Abstract

We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from 1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.

© 2014 Optical Society of America

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  1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  2. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
    [CrossRef]
  3. C. Cohen-Tannoudji, “Amazing light: a volume dedicated to Charles Hard Townes on his 80th birthday,” in The Autler-Townes Effect Revisited,R. Y. Chiao, ed. (Springer, 1996), p. 109.
  4. G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
    [CrossRef]
  5. P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level Λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
    [CrossRef]
  6. T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler–Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
    [CrossRef]
  7. P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler–Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett 107, 163604 (2011).
    [CrossRef]
  8. L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
    [CrossRef]
  9. C. Tan, C. Zhu, and G. Huang, “Analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening,” J. Phys. B 46, 025103 (2013).
    [CrossRef]
  10. C. Zhu, C. Tan, and G. Huang, “Crossover from electromagnetically induced transparency to Autler–Townes splitting in open V-type molecular systems,” Phys. Rev. A 87, 043813 (2013).
    [CrossRef]
  11. In literature, the ladder system is also called cascade system by many authors, e.g. [6].
  12. M. Saffman, T. G. Walker, and K. Mölmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
    [CrossRef]
  13. J. D. Pritchard, K. J. Weatherill, and C. S. Adams, “Non-linear optics using cold Rydberg atoms,” in Annual Review of Cold Atoms and Molecules, K. W. Madison, Y. Wang, A. M. Rey, and K. Bongs, eds. (World Scientific, 2013), Vol. 1, pp. 301–350.
  14. S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
    [CrossRef]
  15. A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
    [CrossRef]
  16. A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4, 890–894 (2008).
    [CrossRef]
  17. K. J. Weatherill, J. D. Pritchard, R. P. Abel, M. G. Bason, A. K. Mohapatra, and C. S. Adams, “Electromagnetically induced transparency of an interacting cold Rydberg ensemble,” J. Phys. B 41, 201002 (2008).
    [CrossRef]
  18. U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
    [CrossRef]
  19. J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
    [CrossRef]
  20. A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
    [CrossRef]
  21. Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
    [CrossRef]
  22. Y.-q. Li and M. Xiao, “Observation of quantum interference between dressed states in an electromagnetically induced transparency,” Phys. Rev. A 51, 4959–4962 (1995).
    [CrossRef]
  23. J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
    [CrossRef]
  24. H. Lee, Y. Rostovtsev, and M. O. Scully, “Asymmetries between absorption and stimulated emission in driven three-level systems,” Phys. Rev. A 62, 063804 (2000).
    [CrossRef]
  25. J. J. Clarke, W. A. van Wijngaarden, and H. Chen, “Electromagnetically induced transparency using a vapor cell and a laser-cooled sample of cesium atoms,” Phys. Rev. A 64, 023818 (2001).
    [CrossRef]
  26. J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra, “Measurement of transition dipole moments in lithium dimers using electromagnetically induced transparency,” Phys. Rev. Lett 88, 173003 (2002).
    [CrossRef]
  27. E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
    [CrossRef]
  28. E. Ahmed and A. M. Lyyra, “Effect of Doppler broadening on Autler–Townes splitting in the molecular cascade excitation scheme,” Phys. Rev. A 76, 053407 (2007).
    [CrossRef]
  29. R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
    [CrossRef]
  30. H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express 16, 12163–12170 (2008).
    [CrossRef]
  31. Y. Zhang, Z. Nie, Z. Wang, C. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
    [CrossRef]
  32. H. Kübler, J. P. Shaffer, T. Baluktsian, R. Löw, and T. Pfau, “Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells,” Nat. Photonics 4, 112–116 (2010).
    [CrossRef]
  33. A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon–photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
    [CrossRef]
  34. D. Petrosyan, J. Otterbach, and M. Fleischhauer, “Electromagnetically induced transparency with Rydberg atoms,” Phys. Rev. Lett. 107, 213601 (2011).
    [CrossRef]
  35. C. Ates, S. Sevincli, and T. Pohl, “Electromagnetically induced transparency in strongly interacting Rydberg gases,” Phys. Rev. A 83, 041802(R) (2011).
    [CrossRef]
  36. Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, “Observation of coherent many-body Rabi oscillations,” Nat. Phys. 8, 790–794 (2012).
    [CrossRef]
  37. B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, “GHz Rabi flopping to Rydberg states in hot atomic vapor cells,” Phys. Rev. Lett 107, 243001 (2011).
    [CrossRef]
  38. H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
    [CrossRef]
  39. T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
    [CrossRef]
  40. F. Bariani, Y. O. Dudin, T. A. B. Kennedy, and A. Kuzmich, “Dephasing of multiparticle Rydberg excitations for fast entanglement generation,” Phys. Rev. Lett 108, 030501 (2012).
    [CrossRef]
  41. J. A. Sedlacek, A. Schwettmann, H. Kbler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8, 819–824 (2012).
    [CrossRef]
  42. E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A 66, 063802 (2002).
    [CrossRef]
  43. H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33–39 (2003).
    [CrossRef]
  44. L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
    [CrossRef]
  45. Note that the wavenumber ratio defined in our paper is the reciprocal of that defined in [20].
  46. H. R. Gray and C. R. Stroud, “Autler–Townes effect in double optical resonance,” Opt. Commun. 25, 359–362 (1978).
    [CrossRef]
  47. S. Papademetriou, M. F. Van Leeuwen, and C. R. Stroud, “Autler–Townes effect for an atom in a 100% amplitude-modulated laser field. II. Experimental results,” Phys. Rev. A 53, 997–1003 (1996).
    [CrossRef]
  48. B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
    [CrossRef]
  49. H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
    [CrossRef]

