Abstract

Locking of a laser frequency to an atomic or molecular resonance line is a key technique in applications of laser spectroscopy and atomic metrology. Modulation transfer spectroscopy (MTS) provides an accurate and stable laser locking method which has been widely used. Normally, the frequency of the MTS signal would drift due to Zeeman shift of the atomic levels and rigorous shielding of stray magnetic field around the vapor cell is required for the accuracy and stability of laser locking. Here on the contrary, by applying a transverse bias magnetic field, we report for the first time observation of a magnetic-enhanced MTS signal on the transition of 87Rb D2-line Fg = 1→ Fe = 0 (close to the repump transition of Fg = 1→ Fe = 2), with signal to noise ratio larger than 100:1. The error signal is immune to the external magnetic fluctuation. Compared to the ordinary MTS scheme, it provides a robust and accurate laser locking approach with more stable long-term performance. This technique can be conveniently applied in areas of laser frequency stabilization, laser manipulation of atoms and precision measurement.

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

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References

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2018 (1)

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

2017 (2)

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

F. Zi, X. -J. Wu, W. C. Zhong, R. H. Parker, C. H. Yu, S. Budker, X. -H. Lu, and H. Müller, “Laser frequency stabilization by combining modulation transfer and frequency modulation spectroscopy,” Appl. Opt. 56(10), 2649–2652 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (2)

2014 (1)

2013 (4)

2012 (1)

X. Liu and R. Boudot, “A Distributed-Feedback Diode Laser Frequency Stabilized on Doppler-Free Cs D1 Line,” IEEE Trans. Instrum. Meas. 61(10), 2852–2855 (2012).
[Crossref]

2011 (2)

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. Japan 80, 074301 (2011).
[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(23), 23444–23452 (2011).
[Crossref] [PubMed]

2010 (1)

Z.-C. Zhou, R. Wei, C.-Y. Shi, and Y.-Z. Wang, “Observation of Modulation Transfer Spectroscopy in the Deep Modulation Regime,” Chinese Phys. Lett. 27(12), 124211 (2010).
[Crossref]

2009 (3)

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(2), 025302 (2009).
[Crossref]

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81(3), 1051–1129 (2009).
[Crossref]

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

2008 (5)

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B At. Mol. Opt. Phys. 41(8), 085401 (2008).
[Crossref]

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19(10), 105601 (2008).
[Crossref]

H. D. Do, G. Moon, and H. -R. Noh, “Polarization spectroscopy of rubidium atoms: Theory and experiment,” Phys. Rev. A 77(3), 032513 (2008).
[Crossref]

P. R. Berman and X. Xu, “Four-wave mixing in a Λ system,” Phys. Rev. A 78(5), 053407 (2008).
[Crossref]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, “Multi-field frequency modulation spectroscopy,” Opt. Express 16(9), 6081–6097 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

2003 (1)

2002 (1)

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “Laser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613–619 (2002).
[Crossref]

2001 (2)

E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001).
[Crossref]

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(2), 490–492 (2001).
[Crossref]

1998 (1)

1996 (1)

E. Arimondo, “Coherent Population Trapping in Laser Spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[Crossref]

1995 (1)

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun. 120, 91–97 (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(2), 167–178 (1994).
[Crossref]

1982 (2)

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25(5), 2606–2621 (1982).
[Crossref]

J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett. 7(11), 537–539 (1982).
[Crossref] [PubMed]

1980 (1)

1976 (1)

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36(20), 1170–1173 (1976).
[Crossref]

Adams, C. S.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

Arimondo, E.

E. Arimondo, “Coherent Population Trapping in Laser Spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[Crossref]

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(2), 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(2), 490–492 (2001).
[Crossref]

Ben-Aroya, I.

Berman, P. R.

P. R. Berman and X. Xu, “Four-wave mixing in a Λ system,” Phys. Rev. A 78(5), 053407 (2008).
[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(2), 490–492 (2001).
[Crossref]

Bize, S.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Bjorklund, G. C.

Black, E. D.

E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001).
[Crossref]

Boudot, R.

