Abstract

We present a simple method for producing a low-drift atomic frequency reference based upon the Zeeman effect. Our Zeeman Shifted Atomic Reference ‘ZSAR’ is demonstrated to have a tens of GHz tuning range, limited only by the strength of the applied field. ZSAR uses Doppler-free laser spectroscopy in a thermal vapor where the vapor is situated in a large, static, and controllable magnetic field. We use a heated 85Rb vapor cell between a pair of position-adjustable permanent magnets capable of applying magnetic fields up to ∼1 T. To demonstrate the frequency reference we use a spectral feature from the Zeeman shifted D1 line in 85Rb at 795 nm to stabilize a laser to the 7S1/2 → 23P1/2 transition in atomic cesium, which is detuned by approximately 19 GHz from the unperturbed Rb transition. We place an upper bound on the stability of the technique by measuring a 2.5 MHz RMS frequency difference between the two spectral features over a 24 hour period. This versatile method could be adapted easily for use with other atomic species and the tuning range readily increased by applying larger magnetic fields.

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References

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    [Crossref]
  42. M. A. Zentile, R. Andrews, L. Weller, S. Knappe, C. S. Adams, and I. G. Hughes, “The hyperfine Paschen–Back Faraday effect,” J. Phys. B 47(7), 075005 (2014).
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    [Crossref]

2018 (2)

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, “Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime,” J. Mod. Opt. 65(2), 119–128 (2018).
[Crossref]

Y. Huang, Y. Guan, T. Suen, J. Shy, and L. Wang, “Absolute frequency measurement of the molecular iodine hyperfine transitions at 647 nm,” Appl. Opt. 57, 2102–2106 (2018).
[Crossref] [PubMed]

2017 (2)

D. J. Whiting, N. Šibalić, J. Keaveney, C. S. Adams, and I. G. Hughes, “Single-photon interference due to motion in an atomic collective excitation,” Phys. Rev. Lett. 118, 253601 (2017).
[Crossref] [PubMed]

N. Šibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, “ARC: An open-source library for calculating properties of alkali Rydberg atoms,” Comput. Phys. Commun. 220, 319 (2017).
[Crossref]

2016 (2)

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

2015 (5)

A. Sargsyan, B. Glushko, and D. Sarkisyan, “Micron-thick spectroscopic cells for studying the Paschen-Back regime on the hyperfine structure of cesium atoms,” J. Exp. Theor. Phys. 120(4), 579–586 (2015).
[Crossref]

S. Scotto, D. Ciampini, C. Rizzo, and E. Arimondo, “Four-level N-scheme crossover resonances in Rb saturation spectroscopy in magnetic fields,” Phys. Rev. A 92, 063810 (2015).
[Crossref]

M. A. Zentile, J. Keaveney, L. Weller, D. J. Whiting, C. S. Adams, and I. G. Hughes, “ElecSus: a program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun. 189, 162–174 (2015).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

J. M. Kondo, N. Šibalić, A. Guttridge, C. G. Wade, N. R. De Melo, C. S. Adams, and K. J. Weatherill, “Observation of interference effects via four-photon excitation of highly excited Rydberg states in thermal cesium vapor,” Opt. Lett. 40, 5570–5573 (2015).
[Crossref] [PubMed]

2014 (3)

2012 (2)

2011 (1)

2010 (1)

2009 (3)

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe in laser spectroscopy?” Am. J. Phys. 77(2), 111–115 (2009).
[Crossref]

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

2008 (2)

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

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in 39K, 85Rb, and 87Rb with ∼ 0.1 ppb uncertainty,” Europhys. Lett. 65(2), 172–178 (2008).
[Crossref]

2006 (2)

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]

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, “DAVLL lineshapes in atomic rubidium,” J. Phys. B 40(1), 187 (2006).
[Crossref]

2003 (1)

