Abstract

An all-optical microwave frequency standard based on coherent population trapping (CPT) in 85Rb is developed. The CPT resonances are detected by an ordinary edge-emitting diode laser in a simple optical setup. A buffer-gas mixture is carefully optimized to yield a narrow linewidth and a reduced temperature dependence of the resonance frequency. With the developed system we are able to measure ultranarrow optically induced hyperfine CPT resonances at <20 Hz, which is in good agreement with the linewidth calculated from experimental parameters. The frequency of an RF-signal generator has been stabilized to the CPT resonance between the two mF=0 magnetic sublevels. The relative frequency stability (square root of Allan variance) follows a slope of 3.5×10-11 τ-1/2 (1 s<τ<2000 s). The best stability of 6.4×10-13 is reached at an integration time of τ=2000 s. This stability is sufficient for many high-precision applications. Frequency-shift measurements were made to evaluate the frequency dependencies on the operation parameters.

© 2003 Optical Society of America

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    [CrossRef]
  3. J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
    [CrossRef]
  4. S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population-trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B 18, 1545-1553 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2001

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
[CrossRef]

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population-trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B 18, 1545-1553 (2001).
[CrossRef]

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

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

2000

M. Erhard, S. Nußmann, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802(R)1-4 (2000).
[CrossRef]

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 47, 466-470 (2000).
[CrossRef]

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

1999

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1-25 (1999); erratum, Appl. Phys. B 70, 315 (2000).
[CrossRef]

1998

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345-2358 (1998).
[CrossRef]

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

H. Talvitie, M. Merimaa, and E. Ikonen, “Frequency stabilization of a diode laser to Doppler-free spectrum of molecular iodine at 633 nm,” Opt. Commun. 152, 182-188 (1998).
[CrossRef]

K. L. Corvin, Z.-T. Lu, C. F. Hand, R. J. Epstein, and C. E. Wieman, “Frequency stabilized diode laser with the Zeeman shift in an atomic vapor,” Appl. Opt. 37, 3295–3298 (1998).
[CrossRef]

1996

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257-354 (1996).
[CrossRef]

1994

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

1993

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

1992

M. O. Scully and M. Fleischnauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360-1363 (1992).
[CrossRef] [PubMed]

M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191-201 (1992).
[CrossRef]

1988

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

1979

G. Orriols, “Nonabsorption resonances by nonlinear coherent effects in a three-level system,” Nuovo Cimento B 53, 1-23 (1979).
[CrossRef]

1976

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of R.F. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento B 36, 5-20 (1976).
[CrossRef]

1975

Ch. Ottinger, R. Scheps, G. W. York, and A. Gallagher, “Broadening of the Rb resonance lines by the noble gases,” Phys. Rev. A 11, 1815-1828 (1975).
[CrossRef]

M. Arditi and J.-L. Picqué, “Precision measurements of light shifts induced by a narrow GaAs laser in the 0-0 133Cs hyperfine transition,” J. Phys. B 8, L331-L335 (1975).
[CrossRef]

1974

J. Vanier, J.-F. Simard, and J.-S. Boulanger, “Relaxation and frequency shifts in the ground state of Rb85,” Phys. Rev. A 9, 1031-1040 (1974).
[CrossRef]

1958

P. L. Bender, E. C. Beaty, and A. R. Chi, “Optical detection of narrow Rb87 hyperfine absorption lines,” Phys. Rev. Lett. 1, 311-313 (1958).
[CrossRef]

1953

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472-473 (1953).
[CrossRef]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of R.F. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento B 36, 5-20 (1976).
[CrossRef]

Arditi, M.

M. Arditi and J.-L. Picqué, “Precision measurements of light shifts induced by a narrow GaAs laser in the 0-0 133Cs hyperfine transition,” J. Phys. B 8, L331-L335 (1975).
[CrossRef]

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257-354 (1996).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

Aspect, A.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

Beaty, E. C.

P. L. Bender, E. C. Beaty, and A. R. Chi, “Optical detection of narrow Rb87 hyperfine absorption lines,” Phys. Rev. Lett. 1, 311-313 (1958).
[CrossRef]

Bender, P. L.

P. L. Bender, E. C. Beaty, and A. R. Chi, “Optical detection of narrow Rb87 hyperfine absorption lines,” Phys. Rev. Lett. 1, 311-313 (1958).
[CrossRef]

Bergquist, J. C.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Bollinger, J. J.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Boulanger, J.-S.

