. Oates, K. R. Vogel, and J. L. Hall, "High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p 2P3/2 lifetime discrepancy," Phys. Rev. Lett. 76, 2866-2869 (1996).
[CrossRef] [PubMed]

Orozco, L. A.

J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
[CrossRef]

Patel, C. K. N.

C. K. N. Patel and R. E. Slusher, "Photon echoes in gases," Phys. Rev. Lett. 20, 1087-1089 (1968).
[CrossRef]

Price, S. D.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Safronova, M. S.

M. S. Safronova, C. J. Williams, and C. W. Clark, "Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium," Phys. Rev. A 69, 022509 (2004).
[CrossRef]

Sanderson, T. B.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Sapirstein, J.

S. A. Blundell, W. R. Johnson, and J. Sapirstein, "Relativistic all-order calculations of energies and matrix elements in cesium," Phys. Rev. A 43, 3407-3418 (1991).
[CrossRef] [PubMed]

Schmoranzer, H.

U. Volz and H. Schmoranzer, "Precision lifetime measurements on alkali atoms and on helium by beam-gas-laser spectroscopy," Phys. Scr., T T65, 48-56 (1996).
[CrossRef]

Shank, C. V.

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

Shelby, R. M.

R. M. Macfarlane and R. M. Shelby, "Sub-kilohertz optical linewidths of the 7F0<->5D0 transition in Y2O3:Eu3+," Opt. Commun. 39, 169-171 (1981).
[CrossRef]

Shim, U.

A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
[CrossRef]

Sibener, S. J.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Simsarian, J. E.

J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
[CrossRef]

Sleator, T.

A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
[CrossRef]

Slusher, R. E.

C. K. N. Patel and R. E. Slusher, "Photon echoes in gases," Phys. Rev. Lett. 20, 1087-1089 (1968).
[CrossRef]

Spinelli, L.

R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
[CrossRef]

Sprouse, G. D.

J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
[CrossRef]

Sushkov, O. P.

V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
[CrossRef]

Tanner, C. E.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Thomas, J. E.

R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
[CrossRef]

Vallery, R. S.

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

Vogel, K. R.

C. W. Oates, K. R. Vogel, and J. L. Hall, "High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p 2P3/2 lifetime discrepancy," Phys. Rev. Lett. 76, 2866-2869 (1996).
[CrossRef] [PubMed]

Volz, U.

U. Volz and H. Schmoranzer, "Precision lifetime measurements on alkali atoms and on helium by beam-gas-laser spectroscopy," Phys. Scr., T T65, 48-56 (1996).
[CrossRef]

Wieman, C. E.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Williams, C. J.

M. S. Safronova, C. J. Williams, and C. W. Clark, "Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium," Phys. Rev. A 69, 022509 (2004).
[CrossRef]

Young, L.

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Zhao, W. Z.

J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
[CrossRef]

Opt. Commun. (2)

A. Flusber, T. Mossberg, and S. R. Hartman, "Excited-state photon-echo relaxation in Na vapor," Opt. Commun. 24, 207-210 (1978).
[CrossRef]

R. M. Macfarlane and R. M. Shelby, "Sub-kilohertz optical linewidths of the 7F0<->5D0 transition in Y2O3:Eu3+," Opt. Commun. 39, 169-171 (1981).
[CrossRef]

Phys. Lett. A (1)

V. A. Dzuba, V. V. Flambaum, A. Y. Krafmakher, and O. P. Sushkov, "Summation of the high orders of perturbation theory in the correlation correction to the hyperfine structure and to the amplitudes of E1-transitions in the cesium atom," Phys. Lett. A 142, 373-377 (1989).
[CrossRef]

Phys. Rev. (3)

E. L. Hahn, "Spin echoes," Phys. Rev. 80, 580-594 (1950).
[CrossRef]

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, "Photon echoes," Phys. Rev. 141, 391-406 (1965).
[CrossRef]

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

Phys. Rev. A (8)

A. Kumarakrishnan, U. Shim, S. B. Cahn, and T. Sleator, "Ground-state grating echoes from Rb vapor at room temperature," Phys. Rev. A 58, 3868-3872 (1998).
[CrossRef]

A. Gallagher and E. L. Lewis, "Resonance broadening of Hanle-effect signals in rubidium," Phys. Rev. A 10, 231-241 (1974).
[CrossRef]

D. L. Moehring, B. B. Blinov, D. W. Gidley, R. N. Kohn, M. J. Madsen, T. B. Sanderson, R. S. Vallery, and C. Monroe, "Precision lifetime measurement of a single trapped ion with ultrafast laser pulses," Phys. Rev. A 73, 023413 (2006).
[CrossRef]