R. W. Fox, C. W. Oates, and L. W. Hollberg, “1. Stabilizing diode lasers to high-finesse cavities,” Exp. Meth. Phys. Sci. 40, 1–46 (2003).
[Crossref]

2002 (1)

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

2000 (2)

1999 (1)

U. Schünemann, H. Engler, R. Grimm, M. Weidemüller, and M. Zielonkowski, “Simple scheme for tunable frequency offset locking of two lasers,” Rev. Sci. Instrum. 70(1), 242–243 (1999).
[Crossref]

1998 (1)

1995 (1)

P. A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R (56) 32-0 near 532 nm,” IEEE Trans. Instrum. Meas. 44(2), 151–154 (1995).
[Crossref]

1991 (1)

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1–20 (1991).
[Crossref]

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy; theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32(3), 145–152 (1983).
[Crossref]

1982 (1)

1981 (1)

J. L. Hall, L. Hollberg, T. Baer, and H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

1980 (2)

T. W. Hänsch and B. Couillard, “Laser frequency stabilization by polarisation spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5(1), 15–17 (1980).
[Crossref] [PubMed]

1979 (1)

T. W. Hänsch, A. L. Schawlow, and G. W. Series, “The spectrum of atomic hydrogen,” Sci. Am. 240(72), 94–111 (1979).
[Crossref]

Abel, R. P.

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

Adams, C. S.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, “Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime,” J. Mod. Opt. 65(2), 119–128 (2018).
[Crossref]

D. J. Whiting, N. Šibalić, J. Keaveney, C. S. Adams, and I. G. Hughes, “Single-photon interference due to motion in an atomic collective excitation,” Phys. Rev. Lett. 118, 253601 (2017).
[Crossref] [PubMed]

N. Šibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, “ARC: An open-source library for calculating properties of alkali Rydberg atoms,” Comput. Phys. Commun. 220, 319 (2017).
[Crossref]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

M. A. Zentile, J. Keaveney, L. Weller, D. J. Whiting, C. S. Adams, and I. G. Hughes, “ElecSus: a program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun. 189, 162–174 (2015).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

J. M. Kondo, N. Šibalić, A. Guttridge, C. G. Wade, N. R. De Melo, C. S. Adams, and K. J. Weatherill, “Observation of interference effects via four-photon excitation of highly excited Rydberg states in thermal cesium vapor,” Opt. Lett. 40, 5570–5573 (2015).
[Crossref] [PubMed]

M. A. Zentile, R. Andrews, L. Weller, S. Knappe, C. S. Adams, and I. G. Hughes, “The hyperfine Paschen–Back Faraday effect,” J. Phys. B 47(7), 075005 (2014).
[Crossref]

C. Carr, C. S. Adams, and K. J. Weatherill, “Polarisation spectroscopy of an excited state transition,” Opt. Lett. 37, 118–120 (2012).
[Crossref] [PubMed]

C. Carr, M. Tanasittikosol, A. Sargsyan, D. Sarkisyan, C. S. Adams, and K. J. Weatherill, “Three-photon electromagnetically induced transparency using Rydberg states,” Opt. Lett. 37(18), 3858–3860 (2012).
[Crossref] [PubMed]

A. L. Marchant, S. Händel, T. P. Wiles, S. A. Hopkins, C. S. Adams, and S. L. Cornish, “Off-resonance laser frequency stabilization using the Faraday effect,” Opt. Lett. 36, 64–66 (2011).
[Crossref] [PubMed]

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[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]

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

Andrews, R.

M. A. Zentile, R. Andrews, L. Weller, S. Knappe, C. S. Adams, and I. G. Hughes, “The hyperfine Paschen–Back Faraday effect,” J. Phys. B 47(7), 075005 (2014).
[Crossref]

Araújo, M. O.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Arimondo, E.

S. Scotto, D. Ciampini, C. Rizzo, and E. Arimondo, “Four-level N-scheme crossover resonances in Rb saturation spectroscopy in magnetic fields,” Phys. Rev. A 92, 063810 (2015).
[Crossref]

Auzinsh, M.

