Abstract

We demonstrate the excitation and low-noise differential detection of a coherent population trapping (CPT) resonance with two modulated optical fields with orthogonal circular polarizations. When a microwave phase delay of λ/4 is introduced in the optical path of one of the fields, the difference in the power transmitted through the cell in each polarization shows a narrow, dispersive resonance. The differential detection allows a high degree of suppression of laser-induced noise and will enable nearly shot-noise-limited operation of atomic frequency references and magnetometers based on CPT.

© 2006 Optical Society of America

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    [CrossRef]
  2. S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  3. G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
    [CrossRef]
  4. E. Arimondo and G. Orriols, "Non-Absorbing Atomic Coherences by Coherent 2-Photon Transitions in a 3-Level Optical-Pumping," Lett. Nuovo Cim. 17, 333-338 (1976).
    [CrossRef]
  5. S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
    [CrossRef]
  6. D. Kosachiov, B. Matisov, and Y. Rozhdestvensky, "Coherent Population Trapping - Sensitivity of an Atomic System to the Relative Phase of Exciting Fields," Opt. Commun. 85, 209-212 (1991).
    [CrossRef]
  7. M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
    [CrossRef]
  8. W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
    [CrossRef]
  9. E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
    [CrossRef]
  10. C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
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    [CrossRef] [PubMed]
  15. S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
    [CrossRef]
  16. Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
    [CrossRef] [PubMed]
  17. A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
    [CrossRef]
  18. T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  20. 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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  24. S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
    [CrossRef]
  25. A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
    [CrossRef]
  26. P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
    [CrossRef]
  27. A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
    [CrossRef] [PubMed]
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2005 (4)

A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
[CrossRef]

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, "On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of Rb-87," JETP Letters 82, 398-403 (2005).
[CrossRef]

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

2004 (6)

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

2002 (2)

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[CrossRef]

M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, "Coherent population trapping resonances in thermal Rb-85 vapor: D-1 versus D-2 line excitation," Opt. Lett. 27, 1472-1474 (2002).
[CrossRef]

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]

1999 (2)

M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

1998 (2)

J. C. Camparo, "Conversion of laser phase noise to amplitude noise in an optically thick vapor," J. Opt. Soc. Am. B 15, 1177-1186 (1998).
[CrossRef]

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

1997 (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

1996 (1)

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

1995 (1)

W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
[CrossRef]

1991 (1)

D. Kosachiov, B. Matisov, and Y. Rozhdestvensky, "Coherent Population Trapping - Sensitivity of an Atomic System to the Relative Phase of Exciting Fields," Opt. Commun. 85, 209-212 (1991).
[CrossRef]

1988 (1)

T. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, "Laser-Noise-Induced Population Fluctuations in 2-Level and 3-Level Systems," Phys. Rev. A 38, 5652-5659 (1988).
[CrossRef] [PubMed]

1986 (1)

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

1976 (2)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
[CrossRef]

E. Arimondo and G. Orriols, "Non-Absorbing Atomic Coherences by Coherent 2-Photon Transitions in a 3-Level Optical-Pumping," Lett. Nuovo Cim. 17, 333-338 (1976).
[CrossRef]

Affolderbach, C.

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[CrossRef]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
[CrossRef]

Arimondo, E.

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

E. Arimondo and G. Orriols, "Non-Absorbing Atomic Coherences by Coherent 2-Photon Transitions in a 3-Level Optical-Pumping," Lett. Nuovo Cim. 17, 333-338 (1976).
[CrossRef]

Baluschev, S.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Barnett, S. M.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

Biancalana, V.

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Braun, A. M.

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

Buckle, S. J.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

Camparo, J. C.

Clairon, A.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Cooper, J.

T. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, "Laser-Noise-Induced Population Fluctuations in 2-Level and 3-Level Systems," Phys. Rev. A 38, 5652-5659 (1988).
[CrossRef] [PubMed]

de Clercq, E.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Dimarcq, N.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Fleishhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Gaggl, R.

