Abstract

We use a 1GHz femtosecond laser as a tool to perform coherent spectroscopy in an atomic vapor. The action of the ultrashort pulse train over the various velocity groups or over a selective group of rubidium atoms is probed by a diode laser using velocity-selective or repetition rate spectroscopies. In particular, we show that the 1GHz frequency separation of the modes in the frequency comb allows distinguishing of the different hyperfine levels within the Doppler broadened profile. The data are in good agreement with numerical and analytical results.

© 2011 Optical Society of America

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  1. Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–236 (2002).
    [CrossRef] [PubMed]
  2. Y. V. Baklanov and V. P. Chebotayev, “Narrow resonances of two-photon absorption of super-narrow pulses in a gas,” Appl. Phys. 12, 97–99 (1977).
    [CrossRef]
  3. R. J. Teets and T. W. Hansch, “Coherent two-photon excitation by multiple light pulses,” Phys. Rev. Lett. 38, 760–764(1977).
    [CrossRef]
  4. A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29, 1081–1083 (2004).
    [CrossRef] [PubMed]
  5. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
    [CrossRef] [PubMed]
  6. W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
    [CrossRef] [PubMed]
  7. M. C. Stowe, A. Pe’er, and J. Ye, “Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb,” Phys. Rev. Lett. 100, 203001 (2008).
    [CrossRef] [PubMed]
  8. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb Technology: Principle, Operation and Application (Springer, 2005).
    [CrossRef]
  9. A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
    [CrossRef] [PubMed]
  10. M. Maric, J. J. McFerran, and A. N. Luiten, “Frequency-comb spectroscopy of the D1 line in laser-cooled rubidium,” Phys. Rev. A 77, 032502 (2008).
    [CrossRef]
  11. J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
    [CrossRef]
  12. D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
    [CrossRef] [PubMed]
  13. T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
    [CrossRef]
  14. L. Arissian and J.-C. Diels, “Repetition rate spectroscopy of the dark line resonance in rubidium,” Opt. Commun. 264, 169–173(2006).
    [CrossRef]
  15. M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
    [CrossRef]
  16. D. A. Steck, “Rubidium 85 D line data,” http://steck.us/alkalidata.
  17. M. P. Moreno and S. S. Vianna, “Coherence induced by a train of ultrashort pulses in a Λ-type system,” J. Opt. Soc. Am. B 28, 1124–1129 (2011).
    [CrossRef]

2011 (1)

2010 (2)

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

2008 (2)

M. C. Stowe, A. Pe’er, and J. Ye, “Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb,” Phys. Rev. Lett. 100, 203001 (2008).
[CrossRef] [PubMed]

M. Maric, J. J. McFerran, and A. N. Luiten, “Frequency-comb spectroscopy of the D1 line in laser-cooled rubidium,” Phys. Rev. A 77, 032502 (2008).
[CrossRef]

2007 (1)

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

2006 (2)

L. Arissian and J.-C. Diels, “Repetition rate spectroscopy of the dark line resonance in rubidium,” Opt. Commun. 264, 169–173(2006).
[CrossRef]

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

2005 (1)

D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
[CrossRef] [PubMed]

2004 (2)

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29, 1081–1083 (2004).
[CrossRef] [PubMed]

2002 (1)

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–236 (2002).
[CrossRef] [PubMed]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

1977 (2)

Y. V. Baklanov and V. P. Chebotayev, “Narrow resonances of two-photon absorption of super-narrow pulses in a gas,” Appl. Phys. 12, 97–99 (1977).
[CrossRef]

R. J. Teets and T. W. Hansch, “Coherent two-photon excitation by multiple light pulses,” Phys. Rev. Lett. 38, 760–764(1977).
[CrossRef]

Acioli, L. H.

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

Arissian, L.

L. Arissian and J.-C. Diels, “Repetition rate spectroscopy of the dark line resonance in rubidium,” Opt. Commun. 264, 169–173(2006).
[CrossRef]

Aumiler, D.

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
[CrossRef] [PubMed]

Baklanov, Y. V.

Y. V. Baklanov and V. P. Chebotayev, “Narrow resonances of two-photon absorption of super-narrow pulses in a gas,” Appl. Phys. 12, 97–99 (1977).
[CrossRef]

Ban, T.