Baer, T.

J. L. Hall, L. Hollberg, T. Baer, and H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Baird, P.

Y. W. Liu and P. Baird, “Measurement of the caesium 6S1/2 8P1/2 transition frequency,” Appl. Phys. B 71, 567 (2000).
[Crossref]

Balushev, S.

Banerjee, A.

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in 39K, 85Rb, and 87Rb with ∼ 0.1 ppb uncertainty,” Europhys. Lett. 65(2), 172–178 (2008).
[Crossref]

Barboza, P. M. T.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Bason, M. G.

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

Bimbard, E.

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy; theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32(3), 145–152 (1983).
[Crossref]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5(1), 15–17 (1980).
[Crossref] [PubMed]

Bolívar, P. H.

Bourassin-Boucheta, C.

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

Calvalcante, H. L. D. de S.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Carasso, D.

Carr, C.

Chevrollier, M.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Ciampini, D.

S. Scotto, D. Ciampini, C. Rizzo, and E. Arimondo, “Four-level N-scheme crossover resonances in Rb saturation spectroscopy in magnetic fields,” Phys. Rev. A 92, 063810 (2015).
[Crossref]

Cornish, S. L.

A. L. Marchant, S. Händel, T. P. Wiles, S. A. Hopkins, C. S. Adams, and S. L. Cornish, “Off-resonance laser frequency stabilization using the Faraday effect,” Opt. Lett. 36, 64–66 (2011).
[Crossref] [PubMed]

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

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, “DAVLL lineshapes in atomic rubidium,” J. Phys. B 40(1), 187 (2006).
[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.

Couillard, B.

T. W. Hänsch and B. Couillard, “Laser frequency stabilization by polarisation spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Cox, S. G.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

da Silva, C. M.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Das, D.

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in 39K, 85Rb, and 87Rb with ∼ 0.1 ppb uncertainty,” Europhys. Lett. 65(2), 172–178 (2008).
[Crossref]

Davidson, Nir

De Melo, N. R.

de Silans, T. P.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
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[Crossref]

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Eickhoff, M.

P. A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R (56) 32-0 near 532 nm,” IEEE Trans. Instrum. Meas. 44(2), 151–154 (1995).
[Crossref]

Engler, H.

U. Schünemann, H. Engler, R. Grimm, M. Weidemüller, and M. Zielonkowski, “Simple scheme for tunable frequency offset locking of two lasers,” Rev. Sci. Instrum. 70(1), 242–243 (1999).
[Crossref]

Epstein, R. J.

Fox, R. W.

R. W. Fox, C. W. Oates, and L. W. Hollberg, “1. Stabilizing diode lasers to high-finesse cavities,” Exp. Meth. Phys. Sci. 40, 1–46 (2003).
[Crossref]

Friederich, F.

Friedman, N.

Gawlik, W.

Glushko, B.

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Griffin, P. F.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

Grimm, R.

U. Schünemann, H. Engler, R. Grimm, M. Weidemüller, and M. Zielonkowski, “Simple scheme for tunable frequency offset locking of two lasers,” Rev. Sci. Instrum. 70(1), 242–243 (1999).
[Crossref]

Guan, Y.

Guttridge, A.

Hakhumyan, G.

Hall, J. L.

P. A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R (56) 32-0 near 532 nm,” IEEE Trans. Instrum. Meas. 44(2), 151–154 (1995).
[Crossref]

J. L. Hall, L. Hollberg, T. Baer, and H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

J. L. Hall, M. S. Taubman, and J. Ye, “Laser stabilization,” in Handbook of Optics, Volume IV: Fiber Optics and Nonlinear Optics, M. Bass, ed. (McGraw-Hill, 2001).

Hand, C. F.

Händel, S.

Hänsch, T. W.

