Abstract

Active frequency stabilization of a laser to an atomic or molecular resonance underpins many modern-day AMO physics experiments. With a flat background and high signal-to-noise ratio, modulation transfer spectroscopy (MTS) offers an accurate and stable method for laser locking. However, despite its benefits, the four-wave mixing process that is inherent to the MTS technique entails that the strongest modulation transfer signals are only observed for closed transitions, excluding MTS from numerous applications. Here we report for the first time, to the best of our knowledge, the observation of a magnetically tunable MTS error signal. Using a simple two-magnet arrangement, we show that the error signal for the Rb87 F=2F=3 cooling transition can be Zeeman-shifted over a range of >15GHzto any arbitrary point on the rubidium D2 spectrum. Modulation transfer signals for locking to the Rb87 F=1F=2 repumping transition, as well as 1 GHz red-detuned to the cooling transition, are presented to demonstrate the versatility of this technique, which can readily be extended to the locking of Raman and lattice lasers.

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References

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2018 (5)

2017 (2)

F. Zi, X. Wu, W. Zhong, R. H. Parker, C. Yu, S. Budker, X. Lu, and H. Müller, Appl. Opt. 56, 2649 (2017).
[Crossref]

D. Whiting, N. Šibalić, J. Keaveney, C. Adams, and I. Hughes, Phys. Rev. Lett. 118, 253601 (2017).
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2016 (1)

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, Phys. Rev. A 93, 043854 (2016).
[Crossref]

2015 (3)

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, Opt. Lett. 40, 4289 (2015).
[Crossref]

A. Sargsyan, A. Tonoyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, and D. Sarkisyan, Europhys. Lett. 110, 23001 (2015).
[Crossref]

A. D. Sargsyan, G. T. Hakhumyan, A. H. Amiryan, C. Leroy, H. S. Sarkisyan, and D. H. Sarkisyan, J. Contemp. Phys. (Armenian Acad. Sci.) 50, 317 (2015).
[Crossref]

2014 (1)

2011 (4)

L. Zhe Li, S. Eon Park, H.-R. Noh, J.-D. Park, and C.-H. Cho, J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, Opt. Express 19, 23444 (2011).
[Crossref]

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A. L. Marchant, S. Händel, T. P. Wiles, S. A. Hopkins, C. S. Adams, and S. L. Cornish, Opt. Lett. 36, 64 (2011).
[Crossref]

2008 (1)

D. J. McCarron, S. A. King, and S. L. Cornish, Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

2007 (1)

D. J. McCarron, I. G. Hughes, P. Tierney, and S. L. Cornish, Rev. Sci. Instrum. 78, 093106 (2007).
[Crossref]

2006 (1)

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, J. Phys. B 40, 187 (2006).
[Crossref]

2003 (1)

2002 (1)

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[Crossref]

1998 (1)

1996 (1)

D. W. Preston, Am. J. Phys. 64, 1432 (1996).
[Crossref]

1982 (2)

J. H. Shirley, Opt. Lett. 7, 537 (1982).
[Crossref]

M. Ducloy and D. Bloch, J. de Phys. 43, 57 (1982).
[Crossref]

1980 (2)

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, Phys. Rev. Lett. 44, 1251 (1980).
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1977 (1)

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1976 (2)

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Phys. Rev. A 14, 236 (1976).
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C. Wieman and T. W. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
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1975 (2)

E. V. Baklanov, B. Y. Dubetskii, V. M. Semibalamut, and E. A. Titov, Sov. J. Quantum Electron. 5, 1374 (1975).
[Crossref]

S. Zienau, Phys. Bull. 26, 545 (1975).

1970 (1)

S. G. Rautian and A. M. Shalagin, J. Exp. Theor. Phys. 31, 518(1970).

1966 (1)

D. W. Allan, Proc. IEEE 54, 221 (1966).
[Crossref]

Adams, C.

