Abstract

We describe the optimization of a Frequency Locked Loop (FLL) in an atomic clock which is based on Coherent Population Trapping (CPT) in 87Rb vapor using the D2 transition. The FLL uses frequency modulation (FM) spectroscopy and we study the effect of FM parameters (modulation frequency and index) on the sensitivity and the signal to noise ratio of the feedback signal in the FLL. The clock which employs a small spherical glass cell containing 87Rb atoms and a buffer gas, exhibits a short term stability of 3×10-11/√τ. The long term relative frequency stability of the 10 MHz output is better than 10-10 with a drift of 10-11 per day.

© 2007 Optical Society of America

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  1. J. Vanier, "Atomic clocks based on coherent population trapping: a review," Appl. Phys. B 81, 421-442 (2005).
    [CrossRef]
  2. S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, "A chip-scale atomic clock based on 87Rb with improved frequency stability," Opt. Express 13, 1249-1253 (2005).
    [CrossRef] [PubMed]
  3. R. Lutwak, P. Vlitas, M. Varghese, M. Mescher, D. K. Serkland and G. M. Peake, "The MAC - a Miniature Atomic Clock," in proceedings of 2005 Joint IEEE International Frequency Control (UFFC) Symposium and the 37th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, D. Coler, ed. (Vancouver, BC, Canada, 2005), pp. 752-757.
  4. R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland and G. M. Peake, "The Miniature Atomic Clock-Pre-Production Results," in proceedings of TimeNav’07: Joint 21th European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D. Coler, ed., (Geneva, Switzerland, 2007), pp. 1327-1333.
  5. N. Cyr, M. Têtu and M. Breton, "All-optical microwave frequency standard: a proposal," IEEE Trans. Instrum. Meas. 42, 640-649 (1993).
    [CrossRef]
  6. D. V. Kuksenkov, H. Temkin and S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
    [CrossRef]
  7. V. Gerginov, V. Shah, S. Knappe, P. D. D. Schwindt, L. Hollberg and J. Kitching, "Atom-based stabilization for laser-pumped atomic clocks, " in Proceedings of the 20th European Frequency and Time Forum (EFTF), D. Coler, ed., (Braunschweig, Germany, 2006), pp. 224-228.
  8. I. Ben-Aroya, M. Kahanov and G. Eisenstein, "A CPT based 87Rb atomic clock employing a small spherical glass vapor cell," in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L. A. Breakiron, ed. (Reston, VA, USA, 2006), pp. 259-270.
  9. 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, 145-152 (1983).
    [CrossRef]
  10. M. Gehrtz, G. C. Bjorklund and E. A. Whittaker, "Quantum-limited frequency-modulation spectroscopy," J. Opt. Soc. Am. B. 2, 1510-1526 (1985).
    [CrossRef]
  11. R. Wynands and A. Nagel, "Inversion of frequency-modulation spectroscopy line shapes," J. Opt. Soc. Am. B. 16, 1617-1622 (1999).
    [CrossRef]
  12. J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
    [CrossRef]
  13. J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
    [CrossRef]
  14. D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
    [CrossRef]

2005 (3)

J. Vanier, "Atomic clocks based on coherent population trapping: a review," Appl. Phys. B 81, 421-442 (2005).
[CrossRef]

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, "A chip-scale atomic clock based on 87Rb with improved frequency stability," Opt. Express 13, 1249-1253 (2005).
[CrossRef] [PubMed]

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[CrossRef]

2001 (1)

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

2000 (1)

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

1999 (1)

R. Wynands and A. Nagel, "Inversion of frequency-modulation spectroscopy line shapes," J. Opt. Soc. Am. B. 16, 1617-1622 (1999).
[CrossRef]

1995 (1)

D. V. Kuksenkov, H. Temkin and S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
[CrossRef]

1993 (1)

N. Cyr, M. Têtu and M. Breton, "All-optical microwave frequency standard: a proposal," IEEE Trans. Instrum. Meas. 42, 640-649 (1993).
[CrossRef]

1985 (1)

M. Gehrtz, G. C. Bjorklund and E. A. Whittaker, "Quantum-limited frequency-modulation spectroscopy," J. Opt. Soc. Am. B. 2, 1510-1526 (1985).
[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, 145-152 (1983).
[CrossRef]

Bjorklund, G. C.