T. W. Hänsch and B. Couillard, “Laser frequency stabilization by polarisation spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

T. W. Hänsch, A. L. Schawlow, and G. W. Series, “The spectrum of atomic hydrogen,” Sci. Am. 240(72), 94–111 (1979).
[Crossref]

Harris, M. L.

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]

Hollberg, L.

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1–20 (1991).
[Crossref]

J. L. Hall, L. Hollberg, T. Baer, and H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Hollberg, L. W.

R. W. Fox, C. W. Oates, and L. W. Hollberg, “1. Stabilizing diode lasers to high-finesse cavities,” Exp. Meth. Phys. Sci. 40, 1–46 (2003).
[Crossref]

Hopkins, S. A.

Huang, Y.

Hughes, I. G.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, “Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime,” J. Mod. Opt. 65(2), 119–128 (2018).
[Crossref]

D. J. Whiting, N. Šibalić, J. Keaveney, C. S. Adams, and I. G. Hughes, “Single-photon interference due to motion in an atomic collective excitation,” Phys. Rev. Lett. 118, 253601 (2017).
[Crossref] [PubMed]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

M. A. Zentile, J. Keaveney, L. Weller, D. J. Whiting, C. S. Adams, and I. G. Hughes, “ElecSus: a program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun. 189, 162–174 (2015).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

M. A. Zentile, R. Andrews, L. Weller, S. Knappe, C. S. Adams, and I. G. Hughes, “The hyperfine Paschen–Back Faraday effect,” J. Phys. B 47(7), 075005 (2014).
[Crossref]

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe in laser spectroscopy?” Am. J. Phys. 77(2), 111–115 (2009).
[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]

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, “DAVLL lineshapes in atomic rubidium,” J. Phys. B 40(1), 187 (2006).
[Crossref]

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

Johns, B.

Jungner, P. A.

P. A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R (56) 32-0 near 532 nm,” IEEE Trans. Instrum. Meas. 44(2), 151–154 (1995).
[Crossref]

Keaveney, J.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, “Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime,” J. Mod. Opt. 65(2), 119–128 (2018).
[Crossref]

D. J. Whiting, N. Šibalić, J. Keaveney, C. S. Adams, and I. G. Hughes, “Single-photon interference due to motion in an atomic collective excitation,” Phys. Rev. Lett. 118, 253601 (2017).
[Crossref] [PubMed]

D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

M. A. Zentile, J. Keaveney, L. Weller, D. J. Whiting, C. S. Adams, and I. G. Hughes, “ElecSus: a program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun. 189, 162–174 (2015).
[Crossref]

D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
[Crossref] [PubMed]

Khaykovich, L.

Kim, J.

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

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]

Knappe, S.

M. A. Zentile, R. Andrews, L. Weller, S. Knappe, C. S. Adams, and I. G. Hughes, “The hyperfine Paschen–Back Faraday effect,” J. Phys. B 47(7), 075005 (2014).
[Crossref]

Kondo, J. M.

Landragina, A.

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

Le Gouët, J.

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy; theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32(3), 145–152 (1983).
[Crossref]

Leroy, C.

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy; theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32(3), 145–152 (1983).
[Crossref]

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy, (Academic Press, 1982).

Li, W.

W. Li, X. Pan, N. Song, X. Xu, and X. Lu, “A phase-locked laser system based on modulation technique for atom interferometry,” arXiv preprint, arXiv:1607.07191 (2016).

Lison, F.

Liu, Y. W.

Y. W. Liu and P. Baird, “Measurement of the caesium 6S1/2 8P1/2 transition frequency,” Appl. Phys. B 71, 567 (2000).
[Crossref]

Loursa, M.

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

Lu, X.

W. Li, X. Pan, N. Song, X. Xu, and X. Lu, “A phase-locked laser system based on modulation technique for atom interferometry,” arXiv preprint, arXiv:1607.07191 (2016).

