Abstract

We present a general analysis for determining the optimal modulation parameters for the modulation transfer spectroscopy scheme. The results are universally valid and can be applied to spectroscopy of any atomic species requiring only the knowledge of the effective linewidth Γeff. A signal with optimized slope and amplitude is predicted for a large modulation index M and a modulation frequency comparable to the natural linewidth of the spectroscopic transition. As a result of competing practical considerations, a modulation index in the range of 3 ≤ M ≤ 10 has been identified as optimal. This parameter regime is experimentally accessible with a setup based on an acousto-optic modulator. An optimized signal for spectroscopy of the rubidium D2 line is presented. The signal shape and the dependence on the modulation parameters are in very good agreement with the theoretical description given. An experimental procedure for achieving a strong suppression of residual amplitude modulation is presented. Based on the optimized signal, we demonstrate long-term laser stabilization resulting in a laser linewidth of 150 kHz (16 s average) and a frequency stability of 18 kHz (rms) over 15 hours.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. W. Demtröder, Laser Spectroscopy 1: Basic Principles (Springer, 2014).
  2. W. Demtröder, Laser Spectroscopy 2: Experimental Techniques (Springer, 2015).
  3. M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant doppler-broadened systems - i. angular dependence of intensity and lineshape of phase-conjugate emission,” J. Phys. France 42, 711–721 (1981).
    [Crossref]
  4. 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, 57–65 (1982).
    [Crossref]
  5. G. Camy, C. Bordé, and M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325–330 (1982).
    [Crossref]
  6. J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett. 7, 537–539 (1982).
    [Crossref] [PubMed]
  7. V. Negnevitsky and L. D. Turner, “Wideband laser locking to an atomic reference with modulation transfer spectroscopy,” Opt. Express 21, 3103–3113 (2013).
    [Crossref] [PubMed]
  8. H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express 19, 23444–23452 (2011).
    [Crossref] [PubMed]
  9. H.-R. Noh and S. E. Park, “Modulation transfer spectroscopy for two-level atoms at high laser intensity,” Opt. Commun. 336, 173–176 (2015).
    [Crossref]
  10. E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91–97 (1995).
    [Crossref]
  11. D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19, 105601 (2008).
    [Crossref]
  12. W. Zhang, M. J. Martin, C. Benko, J. L. Hall, J. Ye, C. Hagemann, T. Legero, U. Sterr, F. Riehle, G. D. Cole, and M. Aspelmeyer, “Reduction of residual amplitude modulation to 1 × 10−6 for frequency modulation and laser stabilization,” Opt. Lett. 39, 1980–1983 (2014).
    [Crossref] [PubMed]
  13. R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
    [Crossref]
  14. J. Eble and F. Schmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41 s 0 to 41 p 1 transition,” Appl. Phys. B 88, 563–568 (2007).
    [Crossref]
  15. C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
    [Crossref]
  16. D. Sun, C. Zhou, L. Zhou, J. Wang, and M. Zhan, “Modulation transfer spectroscopy in a lithium atomic vapor cell,” Opt. Express 24, 10649–10662 (2016).
    [Crossref] [PubMed]
  17. E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69–74 (2008).
    [Crossref]
  18. E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that use electro-optic modulators,” Meas. Sci. Technol. 20, 025302 (2009).
    [Crossref]
  19. X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
    [Crossref]
  20. A. Martin, P. Baus, and G. Birkl, “External cavity diode laser setup with two interference filters,” Appl. Phys. B 122, 298 (2016).
    [Crossref]
  21. Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
    [Crossref]
  22. F. Zi, X. Wu, W. Zhong, R. H. Parker, C. Yu, S. Budker, X. Lu, and H. Müller, “Laser frequency stabilization by combining modulation transfer and frequency modulation spectroscopy,” Appl. Opt. 56, 2649–2652 (2017).
    [Crossref] [PubMed]
  23. Y. N. Martinez de Escobar, S. P. Álvarez, S. Coop, T. Vanderbruggen, K. T. Kaczmarek, and M. W. Mitchell, “Absolute frequency references at 1529 and 1560 nm using modulation transfer spectroscopy,” Opt. Lett. 40, 4731–4734 (2015).
    [Crossref] [PubMed]
  24. J. S. Torrance, B. M. Sparkes, L. D. Turner, and R. E. Scholten, “Sub-kilohertz laser linewidth narrowing using polarization spectroscopy,” Opt. Express 24, 11396–11406 (2016).
    [Crossref] [PubMed]

