Abstract

We have investigated modulation transfer spectroscopy of D2 transitions of 7Li atoms in a vapor cell. The role of the intensity of the probe beam in the spectrum is important, we have seen unique characteristics of the signal in the crossover peak. In order to find the best signal for laser locking, the slope and frequency offset of the zero-crossing signal are determined. The dependence of the modulation transfer spectra on polarizations of pump and probe beam is demonstrated. The residual amplitude modulation in the system is also considered, and the distortion of the spectra due to the modulation is analyzed. It was found that the crossover peak is more suitable for frequency stabilization due to its better residual amplitude modulation compensation.

© 2016 Optical Society of America

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References

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  1. J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett. 7, 537 (1982).
    [Crossref] [PubMed]
  2. M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas. 44, 155 (1995).
    [Crossref]
  3. E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91 (1995).
    [Crossref]
  4. F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
    [Crossref]
  5. J. Zhang, D. Wei, C. Xie, and K. Peng, “Characteristics of absorption and dispersion for rubidium D2 lines with the modulation transfer spectrum,” Opt. Express 11, 1338 (2003).
    [Crossref] [PubMed]
  6. L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
    [Crossref]
  7. H. Noh, S. E. Park, L. Z. Li, J. Park, and C. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express 19, 23444 (2011).
    [Crossref] [PubMed]
  8. V. Negnevitsky and L. D. Turner, “Wideband laser locking to an atomic reference with modulation transfer spectroscopy,” Opt. Express 21, 3103 (2013).
    [Crossref] [PubMed]
  9. M. Ducloy and D. Bloch, “Polarization properties of phase-conjugate mirrors: angular dependence and disorienting collision effects in resonant backward four-wave mixing for Doppler-broadened degenerate transitions,” Phys. Rev. A 30, 3107 (1984).
    [Crossref]
  10. M. A. Hohensee and H. Müller, “Precision tests of general relativity with matter waves,” J. Chem. Phys. 58, 2021 (2011).
  11. A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
    [Crossref]
  12. P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
    [Crossref]
  13. J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
    [Crossref]
  14. A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
    [Crossref]
  15. O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
    [Crossref]
  16. S. E. Park and H. R. Noh, “Modulation transfer spectroscopy mediated by spontaneous emission,” Opt. Express 21, 14066 (2013).
    [Crossref] [PubMed]
  17. I. E. Olivares, A. E. Duarte, T. Lokajczyk, A. Dinklage, and F. J. Duarte, “Doppler-free spectroscopy and collisional studies with tunable diode lasers of lithium isotopes in a heat-pipe oven,” J. Opt. Soc. Am. B 15, 1932–1939 (1998).
    [Crossref]
  18. D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19, 105601 (2008).
    [Crossref]
  19. L. S. Ma and J. L. Hall, Optical heterodyne spectroscopy enhanced by an external optical cavity - toward improved working standards, IEEE J. Quantum Electron.QE 262006–2010(1990).
    [Crossref]
  20. M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. France 43, 57 (1982).
    [Crossref]
  21. L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B 45, 065002 (2012).
    [Crossref]
  22. Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
    [Crossref]
  23. E. A. Whittaker, M. Gehrtz, and G. C. Bjorklund, “Residual amplitude modulation in laser electro-optic phase modulation,” J. Opt. Soc. Am. B 2, 1320 (1985).
    [Crossref]
  24. E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69 (2008).
    [Crossref]
  25. E. Jaatinen and J. M. Chartier, “Possible influence of residual amplitude modulation when using modulation transfer with iodine transitions at 543 nm,” Metrologia. 35, 75 (1998).
    [Crossref]
  26. E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that uses electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
    [Crossref]
  27. E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69C74 (2008).
    [Crossref]
  28. J. F. Eble and F. Shmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41S0 to 41P1 transition,” Appl. Phys. B 88, 563C568 (2007).
    [Crossref]

2014 (3)

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

2013 (3)

2012 (1)

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B 45, 065002 (2012).
[Crossref]

2011 (3)

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

H. Noh, S. E. Park, L. Z. Li, J. Park, and C. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express 19, 23444 (2011).
[Crossref] [PubMed]

M. A. Hohensee and H. Müller, “Precision tests of general relativity with matter waves,” J. Chem. Phys. 58, 2021 (2011).

2009 (1)

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that uses electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
[Crossref]

2008 (3)

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69C74 (2008).
[Crossref]

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69 (2008).
[Crossref]

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

2007 (1)

J. F. Eble and F. Shmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41S0 to 41P1 transition,” Appl. Phys. B 88, 563C568 (2007).
[Crossref]

2003 (1)

2001 (1)

