Abstract

We describe the effects of incoherent pump on an atomic filter based on laser-induced optical anisotropy in a three-level ladder system interacting with a strong pump polarized circularly and a weak probe polarized linearly. According to the analysis of the numerical simulation results with some comparison, at the same time of eliminating noise, the filter can enhance the probe’s transmission or even the probe gain can be achieved without population inversion. Moreover, the incoherent pumping rate and the cell temperature performance are evaluated and measures are taken to improve the filter’s transmission and tunability by selecting proper parameters.

© 2012 Optical Society of America

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  1. M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
    [CrossRef]
  2. M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pump fields,” Phys. Lett. A 357, 66–71 (2006).
    [CrossRef]
  3. M. Mahmoudi, M. Sahrai, and H. Tajalli, “The effects of the incoherent pumping field on the phase control of group velocity,” J. Phys. B 39, 1825–1835 (2006).
    [CrossRef]
  4. M. Sahrai, M. Sharifi, and M. Mahmoudi, “The effect of an incoherent pumping on the dispersive and absorptive properties of a four-level medium,” J. Phys. B 42, 185501 (2009).
    [CrossRef]
  5. M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
    [CrossRef]
  6. Y. Q. Xu and S. G. Murdoch, “Gain spectrum of an optical parametric amplifier with a temporally incoherent pump,” Opt. Lett. 35, 169–171 (2010).
    [CrossRef]
  7. C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
    [CrossRef]
  8. G. Vemuri, K. V. Vasavada, and G. S. Agarwal, “Lasing without inversion in the absence of a coherent coupling field,” Phys. Rev. A 52, 3228–3230 (1995).
    [CrossRef]
  9. J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266–1277 (1988).
    [CrossRef]
  10. J. Tang, Q. Wang, Y. Li, L. Zhang, J. Gan, M. Duan, J. Kong, and L. Zheng, “Experimental study of a model digital space optical communication system with new quantum devices,” Appl. Opt. 34, 2619–2622 (1995).
    [CrossRef]
  11. H. Chen, M. A. White, David. A. Krugger, and C. Y. She, “Daytime mesopause temperature measurements with a sodium-vapor dispersive Faraday filter in a lidar receiver,” Opt. Lett. 21, 1093–1095 (1996).
    [CrossRef]
  12. C. Fricke-Begemann, M. Alpers, and J. Höffner, “Daylight rejection with a new receiver for potassium resonance temperature lidars,” Opt. Lett. 27, 1932–1934 (2002).
    [CrossRef]
  13. J. Höffner and C. Fricke-Begemann, “Accurate lidar temperature with narrowband filters,” Opt. Lett. 30, 890–892 (2005).
    [CrossRef]
  14. A. Landolt and T. Roesgen, “Anomalous dispersion in atomic line filters applied for spatial frequency detection,” Appl. Opt. 48, 5948–5955 (2009).
    [CrossRef]
  15. J. S. Neergaard-Nielsen, B. M. Nielsen, H. Takahashi, A. I. Vistnes, and E. S. Polzik, “High purity bright single photon source,” Opt. Express 15, 7940–7949 (2007).
    [CrossRef]
  16. X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
    [CrossRef]
  17. F. Wolfframm, X. Xing, A. Cere, A. Predojevic, A. M. Steinberg, and M. W. Mitchell, “Bright filter-free source of indistinguishable photon pairs,” Opt. Express 16, 18145–18151 (2008).
    [CrossRef]
  18. S. K. Gayen, R. I. Billmers, V. M. Contarino, M. F. Squicciarini, W. J. Scharpf, G. Yang, P. R. Herczfeld, and D. M. Allocca, “Induced-dichroism-excited atomic line filter at 532 nm,” Opt. Lett. 20, 1427–1429 (1995).
    [CrossRef]
  19. L. D. Turner, V. Karagnanov, and P. J. O. Teubner, “Sub-Doppler bandwidth atomic optical filter,” Opt. Lett. 27, 500–502 (2002).
    [CrossRef]
  20. A. Cerè, V. Parigi, M. Abad, F. Wolfgramm, A. Predojević, and M. W. Mitchell, “Narrowband tunable filter based on velocity-selective optical pumping in an atomic vapor,” Opt. Lett. 34, 1012–1014 (2009).
    [CrossRef]
  21. Z. S. He, Y. D. Zhang, H. Wu, P. Yuan, and S. Q. Liu, “Theoretical model for an atomic optical filter based on optical anisotropy,” J. Opt. Soc. Am. B 26, 1755–1759 (2009).
    [CrossRef]
  22. S. Q. Liu, Y. D. Zhang, H. Wu, and P. Yuan, “Atomic filter with large scale tunability,” J. Opt. Soc. Am. B 28, 1100–1103 (2011).
    [CrossRef]
  23. S. Q. Liu, Y. D. Zhang, D. K. Fan, H. Wu, and P. Yuan, “The selective optical pumping process in Doppler-broadened atoms,” Appl. Opt. 50, 1620–1624 (2011).
    [CrossRef]
  24. C. L. Chen and A. V. Phelps, “Self-broadening of cesium resonance lines at 8521 and 8944 Å,” Phys. Rev. 173, 62–69 (1968).
    [CrossRef]
  25. C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure equations for the metallic elements: 298–2500 K,” Can. Metall. Q. 23, 309–313 (1984).
    [CrossRef]
  26. P. Yeh, “Dispersive magneto-optic filters,” Appl. Opt. 21, 2069–2075 (1982).
    [CrossRef]