X. Liu and R. Boudot, “A Distributed-Feedback Diode Laser Frequency Stabilized on Doppler-Free Cs D1 Line,” IEEE Trans. Instrum. Meas. 61(10), 2852–2855 (2012).
[Crossref]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Brewer, R. G.

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25(5), 2606–2621 (1982).
[Crossref]

Bruce, G. D.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Budker, S.

Chen, P.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Chen, X.

Cho, C. -H.

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(23), 23444–23452 (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. Japan 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(2), 490–492 (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(10), 105601 (2008).
[Crossref]

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B At. Mol. Opt. Phys. 41(8), 085401 (2008).
[Crossref]

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

Corwin, K. L.

Couturier, L.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Cronin, A. D.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81(3), 1051–1129 (2009).
[Crossref]

Demtröder, W.

W. Demtröder, Laser Spectroscopy. (Springer, 2003).
[Crossref]

DeVoe, R. G.

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25(5), 2606–2621 (1982).
[Crossref]

Dholakia, K.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Do, H. D.

H. D. Do, G. Moon, and H. -R. Noh, “Polarization spectroscopy of rubidium atoms: Theory and experiment,” Phys. Rev. A 77(3), 032513 (2008).
[Crossref]

Eichholz, R.

Eisenstein, G.

English, E. M. L.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Epstein, R. J.

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(2), 490–492 (2001).
[Crossref]

Gawlik, W.

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “Laser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613–619 (2002).
[Crossref]

Grahn, H. T.

Hand, C. F.

Hänsch, T. W.

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36(20), 1170–1173 (1976).
[Crossref]

Harris, M. L.

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B At. Mol. Opt. Phys. 41(8), 085401 (2008).
[Crossref]

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

Heavner, T. P.

Hey, R.

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(2), 025302 (2009).
[Crossref]

Hu, F. -C.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Hübers, H. -W.

Hughes, I. G.

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B At. Mol. Opt. Phys. 41(8), 085401 (2008).
[Crossref]

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[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(2), 025302 (2009).
[Crossref]

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

Jefferts, S. R.

Ji, Z. -H.

Jia, S. -T.

Jiang, Y. -H.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Kahanov, M.

Kandrushin, S.

King, S. A.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19(10), 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(2), 167–178 (1994).
[Crossref]

Kobtsev, S.

Kunz, P. D.

Le Coq, Y.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Lemonde, P.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Li, L. Z.

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(23), 23444–23452 (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. Japan 80, 074301 (2011).
[Crossref]

Liu, S.

Liu, X.

X. Liu and R. Boudot, “A Distributed-Feedback Diode Laser Frequency Stabilized on Doppler-Free Cs D1 Line,” IEEE Trans. Instrum. Meas. 61(10), 2852–2855 (2012).
[Crossref]

Lodewyck, J.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Lu, X. -H.

Lu, Z. -T.

Ludlow, A. D.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Magalhães, D. V.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Maker, G. T.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Malcolm, G.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Mandache, C.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Mazilu, M.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

McCarron, D. J.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19(10), 105601 (2008).
[Crossref]

McLeod, I. C.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

Meng, T. -F.

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(2), 167–178 (1994).
[Crossref]

Metzger, N. K.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Miller, B.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Millo, J.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Moon, G.

H. D. Do, G. Moon, and H. -R. Noh, “Polarization spectroscopy of rubidium atoms: Theory and experiment,” Phys. Rev. A 77(3), 032513 (2008).
[Crossref]

Müller, H.

Negnevitsky, V.

Noh, H. -R.

S. E. Park and H. -R. Noh, “Modulation transfer spectroscopy mediated by spontaneous emission,” Opt. Express 21(12), 14066–14073 (2013).
[Crossref] [PubMed]

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(23), 23444–23452 (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. Japan 80, 074301 (2011).
[Crossref]

H. D. Do, G. Moon, and H. -R. Noh, “Polarization spectroscopy of rubidium atoms: Theory and experiment,” Phys. Rev. A 77(3), 032513 (2008).
[Crossref]

Nosske, I.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

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. Japan 80, 074301 (2011).
[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(23), 23444–23452 (2011).
[Crossref] [PubMed]

Park, S. E.

Parker, R. H.

Peik, E.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Peng, K.

Potekhin, A.