J. Vanier, J.-F. Simard, and J.-S. Boulanger, “Relaxation and frequency shifts in the ground state of Rb85,” Phys. Rev. A 9, 1031-1040 (1974).
[CrossRef]

Brandt, S.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

Breton, M.

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

Chi, A. R.

P. L. Bender, E. C. Beaty, and A. R. Chi, “Optical detection of narrow Rb87 hyperfine absorption lines,” Phys. Rev. Lett. 1, 311-313 (1958).
[CrossRef]

Cohen-Tannoudji, C.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

Corvin, K. L.

Cyr, N.

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

Deng, J.

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

Dicke, R. H.

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472-473 (1953).
[CrossRef]

Drullinger, R. E.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

Epstein, R. J.

Erhard, M.

M. Erhard, S. Nußmann, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802(R)1-4 (2000).
[CrossRef]

Fleischnauer, M.

M. O. Scully and M. Fleischnauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360-1363 (1992).
[CrossRef] [PubMed]

Gallagher, A.

Ch. Ottinger, R. Scheps, G. W. York, and A. Gallagher, “Broadening of the Rb resonance lines by the noble gases,” Phys. Rev. A 11, 1815-1828 (1975).
[CrossRef]

Godone, A.

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 47, 466-470 (2000).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345-2358 (1998).
[CrossRef]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of R.F. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento B 36, 5-20 (1976).
[CrossRef]

Hand, C. F.

Helm, H.

M. Erhard, S. Nußmann, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802(R)1-4 (2000).
[CrossRef]

Hollberg, L.

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

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population-trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B 18, 1545-1553 (2001).
[CrossRef]

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
[CrossRef]

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

Ikonen, E.

H. Talvitie, M. Merimaa, and E. Ikonen, “Frequency stabilization of a diode laser to Doppler-free spectrum of molecular iodine at 633 nm,” Opt. Commun. 152, 182-188 (1998).
[CrossRef]

Imamura, T.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

Itano, W. M.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Jeffers, S. R.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Jennings, D. A.

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

Kinugawa, S.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

Kitching, J.

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

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
[CrossRef]

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population-trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B 18, 1545-1553 (2001).
[CrossRef]

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

Knappe, S.

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population-trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B 18, 1545-1553 (2001).
[CrossRef]

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
[CrossRef]

J. Kitching, H. G. Robinson, L. Hollberg, S. Knappe, and R. Wynands, “Optical-pumping 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. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313-1317 (2000).
[CrossRef]

Koga, K.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

Lee, W. D.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Levi, F.

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 47, 466-470 (2000).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345-2358 (1998).
[CrossRef]

Lu, Z.-T.

Meekhof, D.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Merimaa, M.

H. Talvitie, M. Merimaa, and E. Ikonen, “Frequency stabilization of a diode laser to Doppler-free spectrum of molecular iodine at 633 nm,” Opt. Commun. 152, 182-188 (1998).
[CrossRef]

Meschede, D.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

Mieti, G.

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of R.F. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento B 36, 5-20 (1976).
[CrossRef]

Nagel, A.

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1-25 (1999); erratum, Appl. Phys. B 70, 315 (2000).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

Nußmann, S.

M. Erhard, S. Nußmann, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802(R)1-4 (2000).
[CrossRef]

Orriols, G.

G. Orriols, “Nonabsorption resonances by nonlinear coherent effects in a three-level system,” Nuovo Cimento B 53, 1-23 (1979).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of R.F. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento B 36, 5-20 (1976).
[CrossRef]

Ottinger, Ch.

Ch. Ottinger, R. Scheps, G. W. York, and A. Gallagher, “Broadening of the Rb resonance lines by the noble gases,” Phys. Rev. A 11, 1815-1828 (1975).
[CrossRef]

Ouchi, Y.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

Parker, T. E.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Picqué, J.-L.

M. Arditi and J.-L. Picqué, “Precision measurements of light shifts induced by a narrow GaAs laser in the 0-0 133Cs hyperfine transition,” J. Phys. B 8, L331-L335 (1975).
[CrossRef]

Robinson, H. G.

Saburi, Y.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

Scheps, R.