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
[Crossref]

1998 (2)

I. E. Olivares, A. E. Duarte, T. Lokajczyk, A. Dinklage, and F. J. Duarte, “Doppler-free spectroscopy and collisional studies with tunable diode lasers of lithium isotopes in a heat-pipe oven,” J. Opt. Soc. Am. B 15, 1932–1939 (1998).
[Crossref]

E. Jaatinen and J. M. Chartier, “Possible influence of residual amplitude modulation when using modulation transfer with iodine transitions at 543 nm,” Metrologia. 35, 75 (1998).
[Crossref]

1995 (2)

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas. 44, 155 (1995).
[Crossref]

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91 (1995).
[Crossref]

1994 (1)

O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
[Crossref]

1991 (1)

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

1990 (1)

L. S. Ma and J. L. Hall, Optical heterodyne spectroscopy enhanced by an external optical cavity - toward improved working standards, IEEE J. Quantum Electron.QE 262006–2010(1990).
[Crossref]

1985 (1)

1984 (1)

M. Ducloy and D. Bloch, “Polarization properties of phase-conjugate mirrors: angular dependence and disorienting collision effects in resonant backward four-wave mixing for Doppler-broadened degenerate transitions,” Phys. Rev. A 30, 3107 (1984).
[Crossref]

1982 (2)

J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett. 7, 537 (1982).
[Crossref] [PubMed]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. France 43, 57 (1982).
[Crossref]

Back, J.

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that uses electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
[Crossref]

Bava, E.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
[Crossref]

Bertinetto, F.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
[Crossref]

Bjorklund, G. C.

Bloch, D.

M. Ducloy and D. Bloch, “Polarization properties of phase-conjugate mirrors: angular dependence and disorienting collision effects in resonant backward four-wave mixing for Doppler-broadened degenerate transitions,” Phys. Rev. A 30, 3107 (1984).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. France 43, 57 (1982).
[Crossref]

Burchianti, A.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Chartier, J. M.

E. Jaatinen and J. M. Chartier, “Possible influence of residual amplitude modulation when using modulation transfer with iodine transitions at 543 nm,” Metrologia. 35, 75 (1998).
[Crossref]

Chevy, F.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Cho, C.

Cho, C. H.

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

Cordiale, P.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
[Crossref]

Cornish, S. L.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

De Pas, M.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Delehaye, M.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Dieckmann, K.

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

Dinklage, A.

Duarte, A. E.

Duarte, F. J.

Ducloy, M.

M. Ducloy and D. Bloch, “Polarization properties of phase-conjugate mirrors: angular dependence and disorienting collision effects in resonant backward four-wave mixing for Doppler-broadened degenerate transitions,” Phys. Rev. A 30, 3107 (1984).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. France 43, 57 (1982).
[Crossref]

Eble, J. F.

J. F. Eble and F. Shmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41S0 to 41P1 transition,” Appl. Phys. B 88, 563C568 (2007).
[Crossref]

Eickhoff, M. L.

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas. 44, 155 (1995).
[Crossref]

Ferrier-Barbut, I.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Galzerano, G.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
[Crossref]

Gan, H. C. J.

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

Gehrtz, M.

Goldwin, J.

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B 45, 065002 (2012).
[Crossref]

Grier, A. T.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Gross, C.

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

Hall, J. L.

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas. 44, 155 (1995).
[Crossref]

L. S. Ma and J. L. Hall, Optical heterodyne spectroscopy enhanced by an external optical cavity - toward improved working standards, IEEE J. Quantum Electron.QE 262006–2010(1990).
[Crossref]

Hamilton, P.

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

Hohensee, M. A.

M. A. Hohensee and H. Müller, “Precision tests of general relativity with matter waves,” J. Chem. Phys. 58, 2021 (2011).

Hopper, D. J.

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that uses electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
[Crossref]

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69 (2008).
[Crossref]

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69C74 (2008).
[Crossref]

Inguscio, M.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Jaatinen, E.

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that uses electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
[Crossref]

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69 (2008).
[Crossref]

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69C74 (2008).
[Crossref]

E. Jaatinen and J. M. Chartier, “Possible influence of residual amplitude modulation when using modulation transfer with iodine transitions at 543 nm,” Metrologia. 35, 75 (1998).
[Crossref]

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91 (1995).
[Crossref]

Joshi, T.

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

Khaykovich, L.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Kim, G.

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

King, S. A.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

Knaak, K.-M.

O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
[Crossref]

Li, K.

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

Li, L. Z.

H. Noh, S. E. Park, L. Z. Li, J. Park, and C. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express 19, 23444 (2011).
[Crossref] [PubMed]

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

Li, W.