Pritchard, D. E.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81(3), 1051–1129 (2009).
[Crossref]

Qi, X.

Qiao, C.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Richter, H.

Santarelli, G.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Schenzle, A.

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25(5), 2606–2621 (1982).
[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(2), 167–178 (1994).
[Crossref]

Schmidt, P. O.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Schmiedmayer, J.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81(3), 1051–1129 (2009).
[Crossref]

Scholten, R. E.

Schrottke, L.

Shi, C.-Y.

Z.-C. Zhou, R. Wei, C.-Y. Shi, and Y.-Z. Wang, “Observation of Modulation Transfer Spectroscopy in the Deep Modulation Regime,” Chinese Phys. Lett. 27(12), 124211 (2010).
[Crossref]

Shirley, J. H.

Sparkes, B. M.

Spesyvtsev, R.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Su, D. -Q.

Sun, D. L.

Tan, C. Z.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Tarleton, E.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

Torrance, J. S.

Tripathi, A.

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B At. Mol. Opt. Phys. 41(8), 085401 (2008).
[Crossref]

Turner, L. D.

Wang, J.

Wang, Q.

Wang, Y.-Z.

Z.-C. Zhou, R. Wei, C.-Y. Shi, and Y.-Z. Wang, “Observation of Modulation Transfer Spectroscopy in the Deep Modulation Regime,” Chinese Phys. Lett. 27(12), 124211 (2010).
[Crossref]

Wasik, G.

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “Laser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613–619 (2002).
[Crossref]

Wei, D.

Wei, R.

Z.-C. Zhou, R. Wei, C.-Y. Shi, and Y.-Z. Wang, “Observation of Modulation Transfer Spectroscopy in the Deep Modulation Regime,” Chinese Phys. Lett. 27(12), 124211 (2010).
[Crossref]

Weidemüller, M.

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Westergaard, P. G.

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Wieman, C.

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36(20), 1170–1173 (1976).
[Crossref]

Wieman, C. E.

Wienold, M.

Wu, X. -J.

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(2), 167–178 (1994).
[Crossref]

Xiao, L. -T.

Xie, C.

Xu, X.

P. R. Berman and X. Xu, “Four-wave mixing in a Λ system,” Phys. Rev. A 78(5), 053407 (2008).
[Crossref]

Ye, J.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Yu, C. H.

Yu, J.

Yuan, J. -P.

Zachorowski, J.

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “Laser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613–619 (2002).
[Crossref]

Zawadzki, W.

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “Laser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613–619 (2002).
[Crossref]

Zhan, M. -S.

Zhang, J.

Zhao, Y. -T.

Zhong, W. C.

Zhou, C.

Zhou, L.

Zhou, Z.-C.

Z.-C. Zhou, R. Wei, C.-Y. Shi, and Y.-Z. Wang, “Observation of Modulation Transfer Spectroscopy in the Deep Modulation Regime,” Chinese Phys. Lett. 27(12), 124211 (2010).
[Crossref]

Zi, F.

Am. J. Phys. (1)

E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001).
[Crossref]

Appl. Opt. (5)

Appl. Phys. B (2)

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “Laser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613–619 (2002).
[Crossref]

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(2), 167–178 (1994).
[Crossref]

Chinese Phys. Lett. (1)

Z.-C. Zhou, R. Wei, C.-Y. Shi, and Y.-Z. Wang, “Observation of Modulation Transfer Spectroscopy in the Deep Modulation Regime,” Chinese Phys. Lett. 27(12), 124211 (2010).
[Crossref]

IEEE Trans. Instrum. Meas. (2)

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(2), 490–492 (2001).
[Crossref]

X. Liu and R. Boudot, “A Distributed-Feedback Diode Laser Frequency Stabilized on Doppler-Free Cs D1 Line,” IEEE Trans. Instrum. Meas. 61(10), 2852–2855 (2012).
[Crossref]

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

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B At. Mol. Opt. Phys. 41(8), 085401 (2008).
[Crossref]

J. Phys. Soc. Japan (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. Japan 80, 074301 (2011).
[Crossref]

Meas. Sci. Technol. (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(2), 025302 (2009).
[Crossref]

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol. 19(10), 105601 (2008).
[Crossref]

Nat. Commun. (1)