W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
[CrossRef]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
[CrossRef]

Graf, L.

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Guerandel, S.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Happer, W.

A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
[CrossRef]

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Haslwanter, T.

T. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, "Laser-Noise-Induced Population Fluctuations in 2-Level and 3-Level Systems," Phys. Rev. A 38, 5652-5659 (1988).
[CrossRef] [PubMed]

Hollberg, L.

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, "Coherent population trapping resonances in thermal Rb-85 vapor: D-1 versus D-2 line excitation," Opt. Lett. 27, 1472-1474 (2002).
[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]

Holleville, D.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Huss, A.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Huss, A. F.

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

Jau, Y. Y.

A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
[CrossRef]

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

Kargapoltsev, S. V.

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

Kitching, J.

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, "Coherent population trapping resonances in thermal Rb-85 vapor: D-1 versus D-2 line excitation," Opt. Lett. 27, 1472-1474 (2002).
[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.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, "Coherent population trapping resonances in thermal Rb-85 vapor: D-1 versus D-2 line excitation," Opt. Lett. 27, 1472-1474 (2002).
[CrossRef]

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[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]

Knight, P. L.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

Korsunsky, E.

W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
[CrossRef]

Korsunsky, E. A.

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Kosachiov, D.

D. Kosachiov, B. Matisov, and Y. Rozhdestvensky, "Coherent Population Trapping - Sensitivity of an Atomic System to the Relative Phase of Exciting Fields," Opt. Commun. 85, 209-212 (1991).
[CrossRef]

Kuzma, N. N.

A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
[CrossRef]

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Lammegger, R.

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

Lauder, M. A.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

Leinfellner, N.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Liew, L. A.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

Lukin, M. D.

M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Maichen, W.

W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
[CrossRef]

Mariotti, E.

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Matisov, B.

D. Kosachiov, B. Matisov, and Y. Rozhdestvensky, "Coherent Population Trapping - Sensitivity of an Atomic System to the Relative Phase of Exciting Fields," Opt. Commun. 85, 209-212 (1991).
[CrossRef]

Meschede, D.

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Miron, E.

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
[CrossRef]

Moreland, J.

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

Nagel, A.

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Naumov, A.

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Neureiter, C.

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
[CrossRef]

E. Arimondo and G. Orriols, "Non-Absorbing Atomic Coherences by Coherent 2-Photon Transitions in a 3-Level Optical-Pumping," Lett. Nuovo Cim. 17, 333-338 (1976).
[CrossRef]

Pegg, D. T.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

Post, A. B.

A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
[CrossRef]

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

Ritsch, H.

T. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, "Laser-Noise-Induced Population Fluctuations in 2-Level and 3-Level Systems," Phys. Rev. A 38, 5652-5659 (1988).
[CrossRef] [PubMed]

Romalis, M. V.

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

Rozhdestvensky, Y.

D. Kosachiov, B. Matisov, and Y. Rozhdestvensky, "Coherent Population Trapping - Sensitivity of an Atomic System to the Relative Phase of Exciting Fields," Opt. Commun. 85, 209-212 (1991).
[CrossRef]

Schwindt, P. D. D.

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

Scully, M. O.

M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Shah, V.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

Stahler, M.

Taichenachev, A.

Taichenachev, A. V.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, "On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of Rb-87," JETP Letters 82, 398-403 (2005).
[CrossRef]

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[CrossRef]

Vanier, J.

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

Velichansky, V. L.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, "On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of Rb-87," JETP Letters 82, 398-403 (2005).
[CrossRef]

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[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]

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]

Windholz, L.

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
[CrossRef]

Wynands, R.

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[CrossRef]

M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, "Coherent population trapping resonances in thermal Rb-85 vapor: D-1 versus D-2 line excitation," Opt. Lett. 27, 1472-1474 (2002).
[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]

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

Yelin, S. F.