Ch. Ottinger, R. Scheps, G. W. York, and A. Gallagher, “Broadening of the Rb resonance lines by the noble gases,” Phys. Rev. A 11, 1815-1828 (1975).
[CrossRef]

Scully, M. O.

M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191-201 (1992).
[CrossRef]

M. O. Scully and M. Fleischnauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360-1363 (1992).
[CrossRef] [PubMed]

Simard, J.-F.

J. Vanier, J.-F. Simard, and J.-S. Boulanger, “Relaxation and frequency shifts in the ground state of Rb85,” Phys. Rev. A 9, 1031-1040 (1974).
[CrossRef]

Suga, H.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

Sullivan, D. B.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Talvitie, H.

H. Talvitie, M. Merimaa, and E. Ikonen, “Frequency stabilization of a diode laser to Doppler-free spectrum of molecular iodine at 633 nm,” Opt. Commun. 152, 182-188 (1998).
[CrossRef]

Te?tu, M.

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

Vanier, J.

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 47, 466-470 (2000).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345-2358 (1998).
[CrossRef]

J. Vanier, J.-F. Simard, and J.-S. Boulanger, “Relaxation and frequency shifts in the ground state of Rb85,” Phys. Rev. A 9, 1031-1040 (1974).
[CrossRef]

Vansteenkiste, N.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

Vukicevic¸, N.

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

Walls, F. L.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

Weidmann, W.

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

Weis, A.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

Wieman, C. E.

Wineland, J. D.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Wynands, R.

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

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
[CrossRef]

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population-trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B 18, 1545-1553 (2001).
[CrossRef]

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

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1-25 (1999); erratum, Appl. Phys. B 70, 315 (2000).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

York, G. W.

Ch. Ottinger, R. Scheps, G. W. York, and A. Gallagher, “Broadening of the Rb resonance lines by the noble gases,” Phys. Rev. A 11, 1815-1828 (1975).
[CrossRef]

Appl. Opt.

Appl. Phys. B

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1-25 (1999); erratum, Appl. Phys. B 70, 315 (2000).
[CrossRef]

Electron. Lett.

Y. Saburi, K. Koga, S. Kinugawa, T. Imamura, H. Suga, and Y. Ouchi, “Short-term stability of laser-pumped rubidium gas cell frequency standard,” Electron. Lett. 30, 633-635 (1994).
[CrossRef]

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Compact atomic clock based on coherent population trapping,” Electron. Lett. 37, 1449-1451 (2001).
[CrossRef]

IEEE J. Quantum Electron.

G. Mieti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, “Laser-pumped rubidium frequency standards: new analysis and progress,” IEEE J. Quantum Electron. 34, 233-237 (1998).
[CrossRef]

IEEE Trans. Instrum. Meas.

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

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

IEEE Trans. Ultrason. Ferroelect. Freq. Control

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 47, 466-470 (2000).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

M. Arditi and J.-L. Picqué, “Precision measurements of light shifts induced by a narrow GaAs laser in the 0-0 133Cs hyperfine transition,” J. Phys. B 8, L331-L335 (1975).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol.

D. B. Sullivan, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jeffers, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, and J. D. Wineland, “Primary atomic frequency standards at NIST,” J. Res. Natl. Inst. Stand. Technol. 106, 47-63 (2001).
[CrossRef]

Nuovo Cimento B

G. Orriols, “Nonabsorption resonances by nonlinear coherent effects in a three-level system,” Nuovo Cimento B 53, 1-23 (1979).
[CrossRef]

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of R.F. transitions and laser beat resonances in oriented Na vapour,” Nuovo Cimento B 36, 5-20 (1976).
[CrossRef]

Opt. Commun.

H. Talvitie, M. Merimaa, and E. Ikonen, “Frequency stabilization of a diode laser to Doppler-free spectrum of molecular iodine at 633 nm,” Opt. Commun. 152, 182-188 (1998).
[CrossRef]

Phys. Rep.

M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191-201 (1992).
[CrossRef]

Phys. Rev.