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

Lin, Z.

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

Lokajczyk, T.

Ma, L. S.

L. S. Ma and J. L. Hall, Optical heterodyne spectroscopy enhanced by an external optical cavity - toward improved working standards, IEEE J. Quantum Electron.QE 262006–2010(1990).
[Crossref]

McCarron, D. J.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

Meschede, D.

O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
[Crossref]

Mudarikwa, L.

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B 45, 065002 (2012).
[Crossref]

Mukherjee, B.

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

Müller, H.

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

M. A. Hohensee and H. Müller, “Precision tests of general relativity with matter waves,” J. Chem. Phys. 58, 2021 (2011).

Negnevitsky, V.

Noh, H.

Noh, H. R.

S. E. Park and H. R. Noh, “Modulation transfer spectroscopy mediated by spontaneous emission,” Opt. Express 21, 14066 (2013).
[Crossref] [PubMed]

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

Olivares, I. E.

Pace, E.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Pahwa, K.

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B 45, 065002 (2012).
[Crossref]

Park, J.

Park, J. D.

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

Park, S. E.

Peng, K.

Rem, B. S.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Roati, G.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Salomon, C.

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

Schmidt, O.

O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
[Crossref]

Sebastian, J.

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

Seman, J. A.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Shimizu, F.

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

Shimizu, K.

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

Shirley, J. H.

Shmidt-Kaler, F.

J. F. Eble and F. Shmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41S0 to 41P1 transition,” Appl. Phys. B 88, 563C568 (2007).
[Crossref]

Takuma, H.

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

Tiarks, D.

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

Turner, L. D.

Valtolina, G.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Wei, D.

Whittaker, E. A.

Wynands, R.

O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
[Crossref]

Xie, C.

Zaccanti, M.

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
[Crossref]

Zhan, M. S.

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

Zhang, J.

Appl. Phys. B (2)

O. Schmidt, K.-M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited How to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167–178 (1994).
[Crossref]

J. F. Eble and F. Shmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41S0 to 41P1 transition,” Appl. Phys. B 88, 563C568 (2007).
[Crossref]

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F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas. 50, 490(2001).
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J. Chem. Phys. (1)

M. A. Hohensee and H. Müller, “Precision tests of general relativity with matter waves,” J. Chem. Phys. 58, 2021 (2011).

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J. Phys. B (1)

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B 45, 065002 (2012).
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J. Phys. France (1)

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. France 43, 57 (1982).
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J. Phys. Soc. Jpn. (1)

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn. 80, 074301 (2011).
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Jpn. J. Appl. Phys. (1)

Z. Lin, K. Shimizu, M. S. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, 1324 (1991).
[Crossref]

Meas. Sci. Technol. (2)

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that uses electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
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E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91 (1995).
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Opt. Lett. (1)

Phys. Rev. A (5)

A. T. Grier, I. Ferrier-Barbut, B. S. Rem, M. Delehaye, L. Khaykovich, F. Chevy, and C. Salomon, “Λ-enhanced sub-Doppler cooling of lithium atoms in D1 gray molasses,” Phys. Rev. A 87, 063411 (2013).
[Crossref]

P. Hamilton, G. Kim, T. Joshi, B. Mukherjee, D. Tiarks, and H. Müller, “Sisyphus cooling of lithium,” Phys. Rev. A 89, 023409 (2014).
[Crossref]

J. Sebastian, C. Gross, K. Li, H. C. J. Gan, W. Li, and K. Dieckmann, “Two-stage magneto-optical trapping and narrow-line cooling of 6Li atoms to high phase-space density,” Phys. Rev. A 90, 033417 (2014).
[Crossref]

A. Burchianti, G. Valtolina, J. A. Seman, E. Pace, M. De Pas, M. Inguscio, M. Zaccanti, and G. Roati, “Efficient all-optical production of large 6Li quantum gases using D1 gray-molasses cooling,” Phys. Rev. A 90, 043408 (2014).
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Figures (9)

