Abstract

We propose resilient quantum superposition states in closed-loop multilevel system which result in myriad quantum interference phenomena. An interplay of these superposition states results in a whole gamut of atomic phenomena including coherent population trapping (CPT), electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), amplification without inversion (AWI) and enhancement of refractive index accompanied with negligible absorption. The polarization and the phases of the fields transform the underlying superposition of the excited states leading to all these effects, where, given the macroscopic nature of these phenomena the quantum superposition states as well as the synergy between them can be ascertained. Numerical simulations for D1 transition in room temperature Rb87 atomic vapour system bear out these findings.

© 2014 Optical Society of America

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  1. J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
    [CrossRef] [PubMed]
  2. P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
    [CrossRef] [PubMed]
  3. E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
    [CrossRef] [PubMed]
  4. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
    [CrossRef]
  5. M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1855 (1991).
    [CrossRef] [PubMed]
  6. A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
    [CrossRef] [PubMed]
  7. N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101, 147401 (2008).
    [CrossRef] [PubMed]
  8. S.Y. Zhu, M. O. Scully, H. Fearn, and L. M. Narducci, “Lasing without inversion,” Z. Phys. D - Atoms, Molecules and Clusters 22, 483–493 (1992).
    [CrossRef]
  9. E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
    [CrossRef] [PubMed]
  10. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A. 57, 2996 (1998)
    [CrossRef]
  11. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A. 61, 011802 (1999).
    [CrossRef]
  12. A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
    [CrossRef]
  13. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
    [CrossRef]
  14. E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A 60, 4996 (1999).
    [CrossRef]
  15. E. Cerboneschi and E. Arimondo, “Matched pulses and electromagnetically induced transparency for the interaction of laser pulse pairs with a double-vee system,” Opt, Commun. 127, 55–61 (1996).
    [CrossRef]
  16. E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, ed. E. Wolf,ed. (Elsevier, 1996) 35, pp. 257–354.
    [CrossRef]
  17. K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998).
    [CrossRef]
  18. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
    [CrossRef] [PubMed]

2012

A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

2008

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101, 147401 (2008).
[CrossRef] [PubMed]

2006

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
[CrossRef]

2004

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

2002

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

2000

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef] [PubMed]

1999

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A 60, 4996 (1999).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A. 61, 011802 (1999).
[CrossRef]

1998

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A. 57, 2996 (1998)
[CrossRef]

1996

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

E. Cerboneschi and E. Arimondo, “Matched pulses and electromagnetically induced transparency for the interaction of laser pulse pairs with a double-vee system,” Opt, Commun. 127, 55–61 (1996).
[CrossRef]

1993

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

1992

S.Y. Zhu, M. O. Scully, H. Fearn, and L. M. Narducci, “Lasing without inversion,” Z. Phys. D - Atoms, Molecules and Clusters 22, 483–493 (1992).
[CrossRef]

1991

M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1855 (1991).
[CrossRef] [PubMed]

1988

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
[CrossRef] [PubMed]

Akulshin, A. M.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A. 57, 2996 (1998)
[CrossRef]

Arimondo, E.

E. Cerboneschi and E. Arimondo, “Matched pulses and electromagnetically induced transparency for the interaction of laser pulse pairs with a double-vee system,” Opt, Commun. 127, 55–61 (1996).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
[CrossRef] [PubMed]

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, ed. E. Wolf,ed. (Elsevier, 1996) 35, pp. 257–354.
[CrossRef]

Ashhab, S.

A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Aspect, A.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
[CrossRef] [PubMed]

Barreiro, S.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A. 57, 2996 (1998)
[CrossRef]

Bergmann, K.

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Cerboneschi, E.

E. Cerboneschi and E. Arimondo, “Matched pulses and electromagnetically induced transparency for the interaction of laser pulse pairs with a double-vee system,” Opt, Commun. 127, 55–61 (1996).
[CrossRef]

Chen, W.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef] [PubMed]

Claussen, N. R.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
[CrossRef] [PubMed]

Donley, E. A.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Fearn, H.

S.Y. Zhu, M. O. Scully, H. Fearn, and L. M. Narducci, “Lasing without inversion,” Z. Phys. D - Atoms, Molecules and Clusters 22, 483–493 (1992).
[CrossRef]

Friedman, J. R.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef] [PubMed]

Fry, E. S.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Green, J. T.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101, 147401 (2008).
[CrossRef] [PubMed]

Hansch, T. W.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

Hollberg, L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Hommelhoff, P.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
[CrossRef] [PubMed]

Kofman, A. G.