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472-473 (1953).
[CrossRef]

Phys. Rev. A

M. Erhard, S. Nußmann, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802(R)1-4 (2000).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345-2358 (1998).
[CrossRef]

J. Vanier, J.-F. Simard, and J.-S. Boulanger, “Relaxation and frequency shifts in the ground state of Rb85,” Phys. Rev. A 9, 1031-1040 (1974).
[CrossRef]

Ch. Ottinger, R. Scheps, G. W. York, and A. Gallagher, “Broadening of the Rb resonance lines by the noble gases,” Phys. Rev. A 11, 1815-1828 (1975).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, “Selection rules and line strengths of Zeeman-split dark resonances,” Phys. Rev. A 58, 196-203 (1998).
[CrossRef]

Phys. Rev. Lett.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826-829 (1988).
[CrossRef] [PubMed]

M. O. Scully and M. Fleischnauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360-1363 (1992).
[CrossRef] [PubMed]

P. L. Bender, E. C. Beaty, and A. R. Chi, “Optical detection of narrow Rb87 hyperfine absorption lines,” Phys. Rev. Lett. 1, 311-313 (1958).
[CrossRef]

Prog. Opt.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257-354 (1996).
[CrossRef]

Other

J. Vanier, M. Levine, D. Janssen, and M. Delaney, “Coherent population trapping and intensity optical pumping: on their use in atomic frequency standards” in Proceedings of the Sixth Symposium on Frequency Standards and Metrology, P. Gill, ed. (World Scientific, Singapore, 2002), pp. 155-166.

J. C. Camparo, “Reducing the light-shift in diode laser pumped rubidium atomic clock,” in Proceedings of the 1996 IEEE International Frequency Control Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 988-992.

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, London, England, 1989).

M. B. Bloch, J. C. Ho, C. S. Stone, A. Syed, and F. L. Walls, “Stability of high-quality quartz crystal oscillators: an update,” in Proceedings of the 43rd Annual Symposium Frequency Control (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1989), pp. 80–84.

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Figures (9)

Fig. 1
Fig. 1

Three-level Λ system. The two laser modes coupling the ground states to the common upper state are designated by ωL1 and ωL2.

Fig. 2
Fig. 2

Experimental setup: LD, laser diode; μL, microlens; λ/2, half-wave plate; λ/4, quarter-wave plate; ND, neutral-density filter; M, mirror; PBS, polarizing beam splitter; BS, beam splitter; and PD, photodetector.

Fig. 3
Fig. 3

Lock-in amplifier output when the frequency difference of the laser modes is swept over the CPT resonance frequency. This FM-spectroscopy signal was used in the frequency-stabilization experiments.

Fig. 4
Fig. 4

Line shapes of CPT resonances measured with 0.3-μW/cm2 intensity. Modulation amplitudes of 10 Hz (upper curve) and 19 Hz (lower curve) peak-to-peak were used in the measurement. The error estimates ±0.5 Hz and ±1 Hz refer to the uncertainty in fitting, the overall uncertainty being larger especially in the upper graph due to difficulties in determining the zero level.

Fig. 5
Fig. 5

Influence of the total intensity on the measured CPT resonance frequency. A linear model fitted to the measurement yields a 0.3-Hz/μW/cm2 frequency dependence (dashed line) on the total intensity.

Fig. 6
Fig. 6

Measured dependence of the CPT resonance frequency on the intensity ratio of laser modes. A linear model fitted to the measurement yields the frequency dependence -1.3 Hz×η (dashed line). The total intensity in this measurement was 2 μW/cm2.

Fig. 7
Fig. 7

RF frequency as a function of the laser frequency. The operating parameters are the same as typically used in frequency-stabilization experiments. A linear model fitted to the measurement yields a 1.4 mHz/MHz frequency dependence (dashed curve) on the laser frequency. The horizontal scale is the optical detuning from the -130-MHz pressure-shifted F=2F=3 transition.

Fig. 8
Fig. 8

Influence of the applied magnetic field on the measured frequency. As the optical setup is incidentally aligned approximately in the north-south direction, the magnetic field of Earth partially couples into the system through the optical windows. The calculated value is obtained from the Breit–Rabi formula.

Fig. 9
Fig. 9

Measured relative frequency stability (square root of Allan variance) of an RF-signal generator locked to the CPT resonance between the mF=0 magnetic sublevels (circles). For comparison, the relative frequency stability of a high-quality crystal oscillator (squares) and a commercial cesium atomic clock (triangles) are also given. The crystal oscillator data, with prediction to longer integration times, are taken from Ref. 30.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

γ2=C1p0DNeDArDNepAr+DArpNe+N0p0 (ν¯Rb-NeσNepNe+ν¯Rb-ArσArpAr)+C2NRbν¯Rb-Rbσse,
C2=6I+18I+4,

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