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
[CrossRef] [PubMed]

Bartels, A.

Bergquistk, J. C.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Bosco, C. A. C.

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

Chebotayev, V. P.

Y. V. Baklanov and V. P. Chebotayev, “Narrow resonances of two-photon absorption of super-narrow pulses in a gas,” Appl. Phys. 12, 97–99 (1977).
[CrossRef]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb Technology: Principle, Operation and Application (Springer, 2005).
[CrossRef]

Delaney, M. J.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Diddams, S. A.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29, 1081–1083 (2004).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Diels, J.-C.

L. Arissian and J.-C. Diels, “Repetition rate spectroscopy of the dark line resonance in rubidium,” Opt. Commun. 264, 169–173(2006).
[CrossRef]

Donley, E. A.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Felinto, D.

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

Fortier, T. M.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Gerginov, V.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Hansch, T. W.

R. J. Teets and T. W. Hansch, “Coherent two-photon excitation by multiple light pulses,” Phys. Rev. Lett. 38, 760–764(1977).
[CrossRef]

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–236 (2002).
[CrossRef] [PubMed]

Heavner, T. P.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Hollberg, L.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29, 1081–1083 (2004).
[CrossRef] [PubMed]

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–236 (2002).
[CrossRef] [PubMed]

Itano, W. M.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Jefferts, S. R.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Kim, K.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Lawall, J. R.

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

Levix, F.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Luiten, A. N.

M. Maric, J. J. McFerran, and A. N. Luiten, “Frequency-comb spectroscopy of the D1 line in laser-cooled rubidium,” Phys. Rev. A 77, 032502 (2008).
[CrossRef]

Marian, A.

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

Maric, M.

M. Maric, J. J. McFerran, and A. N. Luiten, “Frequency-comb spectroscopy of the D1 line in laser-cooled rubidium,” Phys. Rev. A 77, 032502 (2008).
[CrossRef]

Mbele, V.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

McFerran, J. J.

M. Maric, J. J. McFerran, and A. N. Luiten, “Frequency-comb spectroscopy of the D1 line in laser-cooled rubidium,” Phys. Rev. A 77, 032502 (2008).
[CrossRef]

Moreno, M. P.

Oates, C. W.

Oskay, W. H.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Parker, T. E.

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

Pe’er, A.

M. C. Stowe, A. Pe’er, and J. Ye, “Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb,” Phys. Rev. Lett. 100, 203001 (2008).
[CrossRef] [PubMed]

Pichler, G.

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
[CrossRef] [PubMed]

Polo, M.

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Skenderovic, H.

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
[CrossRef] [PubMed]

Stalnaker, J. E.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

Steck, D. A.

D. A. Steck, “Rubidium 85 D line data,” http://steck.us/alkalidata.

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Stowe, M. C.

M. C. Stowe, A. Pe’er, and J. Ye, “Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb,” Phys. Rev. Lett. 100, 203001 (2008).
[CrossRef] [PubMed]

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

Tanner, C. E.

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

Teets, R. J.

R. J. Teets and T. W. Hansch, “Coherent two-photon excitation by multiple light pulses,” Phys. Rev. Lett. 38, 760–764(1977).
[CrossRef]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–236 (2002).
[CrossRef] [PubMed]

Vdovic, S.

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

Vianna, S. S.

M. P. Moreno and S. S. Vianna, “Coherence induced by a train of ultrashort pulses in a Λ-type system,” J. Opt. Soc. Am. B 28, 1124–1129 (2011).
[CrossRef]

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

Vujicic, N.

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Ye, J.

M. C. Stowe, A. Pe’er, and J. Ye, “Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb,” Phys. Rev. Lett. 100, 203001 (2008).
[CrossRef] [PubMed]

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb Technology: Principle, Operation and Application (Springer, 2005).
[CrossRef]

Appl. Phys. (1)

Y. V. Baklanov and V. P. Chebotayev, “Narrow resonances of two-photon absorption of super-narrow pulses in a gas,” Appl. Phys. 12, 97–99 (1977).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B At. Mol. Opt. Phys. (1)