2013 (4)

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
[CrossRef]

C. Tan, C. Zhu, and G. Huang, “Analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening,” J. Phys. B 46, 025103 (2013).
[CrossRef]

C. Zhu, C. Tan, and G. Huang, “Crossover from electromagnetically induced transparency to Autler–Townes splitting in open V-type molecular systems,” Phys. Rev. A 87, 043813 (2013).
[CrossRef]

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

2012 (4)

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
[CrossRef]

F. Bariani, Y. O. Dudin, T. A. B. Kennedy, and A. Kuzmich, “Dephasing of multiparticle Rydberg excitations for fast entanglement generation,” Phys. Rev. Lett 108, 030501 (2012).
[CrossRef]

J. A. Sedlacek, A. Schwettmann, H. Kbler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8, 819–824 (2012).
[CrossRef]

Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, “Observation of coherent many-body Rabi oscillations,” Nat. Phys. 8, 790–794 (2012).
[CrossRef]

2011 (6)

B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, “GHz Rabi flopping to Rydberg states in hot atomic vapor cells,” Phys. Rev. Lett 107, 243001 (2011).
[CrossRef]

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon–photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[CrossRef]

D. Petrosyan, J. Otterbach, and M. Fleischhauer, “Electromagnetically induced transparency with Rydberg atoms,” Phys. Rev. Lett. 107, 213601 (2011).
[CrossRef]

C. Ates, S. Sevincli, and T. Pohl, “Electromagnetically induced transparency in strongly interacting Rydberg gases,” Phys. Rev. A 83, 041802(R) (2011).
[CrossRef]

P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler–Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett 107, 163604 (2011).
[CrossRef]

S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

2010 (7)

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler–Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
[CrossRef]

J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
[CrossRef]

M. Saffman, T. G. Walker, and K. Mölmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
[CrossRef]

Y. Zhang, Z. Nie, Z. Wang, C. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

H. Kübler, J. P. Shaffer, T. Baluktsian, R. Löw, and T. Pfau, “Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells,” Nat. Photonics 4, 112–116 (2010).
[CrossRef]

L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
[CrossRef]

2009 (1)

U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
[CrossRef]

2008 (5)

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4, 890–894 (2008).
[CrossRef]

K. J. Weatherill, J. D. Pritchard, R. P. Abel, M. G. Bason, A. K. Mohapatra, and C. S. Adams, “Electromagnetically induced transparency of an interacting cold Rydberg ensemble,” J. Phys. B 41, 201002 (2008).
[CrossRef]

H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express 16, 12163–12170 (2008).
[CrossRef]

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level Λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
[CrossRef]

A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
[CrossRef]

2007 (3)

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[CrossRef]

E. Ahmed and A. M. Lyyra, “Effect of Doppler broadening on Autler–Townes splitting in the molecular cascade excitation scheme,” Phys. Rev. A 76, 053407 (2007).
[CrossRef]

R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
[CrossRef]

2006 (1)

E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
[CrossRef]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2003 (2)

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33–39 (2003).
[CrossRef]

B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
[CrossRef]

2002 (2)

E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A 66, 063802 (2002).
[CrossRef]