M. Gehrtz, G. C. Bjorklund and E. A. Whittaker, "Quantum-limited frequency-modulation spectroscopy," J. Opt. Soc. Am. B. 2, 1510-1526 (1985).
[CrossRef]

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, 145-152 (1983).
[CrossRef]

Breton, M.

N. Cyr, M. Têtu and M. Breton, "All-optical microwave frequency standard: a proposal," IEEE Trans. Instrum. Meas. 42, 640-649 (1993).
[CrossRef]

Crescimanno, M.

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[CrossRef]

Cyr, N.

N. Cyr, M. Têtu and M. Breton, "All-optical microwave frequency standard: a proposal," IEEE Trans. Instrum. Meas. 42, 640-649 (1993).
[CrossRef]

Gehrtz, M.

M. Gehrtz, G. C. Bjorklund and E. A. Whittaker, "Quantum-limited frequency-modulation spectroscopy," J. Opt. Soc. Am. B. 2, 1510-1526 (1985).
[CrossRef]

Hollberg, L.

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, "A chip-scale atomic clock based on 87Rb with improved frequency stability," Opt. Express 13, 1249-1253 (2005).
[CrossRef] [PubMed]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

Kitching, J.

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, "A chip-scale atomic clock based on 87Rb with improved frequency stability," Opt. Express 13, 1249-1253 (2005).
[CrossRef] [PubMed]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

Knappe, S.

S. Knappe, P. D. D. Schwindt, V. Shah, L. Liew, J. Moreland, L. Hollberg, and J. Kitching, "A chip-scale atomic clock based on 87Rb with improved frequency stability," Opt. Express 13, 1249-1253 (2005).
[CrossRef] [PubMed]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

Kuksenkov, D. V.

D. V. Kuksenkov, H. Temkin and S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
[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, 145-152 (1983).
[CrossRef]

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, 145-152 (1983).
[CrossRef]

Liew, L.

Moreland, J.

Nagel, A.

R. Wynands and A. Nagel, "Inversion of frequency-modulation spectroscopy line shapes," J. Opt. Soc. Am. B. 16, 1617-1622 (1999).
[CrossRef]

Novikova, I.

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[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, 145-152 (1983).
[CrossRef]

Phillips, D. F.

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[CrossRef]

Robinson, H. G.

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

Schwindt, P. D. D.

Shah, V.

Swirhun, S.

D. V. Kuksenkov, H. Temkin and S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
[CrossRef]

Temkin, H.

D. V. Kuksenkov, H. Temkin and S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
[CrossRef]

Têtu, M.

N. Cyr, M. Têtu and M. Breton, "All-optical microwave frequency standard: a proposal," IEEE Trans. Instrum. Meas. 42, 640-649 (1993).
[CrossRef]

Vanier, J.

J. Vanier, "Atomic clocks based on coherent population trapping: a review," Appl. Phys. B 81, 421-442 (2005).
[CrossRef]

Vukicevic, N.

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[CrossRef]

Wang, C. Y.-T.

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[CrossRef]

Whittaker, E. A.

M. Gehrtz, G. C. Bjorklund and E. A. Whittaker, "Quantum-limited frequency-modulation spectroscopy," J. Opt. Soc. Am. B. 2, 1510-1526 (1985).
[CrossRef]

Wiedmann, W.

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

Wynands, R.

