Abstract

A low-cost, potentially compact and robust microwave frequency reference can be constructed by use of vertical-cavity surface-emitting lasers and coherent population-trapping resonances in Cs vapor cells. Fractional frequency instabilities of 2×10-11/τ/s have been achieved with a minimum of 7×10-13 at τ=1000 s. The performance of this device as a function of external parameters such as light intensity, optical detuning, and cell temperature is discussed. The dependence of the dark-line resonance signal on these parameters can be understood largely by means of a simple, three-level model. The short-term stability depends critically on the optical detuning, whereas the long-term stability is limited currently by line shifts due to drifts in cell temperature.

© 2001 Optical Society of America

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    [CrossRef]
  25. N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54, 1103–1182 (1982).
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  26. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
    [CrossRef]
  27. W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–243 (1972).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2001 (1)

D. Meekhof, S. R. Jefferts, M. Stepanovic, and T. Parker, “Accuracy evaluation of a cesium fountain primary frequency standard at NIST,” IEEE Trans. Instrum. Meas. 50, 507–509 (2001).
[CrossRef]

2000 (3)

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

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

A. Nagel, C. Affolderbach, S. Knappe, and R. Wynands, “Influence of excited state hyperfine structure on ground state coherence,” Phys. Rev. A 61, 012504 (2000).
[CrossRef]

1999 (4)

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent microwave emission in cesium under coherent population trapping,” Phys. Rev. A 59, R12–R15 (1999).
[CrossRef]

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 609–615 (1999).
[CrossRef]

A. Godone, F. Levi, and J. Vanier, “Coherent microwave emission without population inversion: a new atomic frequency standard,” IEEE Trans. Instrum. Meas. 48, 504–507 (1999).
[CrossRef]

1998 (1)

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]

1997 (1)

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas induced linewidth reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56, R1063–R1066 (1997).
[CrossRef]

1996 (1)

E. Arimondo, “Relaxation processes in coherent population trapping,” Phys. Rev. A 54, 2216–2223 (1996).
[CrossRef] [PubMed]

1995 (1)

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

1993 (2)

1991 (1)

1990 (1)

J. R. Zacharias, unpublished (1953), described in N. F. Ramsey, “Nobel lecture: experiments with separated oscillatory fields and hydrogen masers,” Rev. Mod. Phys. 62, 541 (1990).
[CrossRef]

1989 (1)

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[CrossRef] [PubMed]

1987 (1)

C. Rahman and H. G. Robison, “Rb 0–0 hyperfine transition in evacuated wall-coated cell at melting temperature,” IEEE J. Quantum Electron. QE-23, 452–454 (1987).
[CrossRef]

1985 (1)

1983 (2)

1982 (2)

N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54, 1103–1182 (1982).
[CrossRef]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated, resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48, 867–870 (1982).
[CrossRef]

1981 (2)

1972 (1)

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–243 (1972).
[CrossRef]

1971 (1)

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Affolderbach, C.

A. Nagel, C. Affolderbach, S. Knappe, and R. Wynands, “Influence of excited state hyperfine structure on ground state coherence,” Phys. Rev. A 61, 012504 (2000).
[CrossRef]

Allard, N.

N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54, 1103–1182 (1982).
[CrossRef]

Arimondo, E.

E. Arimondo, “Relaxation processes in coherent population trapping,” Phys. Rev. A 54, 2216–2223 (1996).
[CrossRef] [PubMed]

Bahoura, M.

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

Barnes, J.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Bernacki, B. E.

Beverini, N.

N. Beverini, F. Strumia, and G. Rovera, “Buffer gas pressure shifts in the mF=0↔mF=0 ground state hyperfine line in Cs,” Opt. Commun. 37, 394–396 (1981).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Brandt, S.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas induced linewidth reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56, R1063–R1066 (1997).
[CrossRef]

Breton, M.

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

Chi, A.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Chu, S.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[CrossRef] [PubMed]

Clairon, A.

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

Cry, N.

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

Cutler, L.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

De Voe, R.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[CrossRef] [PubMed]

Ezekiel, S.

Ghezali, S.

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

Godone, A.

J. Vanier, A. Godone, and F. Levi, “Coherent microwave emission in cesium under coherent population trapping,” Phys. Rev. A 59, R12–R15 (1999).
[CrossRef]

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 609–615 (1999).
[CrossRef]

A. Godone, F. Levi, and J. Vanier, “Coherent microwave emission without population inversion: a new atomic frequency standard,” IEEE Trans. Instrum. Meas. 48, 504–507 (1999).
[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]

Happer, W.