Fig. 1
Fig. 1 Experimental setup of MTS measurement. Frequency modulation of 6.42 MHz is transferred from the pump to the probe beam within the lithium vapor cell. The beat of the probe frequency components at a two-path photodetector PD is demodulated to produce an error signal. f1, f2, f3, f4, and f5 are lenses with focuses of −50, 100, 100, −50, and 100 mm, respectively. EOM, electro-optic modulator; W, wave plate; PBS, polarization beam splitter; DDS, direct digital synthesizer; TA, tapered amplifier.
Fig. 2
Fig. 2 The influence of different intensities of the probe beam on the spectra when the intensity of pump beams stay the same (I pump = 8I sat , I sat = 5.1 mW/cm2). (a) The signals of MTS when the intensity of the probe beam I probe is 0.5 I sat , I sat and 2 I sat respectively; (b) The peak-peak amplitude of the three peaks in the spectrum; (c) The proportions of three peaks in the whole spectrum. The position of the saturation intensity is shown by a vertical dashed line.
Fig. 3
Fig. 3 The MTS of lithium with lin⊥lin polarization configuration and the SAS for reference.
Fig. 4
Fig. 4 FMS of D2 transitions in 7Li. The inset at the top left shows that the FMS varies with the phase shift Φ(0, π/4, π/2, 3π/4 and π from top to bottom). The inset at the top right shows the comparison of the slopes of the crossover dispersion peaks between MTS and FMS.
Fig. 5
Fig. 5 The in-phase (a) and quadrature (b) components of modulation transfer spectra under different polarization configurations.
Fig. 6
Fig. 6 (a) The spontaneous emission branch ratios in the transition of F g =2 → F e =3. (b) The diagram of FWM processes in the transition of F g =2 → F e =3 when the pump beams are circular polarization of σ and the probe beam is circular polarization of σ (i) or σ+ (ii). (c) The diagram of FWM processes in the transition of F g =2 → F e =3 when the polarization configuration is lin║lin (i) or lin⊥lin (ii).
Fig. 7
Fig. 7 The energy level diagrams for the crossover signal under the parallel (a, c) and perpendicular (b, d) linear polarization configurations. The transitions and spontaneous emissions of the two components, F g = 1, 2 F e = 1 (a, b) and F g = 1, 2F e =2 (c, d), are displayed in the diagrams.
Fig. 8
Fig. 8 The relative amplitude of RAM. The inset at the top left shows the calculated result in a large frequency range. The gray dashed line means the zero level of RAM, and the red shades are the amplitude of the RAM.
Fig. 9
Fig. 9 A theoretical fit to the data from the in-phase part in MTS of the resonance peak [F=2,F′] under lin⊥lin polarization configuration with r = −0.024(1).

Tables (1)

Tables Icon

Table 1 The slope and frequency offset of the signal zero-crossing for MTS and FM. [2,F′] is the resonance peak, [1-2,F′] is the crossover peak, and the slope is relative value in any units.

Equations (13)

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E = E 0 sin ( ω 0 t + δ sin ω m t ) .
E = E 0 [ n = 0 J n ( δ ) sin ( ω 0 + n ω m ) t + n = 0 ( 1 ) n J n ( δ ) sin ( ω 0 + n ω m ) t ] ,
S ( ω m ) = C ( Γ 2 + ω m 2 ) 1 / 2 n = J n ( δ ) J n 1 ( δ ) [ ( L ( n + 1 ) / 2 + L ( n 2 ) / 2 ) cos ( ω m t + Φ ) + ( D ( n + 1 ) / 2 + D ( n 2 ) / 2 ) sin ( ω m t + Φ ) ] ,
S ( ω m ) η ρ C ρ S γ 1 ρ P
S ( ω m ) = S ( ω m ) 2 2 + S ( ω m ) 1 1 + S ( ω m ) 0 0 + S ( ω m ) 1 1 + S ( ω m ) 2 2 ,
S ( ω m ) = 1 2 [ S ( ω m ) 2 3 + S ( ω m ) 2 1 + S ( ω m ) 1 2 + S ( ω m ) 1 0 + S ( ω m ) 0 1 + S ( ω m ) 0 1 + S ( ω m ) 1 0 + S ( ω m ) 1 2 + S ( ω m ) 2 1 + S ( ω m ) 2 3 ] .
S ( ω m ) η ρ C , S γ 1 ρ P γ
r m e d i u m = 1 2 r e x i t = exp [ α ( ω + Ω ) L 2 ] exp [ α ( ω Ω ) L 2 ] 4 ,
α ( ω ) = i = 1 N α i exp [ ( ω ω i ) 2 σ i 2 ] ,
α ( ω ) = α 0 i = 1 N exp [ ( ω ω i ) 2 σ 0 2 ] .
α ( ω ) = α 0 { exp [ ( ω ω 1 ) 2 σ 0 2 ] + exp [ ( ω ω 2 ) 2 σ 0 2 ] } .
Sig ( f ) = C [ { L ( ω m , f ) L ( ω m / 2 , f ) + L ( ω m / 2 , f ) L ( ω m , f ) } + r { L ( ω m , f ) + L ( ω m / 2 , f ) + L ( ω m / 2 , f ) + L ( ω m , f ) } ] ,
L ( ω m , f ) = Γ 2 Γ 2 + ( f 0 f ω m ) 2 .

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