Abstract

We demonstrate a direct correspondence between FM parameters used in a frequency-locked loop that is based on multifield FM spectroscopy and the stability of a small-scale coherent population trapping atomic clock. Optimized FM parameters lead to an Allan deviation of 2.8×1011τ, while the clock stability deteriorates in a predictable manner for the other FM parameters.

© 2008 Optical Society of America

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References

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  1. E. Arimondo, in Progress in Optics Vol. XXXV, E.Wolf, ed. (Elsevier, 1996), p. 257.
    [CrossRef]
  2. J. Vanier, Appl. Phys. B 81, 421 (2005).
    [CrossRef]
  3. S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, Opt. Express 13, 1249 (2005).
    [CrossRef] [PubMed]
  4. R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
    [CrossRef]
  5. I. Ben-Aroya, M. Kahanov, and G. Eisenstein, in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L.A.Breakiron, ed. (Naval Observatory, 2006), p. 259.
  6. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
    [CrossRef]
  7. J. M. Supplee, E. A. Whittaker, and W. Lenth, Appl. Opt. 33, 6294 (1994).
    [CrossRef] [PubMed]
  8. R. Wynands and A. Nagel, J. Opt. Soc. Am. B 16, 1617 (1999).
    [CrossRef]
  9. I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 15, 15060 (2007).
    [CrossRef] [PubMed]
  10. I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 16, 6081 (2008).
    [CrossRef] [PubMed]
  11. J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
    [CrossRef]
  12. D. W. Allan, Proc. IEEE 54, 221 (1966).
    [CrossRef]
  13. F. Levi, A. Godone, and J. Vanier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 466 (2000).
    [CrossRef]

2008 (1)

2007 (1)

2005 (2)

2000 (2)

F. Levi, A. Godone, and J. Vanier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 466 (2000).
[CrossRef]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

1999 (1)

1994 (1)

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

1966 (1)

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

Allan, D. W.

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

Arimondo, E.

E. Arimondo, in Progress in Optics Vol. XXXV, E.Wolf, ed. (Elsevier, 1996), p. 257.
[CrossRef]

Ben-Aroya, I.

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 16, 6081 (2008).
[CrossRef] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 15, 15060 (2007).
[CrossRef] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L.A.Breakiron, ed. (Naval Observatory, 2006), p. 259.

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Eisenstein, G.

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 16, 6081 (2008).
[CrossRef] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 15, 15060 (2007).
[CrossRef] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L.A.Breakiron, ed. (Naval Observatory, 2006), p. 259.

Godone, A.

F. Levi, A. Godone, and J. Vanier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 466 (2000).
[CrossRef]

Hollberg, L.

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, Opt. Express 13, 1249 (2005).
[CrossRef] [PubMed]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Kahanov, M.

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 16, 6081 (2008).
[CrossRef] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, Opt. Express 15, 15060 (2007).
[CrossRef] [PubMed]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L.A.Breakiron, ed. (Naval Observatory, 2006), p. 259.

Kitching, J.

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, Opt. Express 13, 1249 (2005).
[CrossRef] [PubMed]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Knappe, S.

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, Opt. Express 13, 1249 (2005).
[CrossRef] [PubMed]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Leblanc, J.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Lenth, W.

J. M. Supplee, E. A. Whittaker, and W. Lenth, Appl. Opt. 33, 6294 (1994).
[CrossRef] [PubMed]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Levi, F.

F. Levi, A. Godone, and J. Vanier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 466 (2000).
[CrossRef]

Liew, L.

Lutwak, R.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Mescher, M.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Moreland, J.

Nagel, A.

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Peake, G. M.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Rashed, A.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Schwindt, P. D. D.

Serkland, D. K.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Shah, V.

Supplee, J. M.

Tepolt, G.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Vanier, J.

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

F. Levi, A. Godone, and J. Vanier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 466 (2000).
[CrossRef]

Varghese, M.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

Vukicevic, N.

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Whittaker, E. A.

Wiedmann, W.

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

Wynands, R.

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

R. Wynands and A. Nagel, J. Opt. Soc. Am. B 16, 1617 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Wiedmann, IEEE Trans. Instrum. Meas. 49, 1313 (2000).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

F. Levi, A. Godone, and J. Vanier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 466 (2000).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (3)

Proc. IEEE (1)

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

Other (3)

E. Arimondo, in Progress in Optics Vol. XXXV, E.Wolf, ed. (Elsevier, 1996), p. 257.
[CrossRef]

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland, and G. M. Peake, in Proceedings of TimeNav'07: Joint 21st European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D.Coler, ed. (IEEE, 2007), p. 1327.
[CrossRef]

I. Ben-Aroya, M. Kahanov, and G. Eisenstein, in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L.A.Breakiron, ed. (Naval Observatory, 2006), p. 259.

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental setup. (b) Atomic energy level structure and the FM modulated spectrum of the diode laser. There are two sets of sidebands. Each contains an AM sideband (shown in black solid arrows) that is spectrally aligned with a hyperfine split transition (these are separated by 6.8 GHz ). Each also contains first-order FM sidebands shown in square-headed lines (blue online) and round-headed lines (red online) for the higher and lower energy AM sidebands, respectively. The FM frequency is of the order of kilohertz, and therefore the FM sideband spectral placings are not shown to scale. The FM modulation indices have opposite signs. The dashed arrows (green online) show the spectral scanning direction as the rf frequency increases.

Fig. 2
Fig. 2

(a) Measured slope and (b) accompanying noise versus FM parameters. Six FM sets representing various distinct operating regimes are marked. Their details are listed in Table 1.

Fig. 3
Fig. 3

(a) Estimated ADEV at τ = 1 s according to Eq. (1). Six FM sets representing various distinct operating regimes are marked. Their details are listed in Table 1. (b) Measured ADEV for the six parameter sets marked in (a) and Fig. 2 are described in Table 1.

Tables (1)

Tables Icon

Table 1 Estimated and Measured ADEV for Six FM Parameter Sets

Equations (1)

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σ y ( τ = 1 ) = 1 f 0 Δ f sig 2 Δ V sig 2 S Δ V 2 ,

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