2011 (2)

2010 (1)

2009 (4)

2008 (2)

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

F. Wolfframm, X. Xing, A. Cere, A. Predojevic, A. M. Steinberg, and M. W. Mitchell, “Bright filter-free source of indistinguishable photon pairs,” Opt. Express 16, 18145–18151 (2008).
[CrossRef]

2007 (1)

2006 (2)

M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pump fields,” Phys. Lett. A 357, 66–71 (2006).
[CrossRef]

M. Mahmoudi, M. Sahrai, and H. Tajalli, “The effects of the incoherent pumping field on the phase control of group velocity,” J. Phys. B 39, 1825–1835 (2006).
[CrossRef]

2005 (1)

2002 (2)

1999 (1)

M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
[CrossRef]

1997 (1)

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

1996 (1)

1995 (3)

1992 (1)

M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

1988 (1)

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266–1277 (1988).
[CrossRef]

1984 (1)

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure equations for the metallic elements: 298–2500 K,” Can. Metall. Q. 23, 309–313 (1984).
[CrossRef]

1982 (1)

1968 (1)

C. L. Chen and A. V. Phelps, “Self-broadening of cesium resonance lines at 8521 and 8944 Å,” Phys. Rev. 173, 62–69 (1968).
[CrossRef]

Abad, M.

Agarwal, G. S.

G. Vemuri, K. V. Vasavada, and G. S. Agarwal, “Lasing without inversion in the absence of a coherent coupling field,” Phys. Rev. A 52, 3228–3230 (1995).
[CrossRef]

Alcock, C. B.

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure equations for the metallic elements: 298–2500 K,” Can. Metall. Q. 23, 309–313 (1984).
[CrossRef]

Allocca, D. M.

Alpers, M.

Bao, X.-H.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Billmers, R. I.

Cataliotti, F. S.

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

Cere, A.

Cerè, A.

Chen, C. L.

C. L. Chen and A. V. Phelps, “Self-broadening of cesium resonance lines at 8521 and 8944 Å,” Phys. Rev. 173, 62–69 (1968).
[CrossRef]

Chen, H.

Chen, Z.-B.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Contarino, V. M.

Duan, M.

Fan, D. K.

Fleischhauer, M.

M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Fort, C.

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

Fricke-Begemann, C.

Gan, J.

Gawlik, W.

M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
[CrossRef]

Gayen, S. K.

Gelbwachs, J. A.

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266–1277 (1988).
[CrossRef]

Hänsch, T. W.

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

He, Z. S.

Herczfeld, P. R.

Höffner, J.

Horrigan, M. K.

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure equations for the metallic elements: 298–2500 K,” Can. Metall. Q. 23, 309–313 (1984).
[CrossRef]

Inguscio, M.

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

Itkin, V. P.

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure equations for the metallic elements: 298–2500 K,” Can. Metall. Q. 23, 309–313 (1984).
[CrossRef]

Karagnanov, V.

Keitel, C. H.

M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Kong, J.

Krugger, David. A.

Landolt, A.

Li, Y.

Liu, S. Q.

Mahmoudi, M.

M. Sahrai, M. Sharifi, and M. Mahmoudi, “The effect of an incoherent pumping on the dispersive and absorptive properties of a four-level medium,” J. Phys. B 42, 185501 (2009).
[CrossRef]

M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pump fields,” Phys. Lett. A 357, 66–71 (2006).
[CrossRef]

M. Mahmoudi, M. Sahrai, and H. Tajalli, “The effects of the incoherent pumping field on the phase control of group velocity,” J. Phys. B 39, 1825–1835 (2006).
[CrossRef]

Mitchell, M. W.

Murdoch, S. G.

Neergaard-Nielsen, J. S.

Nielsen, B. M.

Pan, J.-W.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Parigi, V.

Phelps, A. V.

C. L. Chen and A. V. Phelps, “Self-broadening of cesium resonance lines at 8521 and 8944 Å,” Phys. Rev. 173, 62–69 (1968).
[CrossRef]

Pinard, M.