M. Polo, C. A. C. Bosco, L. H. Acioli, D. Felinto, and S. S. Vianna, “Coupling between cw lasers and a frequency comb in dense atomic samples,” J. Phys. B At. Mol. Opt. Phys. 43, 055001(2010).
[CrossRef]

Nature (1)

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–236 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

L. Arissian and J.-C. Diels, “Repetition rate spectroscopy of the dark line resonance in rubidium,” Opt. Commun. 264, 169–173(2006).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

T. Ban, D. Aumiler, H. Skenderović, S. Vdović, N. Vujičić, and G. Pichler, “Cancellation of the coherent accumulation in rubidium atoms excited by a train of femtosecond pulses,” Phys. Rev. A 76, 043410 (2007).
[CrossRef]

M. Maric, J. J. McFerran, and A. N. Luiten, “Frequency-comb spectroscopy of the D1 line in laser-cooled rubidium,” Phys. Rev. A 77, 032502 (2008).
[CrossRef]

J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
[CrossRef]

Phys. Rev. Lett. (4)

D. Aumiler, T. Ban, H. Skenderović, and G. Pichler, “Velocity selective optical pumping of Rb hyperfine lines induced by a train of femtosecond pulses,” Phys. Rev. Lett. 95, 233001(2005).
[CrossRef] [PubMed]

R. J. Teets and T. W. Hansch, “Coherent two-photon excitation by multiple light pulses,” Phys. Rev. Lett. 38, 760–764(1977).
[CrossRef]

W. H. Oskay, S. A. Diddams, E. A. Donley, T. M. Fortier, T. P. Heavner, L. Hollberg, W. M. Itano, S. R. Jefferts, M. J. Delaney, K. Kim, F. Levix, T. E. Parker, and J. C. Bergquistk, “Single-atom optical clock with high accuracy,” Phys. Rev. Lett. 97, 020801 (2006).
[CrossRef] [PubMed]

M. C. Stowe, A. Pe’er, and J. Ye, “Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb,” Phys. Rev. Lett. 100, 203001 (2008).
[CrossRef] [PubMed]

Science (2)

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Other (2)

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb Technology: Principle, Operation and Application (Springer, 2005).
[CrossRef]

D. A. Steck, “Rubidium 85 D line data,” http://steck.us/alkalidata.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: dotted and solid lines depict electrical signal and light paths. FP, SA, Ch, and PD indicate, respectively, the Fabry–Perot cavity, saturated absorption setup, chopper, and photodetector.

Fig. 2
Fig. 2

Probe beam transmission variation, Δ T (middle curve), as a function of the diode frequency for the four Doppler profiles of the D 2 line. The saturated absorption signal (upper curve) and the output of the Fabry–Perot cavity (lower curve) are also detected simultaneously.

Fig. 3
Fig. 3

(a) Probe-beam transmission variation, Δ T , as a function of the diode frequency for the 1 GHz laser at the Rb 85 D 1 line and the diode laser at the Rb 85 D 2 line. Inset, position (see arrow) inside the Doppler profile, of the two modes of the frequency comb that drive the transitions. (b) Energy levels of Rb 85 involved in the experiment. (c) Variation of the state | a population for the experimental situation defined in (a): analytical result obtained from Eq. (1) (solid curve) and direct numerical integration of the Bloch equations (filled circles). (d) Frequency domain picture of the modes of the 1 GHz fs laser and the energy levels of one atom at a given velocity.

Fig. 4
Fig. 4

Schematic representation of the three-level lambda system, where ω m is one mode of the frequency comb.

Fig. 5
Fig. 5

Direct measurement of the probe beam transmission, T, as a function of the repetition rate variation, Δ f R , for the diode laser at the Rb 85 D 2 line and the 1 GHz fs laser at the Rb 85 D 1 line. The set of peaks separated by the repetition rate of 1 GHz is associated with the same transitions induced by different modes of the frequency comb.

Equations (1)

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ρ a a = ρ a a ( 0 ) × [ 1 + 2 Ω a c 2 ( γ / Γ ) γ 2 + 4 ( Ω a c 2 + δ c a 2 ) ] 1 + ρ a a ( 0 ) + ρ b b ( 0 ) × [ 1 + γ 2 + 4 ( Ω b c 2 + δ c b 2 ) 2 Ω b c 2 ( γ / Γ ) ] 1 ,

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