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–243 (1972).
[CrossRef]

Healey, D.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Hemmer, P. R.

Hoe, S.-T.

Hollberg, L.

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

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

Jefferts, S. R.

D. Meekhof, S. R. Jefferts, M. Stepanovic, and T. Parker, “Accuracy evaluation of a cesium fountain primary frequency standard at NIST,” IEEE Trans. Instrum. Meas. 50, 507–509 (2001).
[CrossRef]

Kasevich, M.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[CrossRef] [PubMed]

Kielkopf, J.

N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54, 1103–1182 (1982).
[CrossRef]

Kitching, J.

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

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

Knappe, S.

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

A. Nagel, C. Affolderbach, S. Knappe, and R. Wynands, “Influence of excited state hyperfine structure on ground state coherence,” Phys. Rev. A 61, 012504 (2000).
[CrossRef]

Kumar, P.

Lamela-Rivera, H.

Laurent, P.

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

Lea, S.

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

Leeson, D.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Leiby Jr., C. C.

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” 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,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Levi, F.

A. Godone, F. Levi, and J. Vanier, “Coherent microwave emission without population inversion: a new atomic frequency standard,” IEEE Trans. Instrum. Meas. 48, 504–507 (1999).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent microwave emission in cesium under coherent population trapping,” Phys. Rev. A 59, R12–R15 (1999).
[CrossRef]

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 609–615 (1999).
[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]

McGunigal, T.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Meekhof, D.

D. Meekhof, S. R. Jefferts, M. Stepanovic, and T. Parker, “Accuracy evaluation of a cesium fountain primary frequency standard at NIST,” IEEE Trans. Instrum. Meas. 50, 507–509 (2001).
[CrossRef]

Meschede, D.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas induced linewidth reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56, R1063–R1066 (1997).
[CrossRef]

Mullen, J.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Nagel, A.

A. Nagel, C. Affolderbach, S. Knappe, and R. Wynands, “Influence of excited state hyperfine structure on ground state coherence,” Phys. Rev. A 61, 012504 (2000).
[CrossRef]

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas induced linewidth reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56, R1063–R1066 (1997).
[CrossRef]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Parker, T.

D. Meekhof, S. R. Jefferts, M. Stepanovic, and T. Parker, “Accuracy evaluation of a cesium fountain primary frequency standard at NIST,” IEEE Trans. Instrum. Meas. 50, 507–509 (2001).
[CrossRef]

Picard, R. N.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated, resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48, 867–870 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Ultrahigh-resolution spectroscopy and frequency standards in the microwave and far-infrared regions using optical lasers,” Opt. Lett. 6, 298–300 (1981).
[CrossRef] [PubMed]

Poelker, M.

Rahman, C.

C. Rahman and H. G. Robison, “Rb 0–0 hyperfine transition in evacuated wall-coated cell at melting temperature,” IEEE J. Quantum Electron. QE-23, 452–454 (1987).
[CrossRef]

Riis, E.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[CrossRef] [PubMed]

Robinson, H. G.

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

Robison, H. G.

C. Rahman and H. G. Robison, “Rb 0–0 hyperfine transition in evacuated wall-coated cell at melting temperature,” IEEE J. Quantum Electron. QE-23, 452–454 (1987).
[CrossRef]

Rovera, G.

N. Beverini, F. Strumia, and G. Rovera, “Buffer gas pressure shifts in the mF=0↔mF=0 ground state hyperfine line in Cs,” Opt. Commun. 37, 394–396 (1981).
[CrossRef]

Santarelli, G.

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

Shahriar, M. S.

Shapiro, J. H.

Smith, S. P.

Smith, W.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Stepanovic, M.

D. Meekhof, S. R. Jefferts, M. Stepanovic, and T. Parker, “Accuracy evaluation of a cesium fountain primary frequency standard at NIST,” IEEE Trans. Instrum. Meas. 50, 507–509 (2001).
[CrossRef]

Strumia, F.

N. Beverini, F. Strumia, and G. Rovera, “Buffer gas pressure shifts in the mF=0↔mF=0 ground state hyperfine line in Cs,” Opt. Commun. 37, 394–396 (1981).
[CrossRef]

Sydnor, R.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Te?tu, M.

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

Thomas, J. E.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated, resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48, 867–870 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Ultrahigh-resolution spectroscopy and frequency standards in the microwave and far-infrared regions using optical lasers,” Opt. Lett. 6, 298–300 (1981).
[CrossRef] [PubMed]

Vanier, J.

