Abstract

We investigate systematic errors associated with a common modulation technique used for phase-sensitive detection of a coherent-population-trapping (CPT) resonance. In particular, we show that modification of the CPT resonance line shape due to the presence of off-resonant fields leads to frequency shifts that may limit the stability of CPT-based atomic clocks. We also demonstrate that an alternative demodulation technique greatly reduces these effects.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Arimondo, "Coherent population trapping in laser spectroscopy," Prog. Opt. 35, 257-354 (1996).
    [CrossRef]
  2. J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
    [CrossRef]
  3. 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]
  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]
  5. M. Merimaa, T. Lindvall, I. Tittonen, and E. Ikonen, "All-optical atomic clock based on coherent population trapping in 85Rb," J. Opt. Soc. Am. B 20, 273-279 (2003).
    [CrossRef]
  6. J. Kitching, S. Knappe, and L. Hollberg, "Miniature vapor-cell atomic-frequency references," Appl. Phys. Lett. 81, 553-555 (2002).
    [CrossRef]
  7. S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
    [CrossRef] [PubMed]
  8. 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, 1676-1682 (2001).
    [CrossRef]
  9. J. C. Camparo and W. F. Buell, "Laser PM to AM conversion in atomic vapors and short term clock stability," in Proceedings of the 1997 IEEE International Frequency Control Symposium (IEEE, Piscataway, N.J., 1997), pp. 253-258 (1997).
  10. D. Strekalov, D. Aveline, N. Yu, R. Thompson, A. B. Matsko, and L. Maleki, "Stabilizing an optoelectronic microwave oscillator with photonic filters," J. Lightwave Technol. 21, 3052-3061 (2003).
    [CrossRef]
  11. New Focus Vortex laser, Model 6017.
  12. New Focus phase modulator, Model 4431.
  13. S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
    [CrossRef]
  14. A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
    [CrossRef]
  15. For this series of measurements, we used a vapor cell with isotopically enriched 87Rb and 22 Torr of Ne buffer gas. The change in buffer gas leads to both a different overall clock frequency shift and a narrower CPT resonance than the 5 Torr N2 cell we used for the other measurements we report here.
  16. F. L. Walls, "Errors in determining the center of a resonance line using sinusoidal frequency (phase) modulation," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 592-597 (1987).
    [CrossRef] [PubMed]
  17. A. de Marchi, G. D. Rovera, and A. Premoli, "Effects of servo loop modulation in atomic beam frequency standards employing a Ramsey cavity," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 582-591 (1987).
    [CrossRef] [PubMed]

2004 (1)

2003 (5)

M. Merimaa, T. Lindvall, I. Tittonen, and E. Ikonen, "All-optical atomic clock based on coherent population trapping in 85Rb," J. Opt. Soc. Am. B 20, 273-279 (2003).
[CrossRef]

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
[CrossRef]

D. Strekalov, D. Aveline, N. Yu, R. Thompson, A. B. Matsko, and L. Maleki, "Stabilizing an optoelectronic microwave oscillator with photonic filters," J. Lightwave Technol. 21, 3052-3061 (2003).
[CrossRef]

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

2002 (1)

J. Kitching, S. Knappe, and L. Hollberg, "Miniature vapor-cell atomic-frequency references," Appl. Phys. Lett. 81, 553-555 (2002).
[CrossRef]

2001 (2)

2000 (1)

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]

1996 (1)

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

1987 (2)

F. L. Walls, "Errors in determining the center of a resonance line using sinusoidal frequency (phase) modulation," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 592-597 (1987).
[CrossRef] [PubMed]

A. de Marchi, G. D. Rovera, and A. Premoli, "Effects of servo loop modulation in atomic beam frequency standards employing a Ramsey cavity," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 582-591 (1987).
[CrossRef] [PubMed]

Affolderbach, C.

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

Arimondo, E.

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

Aveline, D.

de Marchi, A.