J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra, “Measurement of transition dipole moments in lithium dimers using electromagnetically induced transparency,” Phys. Rev. Lett 88, 173003 (2002).
[CrossRef]

2001 (1)

J. J. Clarke, W. A. van Wijngaarden, and H. Chen, “Electromagnetically induced transparency using a vapor cell and a laser-cooled sample of cesium atoms,” Phys. Rev. A 64, 023818 (2001).
[CrossRef]

2000 (1)

H. Lee, Y. Rostovtsev, and M. O. Scully, “Asymmetries between absorption and stimulated emission in driven three-level systems,” Phys. Rev. A 62, 063804 (2000).
[CrossRef]

1997 (2)

G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
[CrossRef]

Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
[CrossRef]

1996 (1)

S. Papademetriou, M. F. Van Leeuwen, and C. R. Stroud, “Autler–Townes effect for an atom in a 100% amplitude-modulated laser field. II. Experimental results,” Phys. Rev. A 53, 997–1003 (1996).
[CrossRef]

1995 (2)

Y.-q. Li and M. Xiao, “Observation of quantum interference between dressed states in an electromagnetically induced transparency,” Phys. Rev. A 51, 4959–4962 (1995).
[CrossRef]

J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef]

1978 (1)

H. R. Gray and C. R. Stroud, “Autler–Townes effect in double optical resonance,” Opt. Commun. 25, 359–362 (1978).
[CrossRef]

1955 (1)

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[CrossRef]

Abel, R. P.

K. J. Weatherill, J. D. Pritchard, R. P. Abel, M. G. Bason, A. K. Mohapatra, and C. S. Adams, “Electromagnetically induced transparency of an interacting cold Rydberg ensemble,” J. Phys. B 41, 201002 (2008).
[CrossRef]

Abi-Salloum, T. Y.

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler–Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81, 053836 (2010).
[CrossRef]

Adams, C. S.

S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
[CrossRef]

K. J. Weatherill, J. D. Pritchard, R. P. Abel, M. G. Bason, A. K. Mohapatra, and C. S. Adams, “Electromagnetically induced transparency of an interacting cold Rydberg ensemble,” J. Phys. B 41, 201002 (2008).
[CrossRef]

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4, 890–894 (2008).
[CrossRef]

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[CrossRef]

J. D. Pritchard, K. J. Weatherill, and C. S. Adams, “Non-linear optics using cold Rydberg atoms,” in Annual Review of Cold Atoms and Molecules, K. W. Madison, Y. Wang, A. M. Rey, and K. Bongs, eds. (World Scientific, 2013), Vol. 1, pp. 301–350.

Agarwal, G. S.

G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
[CrossRef]

Ahmed, E.

E. Ahmed and A. M. Lyyra, “Effect of Doppler broadening on Autler–Townes splitting in the molecular cascade excitation scheme,” Phys. Rev. A 76, 053407 (2007).
[CrossRef]

E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
[CrossRef]

Ahmed, E. H.

A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
[CrossRef]

Amthor, T.

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P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level Λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
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Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
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B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, “GHz Rabi flopping to Rydberg states in hot atomic vapor cells,” Phys. Rev. Lett 107, 243001 (2011).
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H. Kübler, J. P. Shaffer, T. Baluktsian, R. Löw, and T. Pfau, “Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells,” Nat. Photonics 4, 112–116 (2010).
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H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
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B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
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U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
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R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
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B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
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H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler–Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett 107, 163604 (2011).
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F. Bariani, Y. O. Dudin, T. A. B. Kennedy, and A. Kuzmich, “Dephasing of multiparticle Rydberg excitations for fast entanglement generation,” Phys. Rev. Lett 108, 030501 (2012).
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Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, “Observation of coherent many-body Rabi oscillations,” Nat. Phys. 8, 790–794 (2012).
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R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
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B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
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J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra, “Measurement of transition dipole moments in lithium dimers using electromagnetically induced transparency,” Phys. Rev. Lett 88, 173003 (2002).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
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J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
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J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
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L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
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H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
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S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
[CrossRef]

Hansson, A.

A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
[CrossRef]

E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
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He, Z.-S.

R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
[CrossRef]

Heidemann, R.

U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
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E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A 66, 063802 (2002).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
[CrossRef]

Hofmann, C. S.