Lu, Z.

Marchant, A. L.

Mathew, R. S.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, “Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime,” J. Mod. Opt. 65(2), 119–128 (2018).
[Crossref]

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]

Millett-Sikking, A.

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, “DAVLL lineshapes in atomic rubidium,” J. Phys. B 40(1), 187 (2006).
[Crossref]

Mirzoyan, R.

Mohapatra, A. K.

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

Nascimento, G. G.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Natarajan, V.

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in 39K, 85Rb, and 87Rb with ∼ 0.1 ppb uncertainty,” Europhys. Lett. 65(2), 172–178 (2008).
[Crossref]

Oates, C. W.

R. W. Fox, C. W. Oates, and L. W. Hollberg, “1. Stabilizing diode lasers to high-finesse cavities,” Exp. Meth. Phys. Sci. 40, 1–46 (2003).
[Crossref]

Oriá, M.

P. M. T. Barboza, G. G. Nascimento, M. O. Araújo, C. M. da Silva, H. L. D. de S. Calvalcante, M. Oriá, M. Chevrollier, and T. P. de Silans, “Stabilization of a laser on a large-detuned atomic-reference frequency by resonant interferometry,” J. Phys. B 49(8), 085401 (2016).
[Crossref]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy; theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32(3), 145–152 (1983).
[Crossref]

Pan, X.

W. Li, X. Pan, N. Song, X. Xu, and X. Lu, “A phase-locked laser system based on modulation technique for atom interferometry,” arXiv preprint, arXiv:1607.07191 (2016).

Papoyan, A.

Pashayan-Leroy, Y.

Pearman, C. P.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

Pereira Dos Santosa, F.

J. Le Gouët, J. Kim, C. Bourassin-Boucheta, M. Loursa, A. Landragina, and F. Pereira Dos Santosa, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282(5), 977–980 (2009).
[Crossref]

Pritchard, J. D.

N. Šibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, “ARC: An open-source library for calculating properties of alkali Rydberg atoms,” Comput. Phys. Commun. 220, 319 (2017).
[Crossref]

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

Raitzsch, U.

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

Rizzo, C.

S. Scotto, D. Ciampini, C. Rizzo, and E. Arimondo, “Four-level N-scheme crossover resonances in Rb saturation spectroscopy in magnetic fields,” Phys. Rev. A 92, 063810 (2015).
[Crossref]

Robinson, H. G.

J. L. Hall, L. Hollberg, T. Baer, and H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Roskos, H. G.

Sargsyan, A.

Sarkisyan, D.

Schawlow, A. L.

T. W. Hänsch, A. L. Schawlow, and G. W. Series, “The spectrum of atomic hydrogen,” Sci. Am. 240(72), 94–111 (1979).
[Crossref]

Schünemann, U.

U. Schünemann, H. Engler, R. Grimm, M. Weidemüller, and M. Zielonkowski, “Simple scheme for tunable frequency offset locking of two lasers,” Rev. Sci. Instrum. 70(1), 242–243 (1999).
[Crossref]

Schuricht, G.

Scotto, S.

S. Scotto, D. Ciampini, C. Rizzo, and E. Arimondo, “Four-level N-scheme crossover resonances in Rb saturation spectroscopy in magnetic fields,” Phys. Rev. A 92, 063810 (2015).
[Crossref]

Series, G. W.

T. W. Hänsch, A. L. Schawlow, and G. W. Series, “The spectrum of atomic hydrogen,” Sci. Am. 240(72), 94–111 (1979).
[Crossref]

Sherlock, B. E.

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe in laser spectroscopy?” Am. J. Phys. 77(2), 111–115 (2009).
[Crossref]

Shirley, J. H.

Shy, J.

Šibalic, N.