D. Whiting, N. Šibalić, J. Keaveney, C. Adams, and I. Hughes, Phys. Rev. Lett. 118, 253601 (2017).
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Adams, C. S.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, J. Mod. Opt. 65, 713 (2018).
[Crossref]

D. J. Reed, N. Šibalić, D. J. Whiting, J. M. Kondo, C. S. Adams, and K. J. Weatherill, OSA Continuum 1, 4 (2018).
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D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, Phys. Rev. A 93, 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, Opt. Lett. 40, 4289 (2015).
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A. L. Marchant, S. Händel, T. P. Wiles, S. A. Hopkins, C. S. Adams, and S. L. Cornish, Opt. Lett. 36, 64 (2011).
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C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
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Auzinsh, M.

Baklanov, E. V.

E. V. Baklanov, B. Y. Dubetskii, V. M. Semibalamut, and E. A. Titov, Sov. J. Quantum Electron. 5, 1374 (1975).
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Bimbard, E.

Bjorklund, G. C.

Bloch, D.

M. Ducloy and D. Bloch, J. de Phys. 43, 57 (1982).
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R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, Phys. Rev. Lett. 44, 1251 (1980).
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C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Phys. Rev. A 14, 236 (1976).
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H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, Opt. Express 19, 23444 (2011).
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Cornish, S. L.

A. L. Marchant, S. Händel, T. P. Wiles, S. A. Hopkins, C. S. Adams, and S. L. Cornish, Opt. Lett. 36, 64 (2011).
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D. J. McCarron, S. A. King, and S. L. Cornish, Meas. Sci. Technol. 19, 105601 (2008).
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D. J. McCarron, I. G. Hughes, P. Tierney, and S. L. Cornish, Rev. Sci. Instrum. 78, 093106 (2007).
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A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, J. Phys. B 40, 187 (2006).
[Crossref]

Corwin, K. L.

Cox, S. G.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[Crossref]

Dubetskii, B. Y.

E. V. Baklanov, B. Y. Dubetskii, V. M. Semibalamut, and E. A. Titov, Sov. J. Quantum Electron. 5, 1374 (1975).
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Ducloy, M.

M. Ducloy and D. Bloch, J. de Phys. 43, 57 (1982).
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R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, Phys. Rev. Lett. 44, 1251 (1980).
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Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988).

Eon Park, S.

L. Zhe Li, S. Eon Park, H.-R. Noh, J.-D. Park, and C.-H. Cho, J. Phys. Soc. Jpn. 80, 074301 (2011).
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Epstein, R. J.

Griffin, P. F.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[Crossref]

Hakhumyan, G.

A. Sargsyan, A. Tonoyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, and D. Sarkisyan, Europhys. Lett. 110, 23001 (2015).
[Crossref]

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, D. Sarkisyan, and M. Auzinsh, J. Opt. Soc. Am. B 31, 1046 (2014).
[Crossref]

Hakhumyan, G. T.

A. D. Sargsyan, G. T. Hakhumyan, A. H. Amiryan, C. Leroy, H. S. Sarkisyan, and D. H. Sarkisyan, J. Contemp. Phys. (Armenian Acad. Sci.) 50, 317 (2015).
[Crossref]

Hall, J. L.

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Phys. Rev. A 14, 236 (1976).
[Crossref]

Hand, C. F.

Händel, S.

Hänsch, T. W.

C. Wieman and T. W. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
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Happer, W.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, Phys. Rev. A 84, 063410 (2011).
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Howe, D. A.