S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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C. Tan, C. Zhu, and G. Huang, “Analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening,” J. Phys. B 46, 025103 (2013).
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B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, “GHz Rabi flopping to Rydberg states in hot atomic vapor cells,” Phys. Rev. Lett 107, 243001 (2011).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[CrossRef]

Javan, A.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33–39 (2003).
[CrossRef]

Jia, S.

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

Jin, S.-z.

J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef]

Jones, M. P. A.

S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
[CrossRef]

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J. A. Sedlacek, A. Schwettmann, H. Kbler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8, 819–824 (2012).
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R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
[CrossRef]

Kennedy, T. A. B.

F. Bariani, Y. O. Dudin, T. A. B. Kennedy, and A. Kuzmich, “Dephasing of multiparticle Rydberg excitations for fast entanglement generation,” Phys. Rev. Lett 108, 030501 (2012).
[CrossRef]

Kim, J. B.

Kim, M. K.

Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
[CrossRef]

Kirova, T.

A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
[CrossRef]

E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
[CrossRef]

J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra, “Measurement of transition dipole moments in lithium dimers using electromagnetically induced transparency,” Phys. Rev. Lett 88, 173003 (2002).
[CrossRef]

Kocharovskaya, O.

P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently driven three-level Λ system,” J. Mod. Opt. 55, 3159–3171 (2008).
[CrossRef]

E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A 66, 063802 (2002).
[CrossRef]

Kölle, A.

B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, “GHz Rabi flopping to Rydberg states in hot atomic vapor cells,” Phys. Rev. Lett 107, 243001 (2011).
[CrossRef]

Kollmann, P.

U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
[CrossRef]

Kotochigova, S.

E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
[CrossRef]

Kübler, H.

B. Huber, T. Baluktsian, M. Schlagmüller, A. Kölle, H. Kübler, R. Löw, and T. Pfau, “GHz Rabi flopping to Rydberg states in hot atomic vapor cells,” Phys. Rev. Lett 107, 243001 (2011).
[CrossRef]

H. Kübler, J. P. Shaffer, T. Baluktsian, R. Löw, and T. Pfau, “Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells,” Nat. Photonics 4, 112–116 (2010).
[CrossRef]

Kupriyanov, D. V.

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
[CrossRef]

Kuzmich, A.

F. Bariani, Y. O. Dudin, T. A. B. Kennedy, and A. Kuzmich, “Dephasing of multiparticle Rydberg excitations for fast entanglement generation,” Phys. Rev. Lett 108, 030501 (2012).
[CrossRef]

Y. O. Dudin, L. Li, F. Bariani, and A. Kuzmich, “Observation of coherent many-body Rabi oscillations,” Nat. Phys. 8, 790–794 (2012).
[CrossRef]

Kuznetsova, E.

E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A 66, 063802 (2002).
[CrossRef]

Lam, P. K.

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
[CrossRef]

Laurat, J.

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
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E. Ahmed, A. Hansson, P. Qi, T. Kirova, A. Lazoudis, S. Kotochigova, A. M. Lyyra, L. Li, J. Qi, and S. Magnier, “Measurement of the electronic transition dipole moment by Autler–Townes splitting: comparison of three- and four-level excitation schemes for the Na2A1∑u+−X1∑g+ system,” J. Chem. Phys. 124, 084308 (2006).
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A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
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H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, “From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,” Appl. Phys. B 76, 33–39 (2003).
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H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
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J. A. Sedlacek, A. Schwettmann, H. Kbler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8, 819–824 (2012).
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S. Papademetriou, M. F. Van Leeuwen, and C. R. Stroud, “Autler–Townes effect for an atom in a 100% amplitude-modulated laser field. II. Experimental results,” Phys. Rev. A 53, 997–1003 (1996).
[CrossRef]

van Wijngaarden, W. A.

J. J. Clarke, W. A. van Wijngaarden, and H. Chen, “Electromagnetically induced transparency using a vapor cell and a laser-cooled sample of cesium atoms,” Phys. Rev. A 64, 023818 (2001).
[CrossRef]

Veissier, L.

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler–Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
[CrossRef]

Vuletic, V.

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
[CrossRef]

Walker, T. G.

M. Saffman, T. G. Walker, and K. Mölmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

Wang, L.

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

Wang, Z.

Weatherill, K. J.