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

R. Wynands and A. Nagel, "Inversion of frequency-modulation spectroscopy line shapes," J. Opt. Soc. Am. B. 16, 1617-1622 (1999).
[CrossRef]

Appl. Phys. B (1)

J. Vanier, "Atomic clocks based on coherent population trapping: a review," Appl. Phys. B 81, 421-442 (2005).
[CrossRef]

Appl. Phys. B. (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, 145-152 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

D. V. Kuksenkov, H. Temkin and S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands and W. Wiedmann, "A microwave frequency reference based on VCSEL-driven dark lineresonances in Cs vapor," IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

N. Cyr, M. Têtu and M. Breton, "All-optical microwave frequency standard: a proposal," IEEE Trans. Instrum. Meas. 42, 640-649 (1993).
[CrossRef]

J. Opt. Soc. Am. B. (4)

D. F. Phillips, I. Novikova, C. Y.-T. Wang, R. L. Walsworth and M. Crescimanno, "Modulation-induced frequency shifts in a coherent-population-trapping-based atomic clock," J. Opt. Soc. Am. B. 22, 305-310 (2005).
[CrossRef]

M. Gehrtz, G. C. Bjorklund and E. A. Whittaker, "Quantum-limited frequency-modulation spectroscopy," J. Opt. Soc. Am. B. 2, 1510-1526 (1985).
[CrossRef]

R. Wynands and A. Nagel, "Inversion of frequency-modulation spectroscopy line shapes," J. Opt. Soc. Am. B. 16, 1617-1622 (1999).
[CrossRef]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe and R. Wynands, "Optical-noise in laser-pumped, all-optical microwave frequency references," J. Opt. Soc. Am. B. 18, 1676-1683 (2001).
[CrossRef]

Opt. Express (1)

Other (4)

R. Lutwak, P. Vlitas, M. Varghese, M. Mescher, D. K. Serkland and G. M. Peake, "The MAC - a Miniature Atomic Clock," in proceedings of 2005 Joint IEEE International Frequency Control (UFFC) Symposium and the 37th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, D. Coler, ed. (Vancouver, BC, Canada, 2005), pp. 752-757.

R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. Leblanc, M. Mescher, D. K. Serkland and G. M. Peake, "The Miniature Atomic Clock-Pre-Production Results," in proceedings of TimeNav’07: Joint 21th European Frequency and Time Forum (EFTF) & IEEE International Frequency Control Symposium (IEEE-FCS), D. Coler, ed., (Geneva, Switzerland, 2007), pp. 1327-1333.

V. Gerginov, V. Shah, S. Knappe, P. D. D. Schwindt, L. Hollberg and J. Kitching, "Atom-based stabilization for laser-pumped atomic clocks, " in Proceedings of the 20th European Frequency and Time Forum (EFTF), D. Coler, ed., (Braunschweig, Germany, 2006), pp. 224-228.

I. Ben-Aroya, M. Kahanov and G. Eisenstein, "A CPT based 87Rb atomic clock employing a small spherical glass vapor cell," in Proceedings of the 38th Annual Precise Time & Time Interval (PTTI) Systems & Applications Meeting, L. A. Breakiron, ed. (Reston, VA, USA, 2006), pp. 259-270.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the CPT based atomic clock. On the right is shown a photograph of a small spherical glass cell.

Fig. 2.
Fig. 2.

(a) CPT measurement using FM spectroscopy. The blue dashed-line represents the “in-phase” component while the solid red line represents the ‘quadrature’. (b) Direct measurement of the CPT resonance. The resonance fits a Lorentzian with a width of 186 Hz (red-dotted line).

Fig. 3.
Fig. 3.

(a) Maximum measured slope (in units of μV rms/Hz) of the “in-phase” component versus FM parameters. Each point represents an optimum rotation of the two Lock-in outputs with respect to each other. The (b) Measured noise spectral density accompanying the “in-phase” component (in units of μV rms/Hz1/2).

Fig. 4.
Fig. 4.

(a) Measured Allen deviation of the CPT based clock. The red dashed-line equals 3×10-111/2. (b) Frequency measurement of the 10 MHz output.

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