W. Riley and D. A. Howe, Handbook of Frequency Stability Analysis|NIST, Special Publ. (NIST SP)—1065 (2008).

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D. Whiting, N. Šibalić, J. Keaveney, C. Adams, and I. Hughes, Phys. Rev. Lett. 118, 253601 (2017).
[Crossref]

Hughes, I. G.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, J. Mod. Opt. 65, 713 (2018).
[Crossref]

R. S. Mathew, F. Ponciano-Ojeda, J. Keaveney, D. J. Whiting, and I. G. Hughes, Opt. Lett. 43, 4204 (2018).
[Crossref]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, Phys. Rev. A 93, 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, Opt. Lett. 40, 4289 (2015).
[Crossref]

D. J. McCarron, I. G. Hughes, P. Tierney, and S. L. Cornish, Rev. Sci. Instrum. 78, 093106 (2007).
[Crossref]

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, J. Phys. B 40, 187 (2006).
[Crossref]

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[Crossref]

Hummer, D. G.

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Phys. Rev. A 14, 236 (1976).
[Crossref]

Jau, Y.-Y.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, Phys. Rev. A 84, 063410 (2011).
[Crossref]

Javan, A.

J. E. Thomas, M. J. Kelly, J. P. Monchalin, N. A. Kurnit, and A. Javan, Phys. Rev. A 15, 2356 (1977).
[Crossref]

Keaveney, J.

R. S. Mathew, F. Ponciano-Ojeda, J. Keaveney, D. J. Whiting, and I. G. Hughes, Opt. Lett. 43, 4204 (2018).
[Crossref]

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, J. Mod. Opt. 65, 713 (2018).
[Crossref]

D. Whiting, N. Šibalić, J. Keaveney, C. Adams, and I. Hughes, Phys. Rev. Lett. 118, 253601 (2017).
[Crossref]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, Phys. Rev. A 93, 043854 (2016).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, Opt. Lett. 40, 4289 (2015).
[Crossref]

Kelly, M. J.

J. E. Thomas, M. J. Kelly, J. P. Monchalin, N. A. Kurnit, and A. Javan, Phys. Rev. A 15, 2356 (1977).
[Crossref]

King, S. A.

D. J. McCarron, S. A. King, and S. L. Cornish, Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

Klinger, E.

A. Sargsyan, E. Klinger, A. Tonoyan, C. Leroy, and D. Sarkisyan, J. Phys. B 51, 145001 (2018).
[Crossref]

Kondo, J. M.

Kunasz, C. V.

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, Phys. Rev. A 14, 236 (1976).
[Crossref]

Kurnit, N. A.

J. E. Thomas, M. J. Kelly, J. P. Monchalin, N. A. Kurnit, and A. Javan, Phys. Rev. A 15, 2356 (1977).
[Crossref]

Leroy, C.

A. Sargsyan, E. Klinger, A. Tonoyan, C. Leroy, and D. Sarkisyan, J. Phys. B 51, 145001 (2018).
[Crossref]

A. D. Sargsyan, G. T. Hakhumyan, A. H. Amiryan, C. Leroy, H. S. Sarkisyan, and D. H. Sarkisyan, J. Contemp. Phys. (Armenian Acad. Sci.) 50, 317 (2015).
[Crossref]

A. Sargsyan, A. Tonoyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, and D. Sarkisyan, Europhys. Lett. 110, 23001 (2015).
[Crossref]

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, D. Sarkisyan, and M. Auzinsh, J. Opt. Soc. Am. B 31, 1046 (2014).
[Crossref]

Li, L. Z.

Long, J.-B.

Lu, X.

Lu, Z.-T.

Marchant, A. L.

Mathew, R. S.

R. S. Mathew, F. Ponciano-Ojeda, J. Keaveney, D. J. Whiting, and I. G. Hughes, Opt. Lett. 43, 4204 (2018).
[Crossref]

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, J. Mod. Opt. 65, 713 (2018).
[Crossref]

McCarron, D. J.

D. J. McCarron, S. A. King, and S. L. Cornish, Meas. Sci. Technol. 19, 105601 (2008).
[Crossref]

D. J. McCarron, I. G. Hughes, P. Tierney, and S. L. Cornish, Rev. Sci. Instrum. 78, 093106 (2007).
[Crossref]

Millett-Sikking, A.

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, J. Phys. B 40, 187 (2006).
[Crossref]

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988).

Monchalin, J. P.