M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
[CrossRef]

Polzik, E. S.

Predojevic, A.

Prevedelli, M.

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

Qian, Y.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Roesgen, T.

Sahrai, M.

M. Sahrai, M. Sharifi, and M. Mahmoudi, “The effect of an incoherent pumping on the dispersive and absorptive properties of a four-level medium,” J. Phys. B 42, 185501 (2009).
[CrossRef]

M. Mahmoudi, M. Sahrai, and H. Tajalli, “The effects of the incoherent pumping field on the phase control of group velocity,” J. Phys. B 39, 1825–1835 (2006).
[CrossRef]

M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pump fields,” Phys. Lett. A 357, 66–71 (2006).
[CrossRef]

Scharpf, W. J.

Scully, M. O.

M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Sharifi, M.

M. Sahrai, M. Sharifi, and M. Mahmoudi, “The effect of an incoherent pumping on the dispersive and absorptive properties of a four-level medium,” J. Phys. B 42, 185501 (2009).
[CrossRef]

She, C. Y.

Squicciarini, M. F.

Steinberg, A. M.

Su, C.

M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Tajalli, H.

M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pump fields,” Phys. Lett. A 357, 66–71 (2006).
[CrossRef]

M. Mahmoudi, M. Sahrai, and H. Tajalli, “The effects of the incoherent pumping field on the phase control of group velocity,” J. Phys. B 39, 1825–1835 (2006).
[CrossRef]

Takahashi, H.

Tang, J.

Teubner, P. J. O.

Turner, L. D.

Vasavada, K. V.

G. Vemuri, K. V. Vasavada, and G. S. Agarwal, “Lasing without inversion in the absence of a coherent coupling field,” Phys. Rev. A 52, 3228–3230 (1995).
[CrossRef]

Vemuri, G.

G. Vemuri, K. V. Vasavada, and G. S. Agarwal, “Lasing without inversion in the absence of a coherent coupling field,” Phys. Rev. A 52, 3228–3230 (1995).
[CrossRef]

Vistnes, A. I.

Wang, Q.

Wasik, G.

M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
[CrossRef]

White, M. A.

Wolfframm, F.

Wolfgramm, F.

Wu, H.

Xing, X.

Xu, Y. Q.

Yang, G.

Yang, J.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Yang, T.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Yeh, P.

Yuan, P.

Zachorowski, J.

M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
[CrossRef]

Zhang, H.

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

Zhang, L.

Zhang, Y. D.

Zheng, L.

Appl. Opt. (4)

Can. Metall. Q. (1)

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure equations for the metallic elements: 298–2500 K,” Can. Metall. Q. 23, 309–313 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266–1277 (1988).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (2)

M. Mahmoudi, M. Sahrai, and H. Tajalli, “The effects of the incoherent pumping field on the phase control of group velocity,” J. Phys. B 39, 1825–1835 (2006).
[CrossRef]

M. Sahrai, M. Sharifi, and M. Mahmoudi, “The effect of an incoherent pumping on the dispersive and absorptive properties of a four-level medium,” J. Phys. B 42, 185501 (2009).
[CrossRef]

Opt. Commun. (2)

M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

C. Fort, F. S. Cataliotti, T. W. Hänsch, M. Inguscio, and M. Prevedelli, “Gain without inversion on the cesium D1 line,” Opt. Commun. 139, 31–34 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Phys. Lett. A (1)

M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pump fields,” Phys. Lett. A 357, 66–71 (2006).
[CrossRef]

Phys. Rev. (1)

C. L. Chen and A. V. Phelps, “Self-broadening of cesium resonance lines at 8521 and 8944 Å,” Phys. Rev. 173, 62–69 (1968).
[CrossRef]

Phys. Rev. A (2)

M. Pinard, G. Wasik, W. Gawlik, and J. Zachorowski, “Amplification without inversion in a medium with collisional dephasing,” Phys. Rev. A 59, 848–858 (1999).
[CrossRef]

G. Vemuri, K. V. Vasavada, and G. S. Agarwal, “Lasing without inversion in the absence of a coherent coupling field,” Phys. Rev. A 52, 3228–3230 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

X.-H. Bao, Y. Qian, J. Yang, H. Zhang, Z.-B. Chen, T. Yang, and J.-W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101, 190501 (2008).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Related energy levels of Rb 87 . A strong coherent pump field with the Rabi frequency Ω c which is σ + polarized field (780 nm) drives 5 S 1 / 2 ( F = 2 ) to 5 P 3 / 2 ( F = 3 ) transition in the pumping process, while a linearly polarized field (775.9 nm) with the Rabi frequency Ω p probes 5 P 3 / 2 ( F = 3 ) to 5 D 3 / 2 ( F = 3 ) transition. An indirect incoherent pump field with the pumping rate R is applied to the | 2 | 3 transition.