S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
[CrossRef]

K. J. Weatherill, J. D. Pritchard, R. P. Abel, M. G. Bason, A. K. Mohapatra, and C. S. Adams, “Electromagnetically induced transparency of an interacting cold Rydberg ensemble,” J. Phys. B 41, 201002 (2008).
[CrossRef]

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4, 890–894 (2008).
[CrossRef]

J. D. Pritchard, K. J. Weatherill, and C. S. Adams, “Non-linear optics using cold Rydberg atoms,” in Annual Review of Cold Atoms and Molecules, K. W. Madison, Y. Wang, A. M. Rey, and K. Bongs, eds. (World Scientific, 2013), Vol. 1, pp. 301–350.

Weidemüller, M.

S. Sevinçli, C. Ates, T. Pohl, H. Schempp, C. S. Hofmann, G. Günter, T. Amthor, M. Weidemüller, J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency,” J. Phys. B 44, 184018 (2011).
[CrossRef]

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
[CrossRef]

Weimer, H.

U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
[CrossRef]

Wen, F.

Wu, C.

Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
[CrossRef]

Xiao, M.

Y. Zhang, Z. Nie, Z. Wang, C. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef]

Y.-q. Li and M. Xiao, “Observation of quantum interference between dressed states in an electromagnetically induced transparency,” Phys. Rev. A 51, 4959–4962 (1995).
[CrossRef]

Zhang, H.

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

Zhang, L.

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

Zhang, Y.

Zhao, J.

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

Zhao, Y.

Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
[CrossRef]

Zhu, C.

C. Zhu, C. Tan, and G. Huang, “Crossover from electromagnetically induced transparency to Autler–Townes splitting in open V-type molecular systems,” Phys. Rev. A 87, 043813 (2013).
[CrossRef]

C. Tan, C. Zhu, and G. Huang, “Analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening,” J. Phys. B 46, 025103 (2013).
[CrossRef]

Appl. Phys. B (1)

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[CrossRef]

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[CrossRef]

K. J. Weatherill, J. D. Pritchard, R. P. Abel, M. G. Bason, A. K. Mohapatra, and C. S. Adams, “Electromagnetically induced transparency of an interacting cold Rydberg ensemble,” J. Phys. B 41, 201002 (2008).
[CrossRef]

Nat. Photonics (1)

H. Kübler, J. P. Shaffer, T. Baluktsian, R. Löw, and T. Pfau, “Coherent excitation of Rydberg atoms in micrometre-sized atomic vapour cells,” Nat. Photonics 4, 112–116 (2010).
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[CrossRef]

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[CrossRef]

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4, 890–894 (2008).
[CrossRef]

Nature (1)

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
[CrossRef]

New J. Phys. (1)

U. Raitzsch, R. Heidemann, H. Weimer, B. Butscher, P. Kollmann, R. Löw, H. P. Büchler, and T. Pfau, “Investigation of dephasing rates in an interacting Rydberg gas,” New J. Phys. 11, 055014 (2009).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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E. Ahmed and A. M. Lyyra, “Effect of Doppler broadening on Autler–Townes splitting in the molecular cascade excitation scheme,” Phys. Rev. A 76, 053407 (2007).
[CrossRef]

R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, “Doubly dressed states in a ladder-type system with electromagnetically induced transparency,” Phys. Rev. A 76, 053420 (2007).
[CrossRef]

A. Lazoudis, E. H. Ahmed, L. Li, T. Kirova, P. Qi, A. Hansson, J. Magnes, and A. M. Lyyra, “Experimental observation of the dependence of Autler–Townes splitting on the probe and coupling laser wave-number ratio in Doppler-broadened open molecular cascade systems,” Phys. Rev. A 78, 043405 (2008).
[CrossRef]

Y.-q. Li and M. Xiao, “Observation of quantum interference between dressed states in an electromagnetically induced transparency,” Phys. Rev. A 51, 4959–4962 (1995).
[CrossRef]

J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef]

H. Lee, Y. Rostovtsev, and M. O. Scully, “Asymmetries between absorption and stimulated emission in driven three-level systems,” Phys. Rev. A 62, 063804 (2000).
[CrossRef]

J. J. Clarke, W. A. van Wijngaarden, and H. Chen, “Electromagnetically induced transparency using a vapor cell and a laser-cooled sample of cesium atoms,” Phys. Rev. A 64, 023818 (2001).
[CrossRef]

L. Li and G. Huang, “Linear and nonlinear light propagations in a Doppler-broadened medium via electromagnetically induced transparency,” Phys. Rev. A 82, 023809 (2010).
[CrossRef]