2017 (1)

2016 (3)

2015 (2)

2014 (2)

W. Zhang, M. J. Martin, C. Benko, J. L. Hall, J. Ye, C. Hagemann, T. Legero, U. Sterr, F. Riehle, G. D. Cole, and M. Aspelmeyer, “Reduction of residual amplitude modulation to 1 × 10−6 for frequency modulation and laser stabilization,” Opt. Lett. 39, 1980–1983 (2014).
[Crossref] [PubMed]

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

2013 (1)

2011 (1)

2009 (2)

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

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

2008 (2)

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69–74 (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. Eble and F. Schmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41 s 0 to 41 p 1 transition,” Appl. Phys. B 88, 563–568 (2007).
[Crossref]

2006 (1)

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

1995 (1)

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91–97 (1995).
[Crossref]

1982 (3)

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, 57–65 (1982).
[Crossref]

G. Camy, C. Bordé, and M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325–330 (1982).
[Crossref]

J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett. 7, 537–539 (1982).
[Crossref] [PubMed]

1981 (1)

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant doppler-broadened systems - i. angular dependence of intensity and lineshape of phase-conjugate emission,” J. Phys. France 42, 711–721 (1981).
[Crossref]

1980 (1)

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Álvarez, S. P.

Ao-Peng, X.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Aspelmeyer, M.

Back, J.

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

Baillard, X.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Baus, P.

A. Martin, P. Baus, and G. Birkl, “External cavity diode laser setup with two interference filters,” Appl. Phys. B 122, 298 (2016).
[Crossref]

Benko, C.

Bin, W.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Bing, C.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Birkl, G.

A. Martin, P. Baus, and G. Birkl, “External cavity diode laser setup with two interference filters,” Appl. Phys. B 122, 298 (2016).
[Crossref]

Bize, S.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Bloch, D.

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, 57–65 (1982).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant doppler-broadened systems - i. angular dependence of intensity and lineshape of phase-conjugate emission,” J. Phys. France 42, 711–721 (1981).
[Crossref]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Bordé, C.

G. Camy, C. Bordé, and M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325–330 (1982).
[Crossref]

Budker, S.

Camy, G.

G. Camy, C. Bordé, and M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325–330 (1982).
[Crossref]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Cho, C.-H.

Clairon, A.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Cole, G. D.

Coop, S.

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]

Da-Wei, Zhou

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Demtröder, W.

W. Demtröder, Laser Spectroscopy 1: Basic Principles (Springer, 2014).

W. Demtröder, Laser Spectroscopy 2: Experimental Techniques (Springer, 2015).

Ducloy, M.

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, 57–65 (1982).
[Crossref]

G. Camy, C. Bordé, and M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325–330 (1982).
[Crossref]

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant doppler-broadened systems - i. angular dependence of intensity and lineshape of phase-conjugate emission,” J. Phys. France 42, 711–721 (1981).
[Crossref]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Eble, J.

J. Eble and F. Schmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41 s 0 to 41 p 1 transition,” Appl. Phys. B 88, 563–568 (2007).
[Crossref]

Gauguet, A.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Hagemann, C.

Hall, J. L.

Hopper, D. J.

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that use 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, 69–74 (2008).
[Crossref]

Jaatinen, E.

E. Jaatinen, D. J. Hopper, and J. Back, “Residual amplitude modulation mechanisms in modulation transfer spectroscopy that use 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, 69–74 (2008).
[Crossref]

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91–97 (1995).
[Crossref]

Jun, Duan

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Kaczmarek, K. T.