M. S. Safronova, C. J. Williams, and C. W. Clark, "Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium," Phys. Rev. A 69, 022509 (2004).
[CrossRef]

S. A. Blundell, W. R. Johnson, and J. Sapirstein, "Relativistic all-order calculations of energies and matrix elements in cesium," Phys. Rev. A 43, 3407-3418 (1991).
[CrossRef] [PubMed]

J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, "Lifetime measurements of the 7p levels of atomic francium," Phys. Rev. A 57, 2448-2458 (1998).
[CrossRef]

W. I. McAlexander, E. R. I. Abraham, and R. G. Hulet, "Radiative lifetime of the 2P state of lithium," Phys. Rev. A 54, R5-R8 (1996).
[CrossRef] [PubMed]

L. Young, W. T. Hill III, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, and S. R. Leone, "Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting," Phys. Rev. A 50, 2174-2181 (1994).
[CrossRef] [PubMed]

Phys. Rev. B (1)

Y. C. Chen, K. Chiang, and S. R. Hartmann, "Spectroscopic and relaxation character of the 3P4-3H4 transition in LaF3:Pr3+ measured by photon echoes," Phys. Rev. B 21, 40-47 (1980).
[CrossRef]

Phys. Rev. Lett. (4)

C. K. N. Patel and R. E. Slusher, "Photon echoes in gases," Phys. Rev. Lett. 20, 1087-1089 (1968).
[CrossRef]

C. W. Oates, K. R. Vogel, and J. L. Hall, "High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p 2P3/2 lifetime discrepancy," Phys. Rev. Lett. 76, 2866-2869 (1996).
[CrossRef] [PubMed]

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, "Femtosecond photon echoes from band-to-band transitions in GaAs," Phys. Rev. Lett. 61, 1647-1649 (1988).
[CrossRef] [PubMed]

R. A. Forber, L. Spinelli, J. E. Thomas, and M. S. Feld, "Observation of quantum diffractive velocity-changing collisions by use of two-level heavy optical radiators," Phys. Rev. Lett. 50, 331-335 (1990).
[CrossRef]

Phys. Scr., T (1)

U. Volz and H. Schmoranzer, "Precision lifetime measurements on alkali atoms and on helium by beam-gas-laser spectroscopy," Phys. Scr., T T65, 48-56 (1996).
[CrossRef]

Rev. Mod. Phys. (1)

N. Allard and J. Kielkopf, "The effect of neutral nonresonant collisions on atomic spectral lines," Rev. Mod. Phys. 54, 1103-1182 (1982).
[CrossRef]

Other (4)

A. E. Siegman, Lasers (University Science Books, 1986).

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley-Interscience, 1997).
[CrossRef]

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1998).

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Figures (13)

Fig. 1
Fig. 1

Bloch vector representation. (a) Macroscopic Bloch vector representing all atoms in the ground state. (b) Superposition state immediately after π 2 pulse. (c), (d) Bloch vector dephasing. (e) Inversion due to π pulse. (f) Bloch vector rephasing (photon echo).

Fig. 2
Fig. 2

Optical layout. 1 2 and 1 4 represent λ 2 and λ 4 wave plates, respectively.

Fig. 3
Fig. 3

Oscilloscope signal trace. (a) Signal run. (b) Background run (first pulse off).

Fig. 4
Fig. 4

Echo intensity fits. (a) Exponential decay of the echo intensity as a function of 2 T . (b) Natural logarithm of echo intensity as a function of 2 T with linear fit. The slope results in a lifetime measurement of τ = 25.25 ± 0.38 ns . (c) Residuals: difference between data and fit for (b).

Fig. 5
Fig. 5

Echo intensity dependence on (a) first pulse width, slope = 1.142 ± 3.862 ; (b) second pulse width, slope = 8.539 ± 26.999 ; (c) first pulse amplitude, slope = 1.164 ± 4.377 ; (d) second pulse amplitude, slope = 2.023 ± 6.148 ; (e) temperature, slope = 0.162 ± 0.334 ns ° C ; (f) magnetic field current, slope = 0.775 ± 1.209 ns A ; (g) beam diameter, slope = 0.00152 ± 0.00305 ns μ m .

Fig. 6
Fig. 6

Effective decay time due to transit time. Estimated correction to the decay time at the smallest beam size used is 0.03%, well below the sensitivity of the experiment. Range of beam radii used in the experiment is 500 to 1250 μ m .

Fig. 7
Fig. 7

Distribution of measurement points and Gaussian fit.