J. Vanier, A. Godone, and F. Levi, “Coherent microwave emission in cesium under coherent population trapping,” Phys. Rev. A 59, R12–R15 (1999).
[CrossRef]

A. Godone, F. Levi, and J. Vanier, “Coherent microwave emission without population inversion: a new atomic frequency standard,” IEEE Trans. Instrum. Meas. 48, 504–507 (1999).
[CrossRef]

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 609–615 (1999).
[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]

Vessot, R.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Vukicevic, N.

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

J. Kitching, S. Knappe, N. Vukičević, L. Hollberg, R. Wynands, and W. Weidemann, “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.

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

Weidemann, W.

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

Willis, C. R.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated, resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48, 867–870 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Ultrahigh-resolution spectroscopy and frequency standards in the microwave and far-infrared regions using optical lasers,” Opt. Lett. 6, 298–300 (1981).
[CrossRef] [PubMed]

Winkler, G.

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

Wynands, R.

A. Nagel, C. Affolderbach, S. Knappe, and R. Wynands, “Influence of excited state hyperfine structure on ground state coherence,” Phys. Rev. A 61, 012504 (2000).
[CrossRef]

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

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas induced linewidth reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56, R1063–R1066 (1997).
[CrossRef]

Zacharias, J. R.

J. R. Zacharias, unpublished (1953), described in N. F. Ramsey, “Nobel lecture: experiments with separated oscillatory fields and hydrogen masers,” Rev. Mod. Phys. 62, 541 (1990).
[CrossRef]

Zibrov, A. S.

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

Appl. Phys. B (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Europhys. Lett. (1)

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Rahman and H. G. Robison, “Rb 0–0 hyperfine transition in evacuated wall-coated cell at melting temperature,” IEEE J. Quantum Electron. QE-23, 452–454 (1987).
[CrossRef]

IEEE Trans. Instrum. Meas. (6)

A. Clairon, P. Laurent, G. Santarelli, S. Ghezali, S. Lea, and M. Bahoura, “A cesium fountain frequency standard: preliminary results,” IEEE Trans. Instrum. Meas. 44, 128–131 (1995).
[CrossRef]

D. Meekhof, S. R. Jefferts, M. Stepanovic, and T. Parker, “Accuracy evaluation of a cesium fountain primary frequency standard at NIST,” IEEE Trans. Instrum. Meas. 50, 507–509 (2001).
[CrossRef]

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

A. Godone, F. Levi, and J. Vanier, “Coherent microwave emission without population inversion: a new atomic frequency standard,” IEEE Trans. Instrum. Meas. 48, 504–507 (1999).
[CrossRef]

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

J. Barnes, A. Chi, L. Cutler, D. Healey, D. Leeson, T. McGunigal, J. Mullen, W. Smith, R. Sydnor, R. Vessot, and G. Winkler, “Characterization of frequency stability,” IEEE Trans. Instrum. Meas. IM-20, 105–120 (1971).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

F. Levi, A. Godone, and J. Vanier, “The light shift effect in the coherent population trapping cesium maser,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 609–615 (1999).
[CrossRef]

N. Vukičević, A. S. Zibrov, L. Hollberg, F. L. Walls, J. Kitching, and H. G. Robinson, “Compact diode-laser based rubidium frequency reference,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1122–1126 (2000).
[CrossRef]

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

Opt. Commun. (1)

N. Beverini, F. Strumia, and G. Rovera, “Buffer gas pressure shifts in the mF=0↔mF=0 ground state hyperfine line in Cs,” Opt. Commun. 37, 394–396 (1981).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (5)

J. Vanier, A. Godone, and F. Levi, “Coherent microwave emission in cesium under coherent population trapping,” Phys. Rev. A 59, R12–R15 (1999).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas induced linewidth reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56, R1063–R1066 (1997).
[CrossRef]

E. Arimondo, “Relaxation processes in coherent population trapping,” Phys. Rev. A 54, 2216–2223 (1996).
[CrossRef] [PubMed]

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]

A. Nagel, C. Affolderbach, S. Knappe, and R. Wynands, “Influence of excited state hyperfine structure on ground state coherence,” Phys. Rev. A 61, 012504 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612–615 (1989).
[CrossRef] [PubMed]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. N. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated, resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48, 867–870 (1982).
[CrossRef]

Rev. Mod. Phys. (3)

J. R. Zacharias, unpublished (1953), described in N. F. Ramsey, “Nobel lecture: experiments with separated oscillatory fields and hydrogen masers,” Rev. Mod. Phys. 62, 541 (1990).
[CrossRef]

N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54, 1103–1182 (1982).
[CrossRef]

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–243 (1972).
[CrossRef]

Other (4)

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Frequency-dependent optical pumping in atomic Λ systems,” Opt. Lett. (to be published).