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]

Laurent, P.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Legero, T.

Lemonde, P.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Li, L. Z.

Lin, Yi

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Lu, X.

Martin, A.

A. Martin, P. Baus, and G. Birkl, “External cavity diode laser setup with two interference filters,” Appl. Phys. B 122, 298 (2016).
[Crossref]

Martin, M. J.

Martinez de Escobar, Y. N.

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]

Mitchell, M. W.

Müller, H.

Negnevitsky, V.

Noh, H.-R.

H.-R. Noh and S. E. Park, “Modulation transfer spectroscopy for two-level atoms at high laser intensity,” Opt. Commun. 336, 173–176 (2015).
[Crossref]

H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express 19, 23444–23452 (2011).
[Crossref] [PubMed]

Park, J.-D.

Park, S. E.

H.-R. Noh and S. E. Park, “Modulation transfer spectroscopy for two-level atoms at high laser intensity,” Opt. Commun. 336, 173–176 (2015).
[Crossref]

H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express 19, 23444–23452 (2011).
[Crossref] [PubMed]

Parker, R. H.

Qiang, L.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Qin, Xiao

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Qi-Yu, W.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Raj, R. K.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Riehle, F.

Rosenbusch, P.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

Schmidt-Kaler, F.

J. Eble and F. Schmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41 s 0 to 41 p 1 transition,” Appl. Phys. B 88, 563–568 (2007).
[Crossref]

Scholten, R. E.

Shirley, J. H.

Snyder, J. J.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Sparkes, B. M.

Sterr, U.

Sun, D.

Tong, Zhou

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Torrance, J. S.

Turner, L. D.

Vanderbruggen, T.

Wang, J.

Wen-Lan, Chen

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Wu, X.

Xiang-Hui, Qi

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Xiao-Ji, Zhou

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Xu-Zong, Chen

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

Ye, J.

Yu, C.

Yun-Fei, X.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Zhan, M.

Zhang, W.

Zhao-Ying, W.

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Zhong, W.

Zhou, C.

Zhou, L.

Zi, F.

Appl. Opt. (1)

Appl. Phys. B (2)

A. Martin, P. Baus, and G. Birkl, “External cavity diode laser setup with two interference filters,” Appl. Phys. B 122, 298 (2016).
[Crossref]

J. Eble and F. Schmidt-Kaler, “Optimization of frequency modulation transfer spectroscopy on the calcium 41 s 0 to 41 p 1 transition,” Appl. Phys. B 88, 563–568 (2007).
[Crossref]

Chinese Phys. B (1)

C. Bing, W. Zhao-Ying, W. Bin, X. Ao-Peng, W. Qi-Yu, X. Yun-Fei, and L. Qiang, “Laser frequency stabilization and shifting by using modulation transfer spectroscopy,” Chinese Phys. B 23, 104222 (2014).
[Crossref]

Chinese Phys. Lett. (1)

Qi Xiang-Hui, Chen Wen-Lan, Yi Lin, Zhou Da-Wei, Zhou Tong, Xiao Qin, Duan Jun, Zhou Xiao-Ji, and Chen Xu-Zong, “Ultra-stable rubidium-stabilized external-cavity diode laser based on the modulation transfer spectroscopy Technique,” Chinese Phys. Lett. 26, 044205 (2009).
[Crossref]

J. Phys. France (2)

M. Ducloy and D. Bloch, “Theory of degenerate four-wave mixing in resonant doppler-broadened systems - i. angular dependence of intensity and lineshape of phase-conjugate emission,” J. Phys. France 42, 711–721 (1981).
[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, 57–65 (1982).
[Crossref]

Meas. Sci. Technol. (2)

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

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

Opt. Commun. (4)

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, P. Laurent, A. Clairon, and P. Rosenbusch, “Interference-filter-stabilized external-cavity diode lasers,” Opt. Commun. 266, 609–613 (2006).
[Crossref]