A. de Marchi, G. D. Rovera, and A. Premoli, "Effects of servo loop modulation in atomic beam frequency standards employing a Ramsey cavity," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 582-591 (1987).
[CrossRef] [PubMed]

Delaney, M. J.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
[CrossRef]

Hollberg, L.

S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
[CrossRef] [PubMed]

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

J. Kitching, S. Knappe, and L. Hollberg, "Miniature vapor-cell atomic-frequency references," Appl. Phys. Lett. 81, 553-555 (2002).
[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, 1676-1682 (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]

Ikonen, E.

Janssen, D.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
[CrossRef]

Kitching, J.

S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
[CrossRef] [PubMed]

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

J. Kitching, S. Knappe, and L. Hollberg, "Miniature vapor-cell atomic-frequency references," Appl. Phys. Lett. 81, 553-555 (2002).
[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, 1676-1682 (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, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
[CrossRef] [PubMed]

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

J. Kitching, S. Knappe, and L. Hollberg, "Miniature vapor-cell atomic-frequency references," Appl. Phys. Lett. 81, 553-555 (2002).
[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, 1676-1682 (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]

Levine, M. W.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
[CrossRef]

Lindvall, T.

Maleki, L.

Matsko, A. B.

Merimaa, M.

Premoli, A.

A. de Marchi, G. D. Rovera, and A. Premoli, "Effects of servo loop modulation in atomic beam frequency standards employing a Ramsey cavity," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 582-591 (1987).
[CrossRef] [PubMed]

Robinson, H. G.

Rovera, G. D.

A. de Marchi, G. D. Rovera, and A. Premoli, "Effects of servo loop modulation in atomic beam frequency standards employing a Ramsey cavity," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 582-591 (1987).
[CrossRef] [PubMed]

Stähler, M.

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

Strekalov, D.

Taíchenachev, A. V.

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

Thompson, R.

Tittonen, I.

Vanier, J.

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
[CrossRef]

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.

F. L. Walls, "Errors in determining the center of a resonance line using sinusoidal frequency (phase) modulation," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 592-597 (1987).
[CrossRef] [PubMed]

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]

Wynands, R.

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[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, 1676-1682 (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]

Yu, N.

Yudin, V. I.

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

Appl. Phys. B (1)

S. Knappe, M. Stähler, C. Affolderbach, A. V. Taíchenachev, V. I. Yudin, and R. Wynands, "Simple parametrization of dark-resonance line shapes," Appl. Phys. B 76, 57-63 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

J. Kitching, S. Knappe, and L. Hollberg, "Miniature vapor-cell atomic-frequency references," Appl. Phys. Lett. 81, 553-555 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

J. Vanier, M. W. Levine, D. Janssen, and M. J. Delaney, "On the use of intensity optical pumping and coherent population trapping techniques in the implementation of atomic frequency standards," IEEE Trans. Instrum. Meas. 52, 822-831 (2003).
[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. Ferroelectr. Freq. Control (2)

F. L. Walls, "Errors in determining the center of a resonance line using sinusoidal frequency (phase) modulation," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 592-597 (1987).
[CrossRef] [PubMed]

A. de Marchi, G. D. Rovera, and A. Premoli, "Effects of servo loop modulation in atomic beam frequency standards employing a Ramsey cavity," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34, 582-591 (1987).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Opt. Lett. (1)

Phys. Rev. A (1)

A. V. Taíchenachev, V. I. Yudin, R. Wynands, M. Stähler, J. Kitching, and L. Hollberg, "Theory of dark resonances for alkali-metal vapors in a buffer-gas cell," Phys. Rev. A 67, 033810 (2003).
[CrossRef]

Prog. Opt. (1)

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

Other (4)

For this series of measurements, we used a vapor cell with isotopically enriched 87Rb and 22 Torr of Ne buffer gas. The change in buffer gas leads to both a different overall clock frequency shift and a narrower CPT resonance than the 5 Torr N2 cell we used for the other measurements we report here.