D. J. Whiting, N. Šibalić, J. Keaveney, C. S. Adams, and I. G. Hughes, “Single-photon interference due to motion in an atomic collective excitation,” Phys. Rev. Lett. 118, 253601 (2017).
[Crossref] [PubMed]

N. Šibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, “ARC: An open-source library for calculating properties of alkali Rydberg atoms,” Comput. Phys. Commun. 220, 319 (2017).
[Crossref]

J. M. Kondo, N. Šibalić, A. Guttridge, C. G. Wade, N. R. De Melo, C. S. Adams, and K. J. Weatherill, “Observation of interference effects via four-photon excitation of highly excited Rydberg states in thermal cesium vapor,” Opt. Lett. 40, 5570–5573 (2015).
[Crossref] [PubMed]

Smith, D. A.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141 (2002).
[Crossref]

Song, N.

W. Li, X. Pan, N. Song, X. Xu, and X. Lu, “A phase-locked laser system based on modulation technique for atom interferometry,” arXiv preprint, arXiv:1607.07191 (2016).

Spickermann, G.

Stabrawa, A.

Suen, T.

Swartz, S.

P. A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R (56) 32-0 near 532 nm,” IEEE Trans. Instrum. Meas. 44(2), 151–154 (1995).
[Crossref]

Tanasittikosol, M.

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]

Taubman, M. S.

J. L. Hall, M. S. Taubman, and J. Ye, “Laser stabilization,” in Handbook of Optics, Volume IV: Fiber Optics and Nonlinear Optics, M. Bass, ed. (McGraw-Hill, 2001).

Tierney, P.

A. Millett-Sikking, I. G. Hughes, P. Tierney, and S. L. Cornish, “DAVLL lineshapes in atomic rubidium,” J. Phys. B 40(1), 187 (2006).
[Crossref]

Tononyan, A.

Wade, C. G.

Waltman, S.

P. A. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R (56) 32-0 near 532 nm,” IEEE Trans. Instrum. Meas. 44(2), 151–154 (1995).
[Crossref]

Wang, L.

Weatherill, K. J.

N. Šibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, “ARC: An open-source library for calculating properties of alkali Rydberg atoms,” Comput. Phys. Commun. 220, 319 (2017).
[Crossref]

J. M. Kondo, N. Šibalić, A. Guttridge, C. G. Wade, N. R. De Melo, C. S. Adams, and K. J. Weatherill, “Observation of interference effects via four-photon excitation of highly excited Rydberg states in thermal cesium vapor,” Opt. Lett. 40, 5570–5573 (2015).
[Crossref] [PubMed]

C. Carr, M. Tanasittikosol, A. Sargsyan, D. Sarkisyan, C. S. Adams, and K. J. Weatherill, “Three-photon electromagnetically induced transparency using Rydberg states,” Opt. Lett. 37(18), 3858–3860 (2012).
[Crossref] [PubMed]

C. Carr, C. S. Adams, and K. J. Weatherill, “Polarisation spectroscopy of an excited state transition,” Opt. Lett. 37, 118–120 (2012).
[Crossref] [PubMed]

R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, “Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system,” Appl. Phys. Lett. 94(7), 071107 (2009).
[Crossref]

Weidemüller, M.

U. Schünemann, H. Engler, R. Grimm, M. Weidemüller, and M. Zielonkowski, “Simple scheme for tunable frequency offset locking of two lasers,” Rev. Sci. Instrum. 70(1), 242–243 (1999).
[Crossref]

Weller, L.

M. A. Zentile, J. Keaveney, L. Weller, D. J. Whiting, C. S. Adams, and I. G. Hughes, “ElecSus: a program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun. 189, 162–174 (2015).
[Crossref]

M. A. Zentile, R. Andrews, L. Weller, S. Knappe, C. S. Adams, and I. G. Hughes, “The hyperfine Paschen–Back Faraday effect,” J. Phys. B 47(7), 075005 (2014).
[Crossref]

Whiting, D. J.