S. Papademetriou, M. F. Van Leeuwen, and C. R. Stroud, “Autler–Townes effect for an atom in a 100% amplitude-modulated laser field. II. Experimental results,” Phys. Rev. A 53, 997–1003 (1996).
[CrossRef]

B. K. Teo, D. Feldbaum, T. Cubel, J. R. Guest, P. R. Berman, and G. Raithel, “Autler–Townes spectroscopy of the 5S1/2−5P3/2−44D cascade of cold 85Rb atoms,” Phys. Rev. A 68, 053407 (2003).
[CrossRef]

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, “Autler–Townes splitting of a cascade system in ultracold cesium Rydberg atoms,” Phys. Rev. A 87, 033835 (2013).
[CrossRef]

C. Ates, S. Sevincli, and T. Pohl, “Electromagnetically induced transparency in strongly interacting Rydberg gases,” Phys. Rev. A 83, 041802(R) (2011).
[CrossRef]

Phys. Rev. Lett (5)

J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra, “Measurement of transition dipole moments in lithium dimers using electromagnetically induced transparency,” Phys. Rev. Lett 88, 173003 (2002).
[CrossRef]

Y. Zhao, C. Wu, B.-S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett 79, 641–644 (1997).
[CrossRef]

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Phys. Rev. Lett. (5)

J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded Rydberg ensemble,” Phys. Rev. Lett. 105, 193603 (2010).
[CrossRef]

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[CrossRef]

H. Schempp, G. Günter, C. S. Hofmann, C. Giese, S. D. Saliba, B. D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, and T. Pohl, “Coherent population trapping with controlled interparticle interactions,” Phys. Rev. Lett. 104, 173602 (2010).
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M. Saffman, T. G. Walker, and K. Mölmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
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[CrossRef]

Other (4)

C. Cohen-Tannoudji, “Amazing light: a volume dedicated to Charles Hard Townes on his 80th birthday,” in The Autler-Townes Effect Revisited,R. Y. Chiao, ed. (Springer, 1996), p. 109.

In literature, the ladder system is also called cascade system by many authors, e.g. [6].

J. D. Pritchard, K. J. Weatherill, and C. S. Adams, “Non-linear optics using cold Rydberg atoms,” in Annual Review of Cold Atoms and Molecules, K. W. Madison, Y. Wang, A. M. Rey, and K. Bongs, eds. (World Scientific, 2013), Vol. 1, pp. 301–350.

Note that the wavenumber ratio defined in our paper is the reciprocal of that defined in [20].

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Figures (9)

Fig. 1.
Fig. 1.

(a) Ladder-I system, where states |3 and |2 are coupled by the control field with center angular frequency ωc, and states |2 and |1 are coupled by the probe field with center angular frequency ωp. (b) Ladder-II system. (c) Open ladder system. The state |2 couples to the state |3 by field a (with center angular frequency ωa) and the ground state |1 by field b (with center angular frequency ωb). Δ2 and Δ3 are detunings, Γjl are population decay rates from |l to |j, and γ is the transit rate. Particles occupying the state |2 (|3) may decay to other states besides |1 (|2). Levels |4 and |5 denote these other states rendering the system open.

Fig. 2.
Fig. 2.

Probe-field absorption spectrum Im(K) of the ladder-I system as a function of ω and the wavenumber ratio x.

Fig. 3.
Fig. 3.

(a) Pole (0, ikbvT) of the integrand in Eq. (7) in the lower half-complex plane of v. The closed curve with arrows is the contour chosen for calculating the integration in Eq. (7) by using the residue theorem. (b) Probe-field absorption spectrum Im(K) as a function of ω for the hot ladder-I system with wavenumber ratio x=1. The solid (dashed) line is for |Ωa|=500MHz (|Ωa|=0). Definitions of Im(K)min, Im(K)max, and the width of transparency window ΓTW are indicated in the figure.

Fig. 4.
Fig. 4.

EIT-ATS crossover for hot ladder-I system. (a) Probe-field absorption spectrum Im(K) (solid line) in the region |Ωa|<Ωref is a superposition of the positive L1 (dashed–dotted line) and the negative L2 (dashed line). (b) Im(K) (solid line) composed by two Lorentzians (dashed–dotted line) and destructive interference (dashed line) in the region |Ωa|>Ωref. (c) Im(K) (solid line) composed by two Lorentzians (dashed–dotted line) and destructive interference (dashed line) in the region |Ωa|>Ωref. Panels (a), (b), and (c) correspond to EIT, EIT-ATS crossover, and ATS, respectively. (d) The “phase diagram” of Im(K)ω=0/Im(K)max as a function of |Ωa|/Ωref illustrating the transition from EIT to ATS for the hot ladder-I system. Three regions (EIT, EIT-ATS crossover, and ATS) are divided by two vertical dashed–dotted lines.