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8, 15610 (2017).
[Crossref] [PubMed]

Opt. Commun. (1)

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

Opt. Express (9)

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(23), 23444–23452 (2011).
[Crossref] [PubMed]

V. Negnevitsky and L. D. Turner, “Wideband laser locking to an atomic reference with modulation transfer spectroscopy,” Opt. Express 21(3), 3103–3113 (2013).
[Crossref] [PubMed]

D. L. Sun, C. Zhou, L. Zhou, J. Wang, and M. -S. Zhan, “Modulation transfer spectroscopy in a lithium atomic vapor cell,” Opt. Express 24(10), 10649–10662 (2016).
[Crossref] [PubMed]

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(11), 1338–1344 (2003).
[Crossref] [PubMed]

Q. Wang, X. Qi, S. Liu, J. Yu, and X. Chen, “Laser frequency stabilization using a dispersive line shape induced by Doppler Effect,” Opt. Express 23(3), 2982–2990 (2015).
[Crossref] [PubMed]

J. S. Torrance, B. M. Sparkes, L. D. Turner, and R. E. Scholten, “Sub-kilohertz laser linewidth narrowing using polarization spectroscopy,” Opt. Express 24(11), 11396–11406 (2016).
[Crossref] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, “Multi-field frequency modulation spectroscopy,” Opt. Express 16(9), 6081–6097 (2008).
[Crossref] [PubMed]

R. Eichholz, H. Richter, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H. -W. Hübers, “Frequency modulation spectroscopy with a THz quantum-cascade laser,” Opt. Express 21(26), 32199–32206 (2013).
[Crossref]

S. E. Park and H. -R. Noh, “Modulation transfer spectroscopy mediated by spontaneous emission,” Opt. Express 21(12), 14066–14073 (2013).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (5)

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73(6), 062509 (2006).
[Crossref]

H. D. Do, G. Moon, and H. -R. Noh, “Polarization spectroscopy of rubidium atoms: Theory and experiment,” Phys. Rev. A 77(3), 032513 (2008).
[Crossref]

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25(5), 2606–2621 (1982).
[Crossref]

P. R. Berman and X. Xu, “Four-wave mixing in a Λ system,” Phys. Rev. A 78(5), 053407 (2008).
[Crossref]

J. Millo, D. V. Magalhães, C. Mandache, Y. Le Coq, E. M. L. English, P. G. Westergaard, J. Lodewyck, S. Bize, P. Lemonde, and G. Santarelli, “Ultrastable lasers based on vibration insensitive cavities,” Phys. Rev. A 79(5), 053829 (2009).
[Crossref]

Phys. Rev. Lett. (1)

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36(20), 1170–1173 (1976).
[Crossref]

Prog. Opt. (1)

E. Arimondo, “Coherent Population Trapping in Laser Spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[Crossref]

Rev. Mod. Phys. (2)

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81(3), 1051–1129 (2009).
[Crossref]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Rev. Sci. Instrum. (1)

L. Couturier, I. Nosske, F. -C. Hu, C. Z. Tan, C. Qiao, Y. -H. Jiang, P. Chen, and M. Weidemüller, “Laser frequency stabilization using a commercial wavelength meter,” Rev. Sci. Instrum. 89(4), 043103 (2018).
[Crossref] [PubMed]

Other (1)