M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Yudin, V.

Yudin, V. I.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, "On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of Rb-87," JETP Letters 82, 398-403 (2005).
[CrossRef]

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[CrossRef]

Zanon, T.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Zibrov, S. A.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, "On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of Rb-87," JETP Letters 82, 398-403 (2005).
[CrossRef]

Zoller, P.

T. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, "Laser-Noise-Induced Population Fluctuations in 2-Level and 3-Level Systems," Phys. Rev. A 38, 5652-5659 (1988).
[CrossRef] [PubMed]

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. Lett. (2)

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "A microfabricated atomic clock," Appl. Phys. Lett. 85, 1460-1462 (2004).
[CrossRef]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L. A. Liew, and J. Moreland, "Chip-scale atomic magnetometer," Appl. Phys. Lett. 85, 6409-6411 (2004).
[CrossRef]

Europhys. Lett. (2)

A. Nagel, L. Graf, A. Naumov, E. Mariotti, V. Biancalana, D. Meschede, and R. Wynands, "Experimental realization of coherent dark-state magnetometers," Europhys. Lett. 44, 31-36 (1998).
[CrossRef]

W. Maichen, R. Gaggl, E. Korsunsky, and L. Windholz, "Observation of Phase-Dependent Coherent Population Trapping in Optically Closed Atomic Systems," Europhys. Lett. 31, 189-194 (1995).
[CrossRef]

IEEE Trans. Instrum. Meas. (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]

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

JETP Letters (1)

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, and S. A. Zibrov, "On the unique possibility of significantly increasing the contrast of dark resonances on the D1 line of Rb-87," JETP Letters 82, 398-403 (2005).
[CrossRef]

Laser Phys. Lett (1)

S. V. Kargapoltsev, J. Kitching, L. Hollberg, A. V. Taichenachev, V. L. Velichansky, and V. I. Yudin, "High-contrast dark resonance in sigma(+)-sigma(-) optical field," Laser Phys. Lett 1, 495-499 (2004).
[CrossRef]

Lett. Nuovo Cim. (1)

E. Arimondo and G. Orriols, "Non-Absorbing Atomic Coherences by Coherent 2-Photon Transitions in a 3-Level Optical-Pumping," Lett. Nuovo Cim. 17, 333-338 (1976).
[CrossRef]

Nuovo Cimento (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "Experimental-Method for Observation of Rf Transitions and Laser Beat Resonances in Oriented Na Vapor," Nuovo Cimento 36, 5-20 (1976).
[CrossRef]

Opt. Act. (1)

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, "Atomic Interferometers - phase dependence in multilevel atomic transitions," Opt. Act. 33, 1129-1149 (1986).
[CrossRef]

Opt. Commun. (1)

D. Kosachiov, B. Matisov, and Y. Rozhdestvensky, "Coherent Population Trapping - Sensitivity of an Atomic System to the Relative Phase of Exciting Fields," Opt. Commun. 85, 209-212 (1991).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (5)

T. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, "Laser-Noise-Induced Population Fluctuations in 2-Level and 3-Level Systems," Phys. Rev. A 38, 5652-5659 (1988).
[CrossRef] [PubMed]

M. D. Lukin, S. F. Yelin, M. Fleishhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

C. Affolderbach, S. Knappe, R. Wynands, A. V. Taichenachev, and V. I. Yudin, "Electromagnetically induced transparency and absorption in a standing wave," Phys. Rev. A 65, 043810 (2002).
[CrossRef]

A. B. Post, Y. Y. Jau, N. N. Kuzma, and W. Happer, "Amplitude- versus frequency-modulated pumping light for coherent population trapping resonances at high buffer-gas pressure," Phys. Rev. A 72, 033417 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, "High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system," Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Y. Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, "Push-pull optical pumping of pure superposition states," Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Y. Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, "Intense, narrow atomic-clock resonances," Phys. Rev. Lett. 92, 110801 (2004).
[CrossRef] [PubMed]