J. E. Thomas, M. J. Kelly, J. P. Monchalin, N. A. Kurnit, and A. Javan, Phys. Rev. A 15, 2356 (1977).
[Crossref]

Müller, H.

Noh, H.-R.

H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, Opt. Express 19, 23444 (2011).
[Crossref]

L. Zhe Li, S. Eon Park, H.-R. Noh, J.-D. Park, and C.-H. Cho, J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

Olsen, B. A.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, Phys. Rev. A 84, 063410 (2011).
[Crossref]

Pan, J.-W.

Papoyan, A.

Park, J.-D.

H.-R. Noh, S. E. Park, L. Z. Li, J.-D. Park, and C.-H. Cho, Opt. Express 19, 23444 (2011).
[Crossref]

L. Zhe Li, S. Eon Park, H.-R. Noh, J.-D. Park, and C.-H. Cho, J. Phys. Soc. Jpn. 80, 074301 (2011).
[Crossref]

Park, S. E.

Parker, R. H.

Pashayan-Leroy, Y.

A. Sargsyan, A. Tonoyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, and D. Sarkisyan, Europhys. Lett. 110, 23001 (2015).
[Crossref]

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, D. Sarkisyan, and M. Auzinsh, J. Opt. Soc. Am. B 31, 1046 (2014).
[Crossref]

Patton, B.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, Phys. Rev. A 84, 063410 (2011).
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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of the Zeeman-tunable modulation transfer spectroscopy experimental setup ( λ / 2 , half-wave plate; λ / 4 , quarter-wave plate; BS, 50:50 non-polarizing beam splitter; EOM, electro-optic modulator; PBS, polarizing beam splitter; PD, photodiode). The sideband-modulated pump and unmodulated probe beams are allowed to propagate collinearly through a heated rubidium cell of natural abundance and length 2 mm, across which a uniform magnetic field of 0.6 T is applied. The electronic signal lines are drawn here in black. (b) N52 grade neodynium magnets and (c) 2 mm Rb vapor cell used in the experiment.
Fig. 2.
Fig. 2. Doppler-free spectrum of the D 2 line in Rb vapor with (a)  B = 0 and (b) 0.6 T; and the Zeeman-shifted MTS spectrum using (c) right circularly polarized light and (d) left circularly polarized light. (c) shows the MTS error signal for the Rb 87 F = 2 F = 3 cooling transition Zeeman-shifted onto the Rb 87 F = 1 F = 2 repumping transition. (c) and (d) are interchangeable by a 90° rotation of the quarter-wave plates. Red, with RCP incident light; blue, with LCP incident light.
Fig. 3.
Fig. 3. (a) Normal and (b) Zeeman-shifted pump-probe spectroscopy for the Rb 87 F = 1 F transitions. Note that the dip at the F = 1 F = 0 transition (leftmost in the first panel) is caused by optical pumping. A comparison between (c) Zeeman-shifted MTS and (d) FMS for the Rb 87 F = 1 F = 2 repumping transition.
Fig. 4.
Fig. 4. Plot of (a) detuning and (c) linewidth of the Rb 87 F = 2 F = 3 cooling transition as a function of the magnetic field strength. The solid black lines in (a) and (c) indicate, respectively, the theoretically predicted Zeeman shift of the | F = 2 , m F = 2 | F = 3 , m F = 3 transition and ab initio calculations of its linewidth based on the B -field homogeneity within the cell. The error bars in both plots are too small to be visible. (b) Displays the normalized residuals of (a), with the discrepancies arising due to nonlinearities in the laser scan. Insets: schematics indicating how the experimental shift and linewidth are determined.
Fig. 5.
Fig. 5. Overlapping Allan deviation of the beat note frequency between the locked laser and a separate, MTS-stabilized laser. Taken at 7 MHz detuning, the inset shows a persistence-type plot of the beat signal averaged over 1000 shots. Note that the locking circuits of both lasers were not optimized.

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