W. Demtröder, Laser Spectroscopy. (Springer, 2003).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Energy level diagrams for the two-level MTS (a), and the tripod-level MTSs of two orthogonal linearly-polarized configurations corresponding to the 87Rb D2 line transition Fg = 1 → Fe = 0 (b, c). Left and right of (b, c) are considering the degenerate and non-degenerate ground states respectively. |g1,2,3〉 and |e〉, the ground and excited states; ωp(c), the probe (pump) beam, ωc = ωp = ω; Ω, the modulation frequency; ωc(p)±Ω, the 1st-order sidebands of the pump/probe beam; and δ, energy splitting of the adjacent ground states due to a bias magnetic field shown in Fig. 2.
Fig. 2
Fig. 2 Schematic for the magnetic-enhanced MTS and laser frequency stabilization. The bias field is along z-direction, perpendicular to the optical table. λ/2: half-wave plate, λ/4: quarter-wave plate, PBS: polarization beam splitter, coupler: laser collimator, EOM: electro-optic modulator, BS: 50/50% beam splitter, f: lens, PD: photodiode detector, Amp: preamplifier, PID: proportion-integration-differentiation servo.
Fig. 3
Fig. 3 Error signal comparison when the laser-diode frequency is scanned over the 87Rb D2-line transition of Fg = 1 → Fe = {0, 1, 2}. Inset is enlarged of the gray part. MTS-a, the magnetic-enhanced MTS with orthogonal linear polarization setting; MTS-b, the ordinary MTS with orthogonal linear polarization setting; MTS-c, the ordinary MTS with parallel linear polarization setting; and FMS, the frequency modulation spectroscopy. The zero point in x-axis corresponds to the resonant transition of Fg = 1 → Fe = 0. CO01 is the crossover transition of Fe = 0 & 1. The modulation frequency is 4 MHz. A 10-point moving average has been applied to all the data.
Fig. 4
Fig. 4 (a) Residual error signal fluctuation of three spectroscopy methods after laser lock; and (b) the corresponding statistical distribution of it. MTS [2, 3] (black square): the ordinary MTS lock on the transition of Fg = 2 → Fe = 3; MTS [1, 0] (red circle): the magnetic-enhanced MTS lock on the transition of Fg = 1 → Fe = 0; and FMS [1, CO01] (blue triangle): the FMS lock on the crossover transition of Fg = 1 → Fe = 0 & 1. Sample interval in (a) is 100 μs and the total duration is 0.25 s; the y-axis in (b) is normalized to the peak value of the Gaussian fit. The FWHMs (full width at half maximum) of them are 82(1), 85(2) and 229(6) kHz respectively.
Fig. 5
Fig. 5 Measurement of laser linewidth and long-term stability by light beat of two independent laser diodes after lock. (a) Beat signal of the magnetic-enhanced MTS locking, fitting with a Lorentz-Gaussian function. Linewidth (FWHM) of the laser is about 209 kHz. All the data is 10-times averaged. (b) Beat frequency variation of the two independent laser diodes after lock for 10 hours. Three spectroscopy methods as discussed in Fig. 4 are carried out here. The gate time of the frequency measurement is 0.5 s. (c) Allan variance of the beat frequency.
Fig. 6
Fig. 6 The peak-to-peak amplitude of the magnetic-enhanced MTS signal for various parameter settings, including (a) light polarization, (b) modulation frequency Ω and (c) modulation index β when changing the bias magnetic strength B. Polarizations within parentheses in (a) corresponds to the probe and pump beams respectively. H/V, horizontal/vertical-linearly polarization; R/L, right/left-circularly polarization. Polarization configuration in (b) and (c) is (V, H). The x-axis is Zeeman splitting between the ground states of Fg = 1, mFg =±1.
Fig. 7
Fig. 7 The signal to noise ratio (left, black circle) and the zero-crossing gradient (right, blue square) of the MTS signal on the transition of Fg = 1 → Fe = 0 while changing the modulation frequency. Modulation index β is fixed at 1.43.

Equations (4)

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E c = E 0 sin ( ( ω 0 + Δ ) t + β sin Ω t ) = E 0 n = J n ( β ) sin ( ω 0 + Δ + n Ω ) t ,
S ( Ω ) = C [ Γ 2 + Ω 2 ] 1 / 2 n = J n ( β ) J n 1 ( β ) [ ( L ( n + 1 ) / 2 + L ( n 2 ) / 2 ) cos ( Ω t + ϕ ) + ( D ( n + 1 ) / 2 D ( n 2 ) / 2 ) sin ( Ω t + ϕ ) ] ,
S ( Ω ) = C [ Γ 2 + Ω 2 ] 1 / 2 J 0 ( β ) J 1 ( β ) [ ( L 1 + L 1 / 2 L 1 / 2 + L 1 ) cos ( Ω t + ϕ ) + ( D 1 D 1 / 2 D 1 / 2 + D 1 ) sin ( Ω t + ϕ ) ] .
S ( Ω ) = X cos ( Ω t + ϕ ) + Y sin ( Ω t + ϕ ) .

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