S. Knappe, Institute für Angeuwandte Physik, Universität Bonn, Weglestrasse 8, D-53115 Bonn, Germany; J. Kitching and L. Hollberg, Time and Frequency Division, Mail Stop 847.10, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303 (personal communication, 2000).

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

J. A. Kusters and C. A. Adams, “Performance requirements of communication base station time standards,” RF Design (May 1999), pp. 28–38.

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Figures (12)

Fig. 1
Fig. 1

Left: Spectrum of the dark-resonance absorption signal with dc detection of the laser power transmitted through the cell, normalized to the maximum absorbed power. Right: Level diagram of the Cs D2 line. Λ systems can be formed with the ground states and the excited states F=3 and 4.

Fig. 2
Fig. 2

Three-level scheme used to model the CPT resonances. The optical detuning δL and the detuning from the dark-line resonance in this diagram are negative.

Fig. 3
Fig. 3

Experimental setup of the compact dark-resonance Cs clock. The 4.6-GHz signal modulates the laser injection current to produce two sidebands separated by 9.2 GHz, which probe the dark-line resonance in the Cs cell. The lock-in at 10 kHz is used to lock the laser to the Cs resonance, and the lock-in at 530 Hz is used to lock the 5-MHz quartz crystal that in turn controls the frequency of the 4.6-GHz source.

Fig. 4
Fig. 4

Full width of the dark-resonance error signal measured at 1-kHz modulation frequency as a function of the laser intensity contained in the two first-order sidebands incident on the cell (squares). The solid line is a fit of Eq. (2).

Fig. 5
Fig. 5

Height of the dark-resonance error signal measured in a 2-cm cell containing 5.1-kPa neon as a function of the laser intensity contained in the two first-order sidebands incident on the cell. The squares are the measured values, and the solid curve is relation (3) plotted for the parameter values determined from slope and offset in a plot like Fig. 4.

Fig. 6
Fig. 6

Frequency shift of the 0–0 resonance from the unperturbed ground-state hyperfine frequency as a function of total laser intensity, measured under the locked condition and compared with a hydrogen maser reference.

Fig. 7
Fig. 7

Power spectral density at 530 Hz as a function of the optical detuning δL, normalized to the power on the detector (squares). The solid curve in the plot is the calculated noise level when the detector’s electronic noise and the laser’s intensity and frequency noise are taken into account.15

Fig. 8
Fig. 8

Measured amplitude of the dark-resonance error signal as a function of optical detuning δL taken for a total resonant laser intensity of 45 µW/cm2 and 9.7 kPa of Ne. The inset shows fitted curves for the amplitude of the dark line for data from Ref. 24 taken for a laser intensity of 0.97 mW/cm2 and 7.2 kPa of Ne. The vertical lines show the position of the excited state’s hyperfine levels.

Fig. 9
Fig. 9

Full width at half-maximum of the dark-resonance error signal as a function of optical detuning δL taken for a total resonant laser intensity of 45 µW/cm2 and 9.7-kPa Ne. The inset shows curves fitted to the data of Ref. 24 taken for a laser intensity of 0.97 mW/cm2 and 7.2 kPa of Ne. The vertical lines show the position of the excited state’s hyperfine levels.

Fig. 10
Fig. 10

Measured frequency shift of the 0–0 resonance from the unperturbed ground state’s hyperfine frequency as a function of optical detuning δL, taken for a total resonant laser intensity of 45 µW/cm2 and 9.7 kPa of Ne. The inset shows curves fitted to the data of Ref. 24 taken for a laser intensity of 0.97 mW/cm2 and 7.2 kPa of Ne.

Fig. 11
Fig. 11

Measured amplitude of the dark-resonance error signal as a function of cell temperature.

Fig. 12
Fig. 12

Allan deviation of the 4.6-GHz signal as a function of averaging time τ, when locked as measured for the tabletop setup with a cell containing 9.7 kPa of neon (filled squares) or 5.3 kPa of a Ne–Ar mixture (open squares). The mixed gas cell has a lower temperature dependence of the frequency of the dark-line resonance and hence better stability for larger times. This is at the expense of somewhat worse stability of short times.

Equations (3)

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|NCg1|2-g2 exp(-iΔt)|1,
γCPT=2Γ12+g2Γ,
HnCsg4Γ312Γ12+g2/Γ.

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