New Focus Vortex laser, Model 6017.

New Focus phase modulator, Model 4431.

J. C. Camparo and W. F. Buell, "Laser PM to AM conversion in atomic vapors and short term clock stability," in Proceedings of the 1997 IEEE International Frequency Control Symposium (IEEE, Piscataway, N.J., 1997), pp. 253-258 (1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Energy-level diagram for a three-level atom coupled via two near-resonant fields: the +1 and -1 sidebands from a modulated carrier laser field, with one-photon detuning Δ. Also shown are nonresonant fields (the carrier, 0, and the +2 and -2 sidebands), which can produce shifts and distortions in the CPT resonance. For the current experiments that use  87Rb, the two lower levels correspond to the ground-electronic-state hyperfine levels F=2 and F=1; the upper level corresponds to 52P1/2 F=2.

Fig. 2
Fig. 2

Schematic of the apparatus.

Fig. 3
Fig. 3

Typical dispersivelike CPT resonance measured with a slow-phase-modulation frequency fm=230 Hz and index =0.6 (solid curve). Also shown is a numerical calculation of the line shape expected from an ideal three-level system and just two near-resonant optical fields, for our observed Rabi frequencies and slow-phase-modulation index (dotted line). (The width and center frequency of the calculated resonance were scaled to match the measured resonance.) Note the asymmetry of the measured resonance compared with the calculation for the ideal three-level, two-field system.

Fig. 4
Fig. 4

(a) Measured  87Rb CPT clock frequency shift (δ) as a function of detuning (Δ) of the laser carrier frequency and resonant sidebands from F=2 resonance, for various slow-phase-modulation indices (). Here a zero frequency shift (δ=0) corresponds to the free-space  87Rb hyperfine frequency. The large offset of δ1360 Hz is due to the nitrogen buffer-gas pressure shift. (b) Dependence of the clock frequency on laser detuning (δ/Δ), determined from the slope of each individual line on plot (a), as a function of the slow-phase-modulation index. (c) Measured laser-frequency-independent shift, at Δ=0, as a function of the slow-phase-modulation index [see vertical line in plot (a)]. All data were taken at a slow-phase-modulation (lock-in) frequency fm=69 Hz. In graphs (a) and (c), measurement uncertainties were comparable with the size of the symbols shown.

Fig. 5
Fig. 5

Measured dependence of the CPT clock frequency on carrier field power at one-photon resonance (Δ=0), for two slow-phase-modulation frequencies and two total powers in the first-order sidebands. (Uncertainties in the measured clock frequencies are approximately equal to the size of the points.) Linear fits are shown for all data points at each of the two modulation frequencies.

Fig. 6
Fig. 6

CPT resonances with (solid curve) and without (dotted curve) the carrier field present. Both data sets were taken with fm=98 Hz and 0.6 and with a vapor cell containing isotopically enriched  87Rb and 22 Torr of Ne buffer gas.15

Fig. 7
Fig. 7

(a) Clock frequency dependence on laser frequency (δ/Δ) as a function of slow-phase-modulation frequency (fm) for both first- and third-harmonic demodulations. The modulation index =1.87 for both data sets. (b) Dependence of the clock transition’s measurement sensitivity (defined in text) on the slow-phase-modulation index () for fm=153 Hz. A much larger slow-phase-modulation index is required for optimal sensitivity in third-harmonic modulation. The lines are the results of a fit to the sensitivity expected for an ideal Lorentzian line shape.

Equations (3)

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

ε=ε0 cos 2πνoptt+ε-1 cos 2π(νopt-νμ)t+ε+1 cos 2π(νopt+νμ)t+ε-2 cos 2π(νopt-2νμ)t+ε+2 cos 2π×(νopt+2νμ)t+,
2πνμt2πνμt+ sin(2πfmt),
δ-Δ |Ω+1|2-|Ω-1|2γ2,

Metrics