Fig. 5.
Fig. 5.

Probe absorption spectrum Im(K) as a function of ω for (a) x=0.896 and Ωa=265MHz (corresponding to system B of [20]), and (b) x=1.08 and Ωa=242.5 MHz (corresponding to system A of [20]). The red-dashed lines are our theoretical results, and the black-solid lines are the experimental ones from [20].

Fig. 6.
Fig. 6.

(a) Probe-field absorption spectrum Im(K) as a function of ω. The blue solid (red dashed) line is for |Ωa|=10MHz (|Ωa|=0). (b) Im(K) (blue solid line), AEIT (red-dashed line) and AATS (black dashed–dotted line) as a function of ω for the weak control-field Ωa=3MHz where AEIT has a good fit. (c) The case for the intermediate control field Ωa=15MHz, where both AEIT and AATS have poor fit.

Fig. 7.
Fig. 7.

Probe-field absorption spectrum Im(K) of the ladder-II system as a function of ω and the wavenumber ratio x=ka/kb.

Fig. 8.
Fig. 8.

EIT-ATS crossover for the hot atoms in the ladder-II system for the wavenumber ratio x=1. (a) Probe-field absorption spectrum Im(K) in the weak control field region (|Ωa|<Ωref). The dashed–dotted line is the contribution by positive L1, the dashed line is by negative L2. The sum of L1 and L2 gives Im(K) (solid line). (b) Probe-field absorption spectrum Im(K) (solid line) composed by two Lorentzians (dashed–dotted line) and the destructive interference (dashed line) in the intermediate control field region |Ωa|>Ωref. (c) Probe-field absorption spectrum Im(K) (solid line) composed by two Lorentzians (dashed–dotted line) and the destructive interference (dashed line) in the strong control field region |Ωa|Ωref. Panels (a), (b), and (c) correspond to EIT, EIT-ATS crossover, and ATS, respectively.

Fig. 9.
Fig. 9.

Microwave field driven ladder-II configuration. All notations are given in the text.

Tables (1)

Tables Icon

Table 1. Quantum Interference Characters for Various Ladder Systems with Different Wavenumber Ratio xa

Equations (63)