Fig. 2.
Fig. 2.

(a) Transmission, (b) absorption coefficient, and (c) rotation angle versus the probe detuning from resonance of 5 P 3 / 2 ( F = 3 ) 5 D 3 / 2 ( F = 3 ) transition for the incoherent pumping rate R = 0 (black solid), 10 MHz (red dash), 20 MHz (blue dot). Other common parameters of above curves are Δ c = 0 , T = 350 K , Ω c = 50 MHz , γ 2 / 2 π = 6.07 MHz , γ 3 / 2 π = 0.776 MHz .

Fig. 3.
Fig. 3.

Peak transmission as function of the incoherent pumping rate R when the cell temperature T = 340 K (black solid), 350 K (red dash), and 360 K (blue dot). Other parameters are the same as Fig. 2. Peak transmission equal to 2.15 means the probe can be enhanced by 2.15 times.

Fig. 4.
Fig. 4.

Typical transmission spectra as a function of the probe detuning. Δ c = 0 , R = 0 (black solid), Δ c = 0 , R = 7 MHz (red solid), Δ c = 1 GHz , R = 0 (black dash), Δ c = 1 GHz , R = 7 MHz (red dash), Δ c = 3 GHz , R = 0 (black dot), Δ c = 3 GHz , R = 7 MHz (red dot). Other parameters are the same as Fig. 2.

Fig. 5.
Fig. 5.

Peak transmission as function of the pump detuning from resonance of 5 S 1 / 2 ( F = 2 ) 5 P 3 / 2 ( F = 3 ) transition when T = 350 K , R = 0 (red solid), T = 350 K , R = 7 MHz (red dash), T = 360 K , R = 0 (blue solid), T = 360 K , R = 15 MHz (blue dash). Other parameters are the same as Fig. 2.

Equations (11)

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ρ ˙ 11 = i Ω c 2 ( ρ 21 ρ 12 ) + Γ 2 ρ 22 ρ ˙ 33 = i 2 Ω p ( ρ 32 ρ 23 ) + R ( ρ 22 ρ 33 ) Γ 3 ρ 33 ρ ˙ 21 = ( i Δ c + γ 21 ) ρ 21 + i 2 Ω c ( ρ 11 ρ 22 ) + i 2 Ω p ρ 31 ρ ˙ 31 = [ i ( Δ c + Δ p ) + γ 31 ] ρ 31 + i 2 Ω p ρ 21 i 2 Ω c ρ 32 ρ ˙ 32 = ( i Δ p + γ 32 ) ρ 32 + i 2 Ω p ( ρ 22 ρ 33 ) i 2 Ω c ρ 31 ρ 11 + ρ 22 + ρ 33 = 1 .
ρ 11 = Ω c 2 γ 21 ( R + Γ 3 ) + 2 Γ 2 ( R + Γ 3 ) ( γ 21 2 + Δ c 2 ) Ω c 2 γ 21 ( 3 R + 2 Γ 3 ) + 2 Γ 2 ( R + Γ 3 ) ( γ 21 2 + Δ c 2 ) ,
ρ 22 = Ω c 2 γ 21 ( R + Γ 3 ) Ω c 2 γ 21 ( 3 R + 2 Γ 3 ) + 2 Γ 2 ( R + Γ 3 ) ( γ 21 2 + Δ c 2 ) ,
ρ 33 = Ω c 2 γ 21 R Ω c 2 γ 21 ( 3 R + 2 Γ 3 ) + 2 Γ 2 ( R + Γ 3 ) ( γ 21 2 + Δ c 2 ) ,
ρ 21 = i 2 Ω c ( ρ 11 ρ 22 ) i Δ c + γ 21 ,
ρ 32 = 2 i Ω p [ i ( Δ c + Δ p ) + γ 31 ] ( ρ 22 ρ 33 ) + Ω c Ω p ρ 21 4 [ i ( Δ c + Δ p ) + γ 31 ] ( i Δ p + γ 32 ) + Ω c 2 .
χ = 2 μ 23 2 N 0 ρ 32 / ( ε 0 Ω p ) .
N 0 = 9.66 × 10 24 P ( Torr ) T ( K ) ,
log 10 P = 2.881 + 4.857 4215 / T ( solid phase ) log 10 P = 2.881 + 4.312 4040 / T ( liquid phase ) .
χ = 2 μ 2 2 N 0 π u ε 0 Ω p ρ 32 e v 2 / u 2 d v .
T r = 1 2 exp ( α L ) [ cosh ( Δ α L ) cos ( 2 θ ) ] .

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