A. F. Huss, R. Lammegger, C. Neureiter, E. A. Korsunsky, and L. Windholz, "Phase correlation of laser waves with arbitrary frequency spacing," Phys. Rev. Lett. 93, 223601 (2004).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Prog. Opt. (1)

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

Other (3)

M. Zhu, Patent No. 6,359,916 (2002).

M. Zhu, "High contrast signal in a coherent population trapping based atomic frequency standard application," presented at the IEEE International Frequency Control Symposium and 17th European Frequency and Time Forum, Tampa, FL, 2003 (unpublished).

H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, MA, 1980).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Experimental configuration for differential detection of CPT resonances. (b) Atomic level diagram showing detunings and polarizations of the incident optical fields. Here Ωij is the Rabi frequency connecting levels i and j, Γ/2 is the population decay rate from the excited states to each hyperfine state and γ is the decay rate of the hyperfine coherence. The optical fields are assumed to be on resonance and δr is the Raman detuning.

Fig. 2.
Fig. 2.

Lineshapes of atomic-coherence-induced resonances for phase-shifted, two-beam excitation. (a) One beam blocked, conventional CPT resonance, (b) both beams present, signals from balanced photodetectors subtracted, (c) both beams present, phase-advanced signal only, (d) both beams present, phase-delayed signal only.

Fig. 3.
Fig. 3.

Noise spectra taken with the local oscillator tuned to resonance with the center of the CPT transition (δr = 0). Trace A is the sum of the balanced detector channels, Traces B and C are the phase advanced and delayed detector channel respectively, Trace D is the difference of the channels and Trace E is the electronic noise floor (both beams blocked). The inset shows a smaller frequency range and the white noise component of the spectrum around 200 Hz. The dashed line indicates the approximate shot noise level for the sum and difference configurations, as estimated from the DC detector photocurrents.

Fig. 4.
Fig. 4.

Calculated resonance lineshapes for the model in Fig. 1(b) for ψ/γ = 1. Fractional absorption for the (a) phase-delayed and (b) phase-advanced field as a function of Raman detuning. Trace A: ϕ = 0; Trace B: ϕ = π/4; Trace C: ϕ = 3π/8; Trace D: ϕ = π/2. These results for ϕ = π/4 correspond closely to the experimental data shown in Fig. 2(c) and (d).

Equations (6)

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

ρ 12 = Ψ cos ( ϕ ) γ + 2 Ψ + i δ r
Im [ Ω i 4 * ρ i 4 ] = Ψ 2 ( γ + 2 Ψ ) Ψ 2 cos 2 ( ϕ ) δ r 2 + ( γ + 2 Ψ ) 2 δ r Ψ 2 sin ( 2 ϕ ) δ r 2 + ( γ + 2 Ψ ) 2
Im [ Ω i 3 * ρ i 3 ] = Ψ 2 ( γ + 2 Ψ ) Ψ 2 cos 2 ( ϕ ) δ r 2 + ( γ + 2 Ψ ) 2 + δ r Ψ 2 sin ( 2 ϕ ) δ r 2 + ( γ + 2 Ψ ) 2
β = Ω 2 2 ( γ Γ + Ω 2 ) ΔΩ Ω γ .
Im [ F 1 * ρ ] = 2 γ ( Ω 2 2 ω 12 ) cos 2 ( ϕ ) δ 2 + γ 2 + δ ( Ω 2 2 ω 12 ) sin ( 2 ϕ ) δ 2 + γ 2
Im [ F 2 * ρ ] = 2 γ ( Ω 2 2 ω 12 ) cos 2 ( ϕ ) δ 2 + γ 2 + δ ( Ω 2 2 ω 12 ) sin ( 2 ϕ ) δ 2 + γ 2

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