D. J. Whiting, R. S. Mathew, J. Keaveney, C. S. Adams, and I. G. Hughes, “Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime,” J. Mod. Opt. 65(2), 119–128 (2018).
[Crossref]

D. J. Whiting, N. Šibalić, J. Keaveney, C. S. Adams, and I. G. Hughes, “Single-photon interference due to motion in an atomic collective excitation,” Phys. Rev. Lett. 118, 253601 (2017).
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D. J. Whiting, J. Keaveney, C. S. Adams, and I. G. Hughes, “Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime,” Phys. Rev. A 93(4), 043854 (2016).
[Crossref]

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D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
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D. J. Whiting, E. Bimbard, J. Keaveney, M. A. Zentile, C. S. Adams, and I. G. Hughes, “Electromagnetically induced absorption in a nondegenerate three-level ladder system,” Opt. Lett. 40(18), 4289–4292 (2015).
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M. A. Zentile, J. Keaveney, L. Weller, D. J. Whiting, C. S. Adams, and I. G. Hughes, “ElecSus: a program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun. 189, 162–174 (2015).
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Figures (4)

Fig. 1
Fig. 1 (a) A theoretical plot generated by ElecSus showing the transmission spectra of the D1 line of 85Rb at 0.954 T and 95 °C as well as the same spectral line at zero field and 20 °C displayed in gray for comparison. The region within the dashed box is used to provide the frequency reference in the experimental section. (b) A Breit-Rabi diagram showing the evolution of the spectral feature locations with increasing magnetic field, where σ+ and σ transitions are colored red and blue respectively. The opacity of each line indicates its transition strength, normalized to the strongest transition of this set. The small features at approximately ±9.5 GHz are weak transitions that are allowed due to residual hyperfine mixing. (c) To scale diagram of the apparatus showing the B-field orientation relative to the probe and pump beam propagation directions. The experiment cell is a heated 85Rb cell with a 2 mm optical path length, flanked by NdFeB magnets.
Fig. 2
Fig. 2 85Rb Doppler broadened spectra which focuses on the positively detuned, σ+ transition at B = 0.954 T with cell temperature of ≈ 95 °C as denoted on Fig. 1(b) by the dashed box. The black line corresponds to an ElecSus theory plot using these experimental parameters, whilst the cyan line is the experimental Doppler spectra data. The residuals between theory and experiment are shown in the lower pane. The green line shows the sub-Doppler spectra of the Rb once a counter-propagating pump beam has been applied. It is from these resolved features that the FM signal is derived.
Fig. 3
Fig. 3 (a) Experimentally measured FM spectra showing the six dispersive features associated with the six sub-Doppler resonances appearing on the positively detuned part of the probe transmission spectrum. The feature highlighted by the black box was used to characterize our signal. (b) A study of the gradient, κ of the FM feature contained within the black box as defined by α, its peak to peak height, and Γ; its width. The data exhibits a linear relationship between κ and the pump beam power. (c) An analysis of the uncertainty of the position of our locking feature Πrms, in relation to both probe and pump powers. The minimum uncertainty was found to be 2.2±0.6 MHz.
Fig. 4
Fig. 4 (a) Frequency modulation (FM) signal generated using the 5S1/2 → 5P1/2 transition in 85Rb at B = 0.954 T and (b) the simultaneous Rydberg EIT signal generated using Cs atoms on the 7S1/2 → 23P1/2 transition. Both plots are an average of 3 data sets. The FM signal probe and pump powers were 2 μW, and 300 μW respectively. Because of the addition of a double passed AOM to our EIT setup, the EIT signal is shifted by ∼ 400 MHz and therefore coincides with the 5th dispersive feature of the FM spectra. Characteristics of this alternate feature are consistent with our original analysis. (c) The measured long term drift in the relative positions of the EIT and FM spectral features, over a period of 24 hours. The maximum drift values were +4.3 MHz and −6.8 MHz with an RMS deviation of 2.5 MHz.

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