H.-R. Noh and S. E. Park, “Modulation transfer spectroscopy for two-level atoms at high laser intensity,” Opt. Commun. 336, 173–176 (2015).
[Crossref]

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91–97 (1995).
[Crossref]

G. Camy, C. Bordé, and M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325–330 (1982).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (1)

E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46, 69–74 (2008).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251–1254 (1980).
[Crossref]

Other (2)

W. Demtröder, Laser Spectroscopy 1: Basic Principles (Springer, 2014).

W. Demtröder, Laser Spectroscopy 2: Experimental Techniques (Springer, 2015).

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Figures (6)

Fig. 1
Fig. 1 Signal slope (a) and amplitude (c) as a function of modulation index M and modulation frequency ωm in units of the linewidth Γeff. Both are normalized to the maximal values appearing in the plot. Amplitudes are calculated for the optimal demodulation phase ϕ = ϕa and slopes for ϕ = ϕs. The optimal phases ϕs and ϕa are shown in (b) and (d). The black dots mark the experimental parameters discussed in Section 4.
Fig. 2
Fig. 2 AOM-based MTS setup (see text for details). Designation of optical elements: PBS for polarizing beam splitter, PD for photodiode, L for focusing lens. PBS1 serves for cleaning the input beam polarization. Optical beam paths are colored in red and electronic signal lines in blue.
Fig. 3
Fig. 3 Beat spectrum between pump and probe beam for a modulation depth Δω = 2π · 10.35 MHz at ωm = 2π · 2.5 MHz compared to a calculated ideal spectrum with M = 4.14.
Fig. 4
Fig. 4 Experimental MTS signal of the dominant 85Rb hyperfine transition |52S1/2, F = 3, mF〉 → |52P3/2, F′ = 4, m′F〉 (orange). The theoretical model of Eq. (3) is fitted to the data yielding Γeff = 2π · (9.03 ± 0.42) MHz (blue line). The frequency scale has been centered to the zero-crossing of the signal.
Fig. 5
Fig. 5 Experimentally obtained signal slopes (a) and amplitudes (b) as a function of M for different ωm compared to the theoretically predicted values (lines). The shaded areas mark the uncertainty of the theoretical prediction due to uncertainties in the determination of Γeff.
Fig. 6
Fig. 6 (a) Beat note spectrum between the MTS-stabilized ECDL system and a PS-stabilized ECDL system. The Gaussian fit yields a combined linewidth of 260 kHz. The laser linewidth of the MTS-stabilized system is (150 ± 7) kHz. (b) Center frequency of the beat note spectrum of an MTS-stabilized ECDL and MSHB-stabilized ECDL observed over a period of 15 hours. Both laser systems stayed in lock over the full duration. The variation in beat frequency tracks the change in ambient temperature.

Equations (8)

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E pump ( t ) = E 0 cos ( ω t + M sin ( ω m t ) ) .
E pump ( t ) = E 0 k J k ( M ) cos ( ( ω + k ω m ) t ) .
S M , ω m , ϕ ( Δ ) = C ω m 2 + Γ eff 2 k J k ( M ) J k 1 ( M ) × [ ( L k 2 2 , ω m ( Δ ) + L k + 1 2 , ω m ( Δ ) ) cos ϕ + ( D k 2 2 , ω m ( Δ ) D k + 2 2 , ω m ( Δ ) ) sin ϕ ]
L n , ω m ( Δ ) = 1 1 + ( Δ n ω m Γ eff ) 2
D n , ω m ( Δ ) = Δ n ω m Γ eff 1 + ( Δ n ω m Γ eff ) 2
S M , ω m , ϕ ( Δ ) = A M , ω m ( Δ ) cos ϕ + B M , ω m ( Δ ) sin ϕ
tan ϕ s = d d Δ B M , ω m d d Δ A M , ω m | Δ = 0
σ beat = σ 1 2 + σ 2 2

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