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^=j=15ωj|jj|(Ωaei[ka·(r+vt)ωat]|32|+Ωbei[kb·(r+vt)ωbt]|21|+h.c.),
itσ11iΓ12σ22iγσ44iΓ15σ55+Ωb*σ21Ωbσ21*=0,
itσ22+iΓ2σ22iΓ23σ33+Ωbσ21*+Ωa*σ32Ωb*σ21Ωaσ32*=0,
itσ33+iΓ3σ33+Ωaσ32*Ωa*σ32=0,
itσ44+iγσ44iΓ42σ22iΓ45σ55=0,
itσ55+iΓ5σ55iΓ53σ33=0,
(it+d21)σ21+Ωa*σ31+Ωb(σ11σ22)=0,
(it+d31)σ31Ωbσ32+Ωaσ21=0,
(it+d32)σ32Ωb*σ31+Ωa(σ22σ33)=0,
2E1c22Et2=1ϵ0c22Pt2.
P=Ndvf(v)[μ12σ21ei(kbzωbt)+μ23σ32ei(kazωat)+c.c.],
i(z+1ct)Ωb+κ12dvf(v)σ21(v)=0,
Ωb(1)=Feiθ
σ21(1)=ω+d31|Ωa|2(ω+d21)(ω+d31)Feiθ,
σ31(1)=Ωa|Ωa|2(ω+d21)(ω+d31)Feiθ;
K(ω)=ωc+κ12dvf(v)ω+d31|Ωa|2(ω+d21)(ω+d31).
K(ω)=ωc+πκ12(ω+iγ31)|Ωa|2(ω+iγ21+iΔωD)(ω+iγ31),
K(ω)=ωcπκ12ω+iγ31(ωω+)(ωω),
ω±=12{i(γ21+γ31+ΔωD)±2[|Ωa|2|Ωref|2]1/2},
Ωref12(γ21+ΔωDγ31).
K(ω)=ωc+πκ12(A+ωω++Aωω),
Im(K)=πκ12(B+ω2+δ+2+Bω2+δ2)L2+L1
K(ω)=ωcπκ12[ω+iW(ω+iWδ)(ω+iW+δ)+i(γ31-W)(ω+iWδ)(ω+iW+δ)],
Im(K)=πκ122{W(ωδ)2+W2+W(ω+δ)2+W2+gδ[ωδ(ωδ)2+W2ω+δ(ω+δ)2+W2]}
Im(K)=πκ122[W(ωδ)2+W2+W(ω+δ)2+W2].
AEIT=B+2ω2+δ+2B2ω2+δ2,
AATS=C[1(ωδ)2+W2+1(ω+δ)2+W2],
i(z+1ct)Ωa+κ23dvf(v)σ32(v)=0,
σ11(0)=(γΓ2|d21|2+2γγ21|Ωb|2)1D1,
σ22(0)=2γγ21|Ωb|21D1,
σ44(0)=2γ21Γ42|Ωb|21D1,
σ21(0)=γΓ2Ωbd21*1D1,
K(ω)=ωc+κ23dvf(v)(ω+d31)2γγ21|Ωb|2γΓ2|Ωb|2d21*D1[|Ωb|2(ω+d31)(ω+d32)].
K(ω)=ω/c+K1+K2
K1=2πκ23γ21|Ωb|2{ω+i[γ31+Γ2(ΔωD+γ21)/(2γ21)]}Γ2(C2ΔωD2)[|Ωb|2(ω+iγ31)(ω+iγ32+iΔωD)],
K2=2πκ23γ21ΔωD|Ωb|2{ω+i[γ31+Γ2(C+γ21)/(2γ21)]}Γ2C(ΔωD2C2)[|Ωb|2(ω+iγ31)(ω+iγ32+iC)].
K(ω)=ωc+κ232dvf(v)ω+d31|Ωb|2(ω+d31)(ω+d32),
K(ω)=ωc+πκ232ω+iγ31+iΔωD|Ωb|2(ω+iγ31+iΔωD)2.
Im(K)=πκ232[W(ωδ)2+W2+W(ω+δ)2+W2],
Kj=ηj(Aj+ωδj++Ajωδj),
η1=2πκ23γ21|Ωb|2Γ2(C2ΔωD2),
η2=2πκ23γ21ΔωD|Ωb|2Γ2C(ΔωD2C2),
δ1±=12[i(γ32+ΔωD+γ31)±4|Ωb|2(γ32+ΔωDγ31)2],
δ2±=12[i(γ32+C+γ31)±4|Ωb|2(γ32+Cγ31)2],
A1±={δ1±[γ31+Γ22γ21(ΔωD+γ21)]}/(δ1+δ1),
A2±={δ2±[γ31+Γ22γ21(C+γ21)]}/(δ2+δ2).
Im(K)=j=12Im(Kj)=j=12ηj(Bj+ω2+Wj+2+Bjω2+Wj2)=L1+L2,
L1=η1B1ω2+W12+η2B2ω2+W22
L2=η1B1+ω2+W1+2+η2B2+ω2+W2+2
Cj+=Wj+(Wj++Γjw)/(Wj+Wj),
Cj=Wj(Wj+Γjw)/(Wj+Wj),
W1±=12[γ32+γ31+ΔωD±[γ32+ΔωDγ31]24|Ωb|2],
W2±=12[γ32+γ31+C±[γ32+Cγ31]24|Ωb|2],
Γ1w=γ31+Γ22γ21(ΔωD+γ21),
Γ2w=γ31+Γ22γ21(C+γ21).
Im(Kj)=ηj{12[Wj(ωδjr)2+Wj2+Wj(ω+δjr)2+Wj2]+gj2δjr[ωδjr(ωδjr)2+Wj2ω+δjr(ω+δjr)2+Wj2]},
W1=(γ31+γ32+ΔωD)/2,
W2=(γ31+γ32+C)/2,
δ1r=4|Ωb|2(γ32+ΔωDγ31)2/2,
δ2r=4|Ωb|2(γ32+Cγ31)2/2,
g1=Γ24+γ21Γ22γ21ΔωD,
g2=Γ24+γ21Γ22γ21C.
Im(Kj)ηj2[Wj(ωδjr)2+Wj2+Wj(ω+δjr)2+Wj2].

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