Fig. 8
Fig. 8

Echo intensity measured as a function of first pulse area (squares), while keeping the second pulse area fixed at signal maximum; echo intensity measured as a function of second pulse area (triangles), while keeping the first pulse area fixed at signal maximum.

Fig. 9
Fig. 9

Simulation of echo intensity as a function of pulse areas for temporally varying Gaussian pulses, including the effect of spontaneous emission and spatial intensity profile. These results correspond to case 3 in Appendix A. Ratio of the pulse areas that give maximum echo signals is θ 2 θ 1 = 1.44 ± 0.09 . Error in the measurement was computed from fit errors.

Fig. 10
Fig. 10

Square pulse sequence.

Fig. 11
Fig. 11

Simulation of echo intensity as a function of pulse areas for case 1. Ratio of the pulse areas that give maximum echo signals is θ 2 θ 1 = 1.89 ± 0.02 . Error in the measurement was computed from fit errors.

Fig. 12
Fig. 12

Gaussian pulse sequence.

Fig. 13
Fig. 13

Simulation of echo intensity as a function of pulse areas for case 2. Ratio of the pulse areas that give maximum echo signals is θ 2 θ 1 = 1.70 ± 0.06 . Error in the measurement was computed from fit errors.

Equations (28)

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I = I 0 exp [ 2 T τ ] .
I = ( π a u ) 4 ( 7 + 10 u T 2 a 2 ) 2 e 2 T τ .
I ( Δ t ) [ i = 1 N u i ( Δ t ) ] 2 + [ i = 1 N v i ( Δ t ) ] 2 + [ i = 1 N w i ( Δ t ) ] 2 ,
d = 2 g d e [ u cos ( ω L t ) v sin ( ω L t ) ] .
[ u ̇ ( t ) v ̇ ( t ) w ̇ ( t ) ] = [ 0 Δ 0 Δ 0 Ω 0 ( t ) 0 Ω 0 ( t ) 0 ] [ u ( t ) v ( t ) w ( t ) ] ,
Ω 0 ( t ) = 2 d E ( t ) .
[ u ( t ) v ( t ) w ( t ) ] = [ Ω 0 2 + Δ 2 cos Ω t Ω 2 Δ Ω sin Ω t Δ Ω 0 Ω 2 ( 1 cos Ω t ) Δ Ω sin Ω t cos Ω t Ω 0 Ω sin Ω t Δ Ω 0 Ω 2 ( 1 cos Ω t ) Ω 0 Ω sin Ω t Δ 2 + Ω 0 2 cos Ω t Ω 2 ] [ u 0 v 0 w 0 ] .
Ω ( Δ ) = Ω 0 2 + Δ 2 .
Δ ( V z ) = δ + V z λ L .
V 0 = 2 k B T M Rb .
Ω 0 ( r ) = Ω 0 e ( r r 0 ) 2 .
θ 1 = Ω 1 t 0 = π 2 ,
θ 2 = Ω 2 t 0 = π ,
F ( θ ) = A exp [ ( θ θ 0 ) 2 2 σ 2 ] + B θ + C ,
( θ θ 0 ) exp [ ( θ θ 0 ) 2 2 σ 2 ] = σ 2 B A .
θ max = θ 0 + σ 2 B A ,
( δ θ max ) 2 = ( δ θ 0 ) 2 + ( 2 σ B A δ σ ) 2 + ( σ 2 A δ B ) 2 + ( σ 2 B A 2 δ A ) 2 .
Ω 0 ( r , t ) = { Ω 1 exp [ ( t t 01 ) 2 2 σ 1 2 ] + Ω 2 exp [ ( t t 02 ) 2 2 σ 2 2 ] } exp [ ( r r 0 ) 2 ] .
t 1 = 2 2 ln ( 2 ) σ 1 ,
t 2 = 2 2 ln ( 2 ) σ 2 .
Ω 1 = π 2 1 2 σ 0 ,
Ω 2 = 2 Ω 1 ,
σ 0 = t 0 2 2 ln ( 2 ) .
θ 1 = 2 π Ω 1 σ 1 = σ 1 2 σ 0 π = t 1 2 t 0 π ,
θ 2 = 2 π Ω 2 σ 2 = σ 2 σ 0 π = t 1 t 0 π .
u ̇ ( t ) = u ( t ) τ 2 Δ v ( t ) ,
v ̇ ( t ) = Δ u ( t ) v ( t ) τ 2 + Ω 0 w ( t ) ,
w ̇ ( t ) = Ω 0 v ( t ) w ( t ) τ 1 + w eq τ 1 .

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