A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Korsunsky, E. A.

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Kosachiov, D. V.

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Lezama, A.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A. 57, 2996 (1998)
[CrossRef]

Li, X.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Lukens, J. E.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef] [PubMed]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Narducci, L. M.

S.Y. Zhu, M. O. Scully, H. Fearn, and L. M. Narducci, “Lasing without inversion,” Z. Phys. D - Atoms, Molecules and Clusters 22, 483–493 (1992).
[CrossRef]

Nikonov, D.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Nikonov, D. E.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Nori, F.

A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Padmabandu, G. G.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Patel, V.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef] [PubMed]

Proite, N. A.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101, 147401 (2008).
[CrossRef] [PubMed]

Reichel, J.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

S.Y. Zhu, M. O. Scully, H. Fearn, and L. M. Narducci, “Lasing without inversion,” Z. Phys. D - Atoms, Molecules and Clusters 22, 483–493 (1992).
[CrossRef]

M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1855 (1991).
[CrossRef] [PubMed]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
[CrossRef]

Shore, B.W.

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Smith, A. V.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Steinmetz, T.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

Taichenachev, A. V.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A. 61, 011802 (1999).
[CrossRef]

Theuer, H.

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Thompson, S. T.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Tittel, F. K.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Tolpygo, S. K.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef] [PubMed]

Treutlein, P.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, “Coherence in microchip traps,” Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

Tumaikin, A. M.

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A. 61, 011802 (1999).
[CrossRef]

Unks, B. E.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101, 147401 (2008).
[CrossRef] [PubMed]

Vansteenkiste, N.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826 (1988).
[CrossRef] [PubMed]

Velichansky, V. L.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
[CrossRef]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Wang, C.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Wieman, C. E.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Wilkinson, S. R.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Yavuz, D. D.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, “Refractive index enhancement with vanishing absorption in an atomic vapor,” Phys. Rev. Lett. 101, 147401 (2008).
[CrossRef] [PubMed]

Yudin, V. I.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
[CrossRef]

A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A. 61, 011802 (1999).
[CrossRef]

Zhu, S. Y.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
[CrossRef] [PubMed]

Zhu, S.Y.

S.Y. Zhu, M. O. Scully, H. Fearn, and L. M. Narducci, “Lasing without inversion,” Z. Phys. D - Atoms, Molecules and Clusters 22, 483–493 (1992).
[CrossRef]

Zibrov, A. S.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
[CrossRef]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Zibrov, S. A.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
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Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
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Nature

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
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E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
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E. Cerboneschi and E. Arimondo, “Matched pulses and electromagnetically induced transparency for the interaction of laser pulse pairs with a double-vee system,” Opt, Commun. 127, 55–61 (1996).
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Phys. Rev. A

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, “Pure superposition states of atoms generated by a bichromatic elliptically polarized field,” Phys. Rev. A 73, 013812 (2006).
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A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A. 57, 2996 (1998)
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A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A. 61, 011802 (1999).
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Phys. Rev. Lett.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: Lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235 (1993).
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A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb,” Phys. Rev. Lett. 76, 3935 (1996).
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M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
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Figures (6)

Fig. 1
Fig. 1

[Left] The bare Double-V system associated with an m-m transition (total angular quantum F) coupled to a bi-chromatic field. The single photon detuning δ is as indicated. [Right] The double-V system in the superposed basis of the ω1 field.

Fig. 2
Fig. 2

The double-V configuration of the bare system (center) transforms to the Λ system (left), and two uncoupled two-level systems (right) in the superposed basis.

Fig. 3
Fig. 3

Absorption experienced by the four fields are shown in arbitrary units for Case-1 (orange) leads to EIT, and Case-3 (blue) with Ω̃N2 being negative, leads to AWI. The sharp dips at the two-photon resonance are magnified in the insets. The parameters are θ = π/2, for Case-1 ε1 = ε2 = 0° and for Case-3 ε1 = 23.5°, ε2 = 0° with Ω32 = −Ω42, Ω31 = −i0.41Ω42 and Ω41 = i1.05Ω42.

Fig. 4
Fig. 4

Absorption experienced by the four fields are shown in arbitrary units for Case-2 (orange) devoid of any quantum interference, and Case-4 (blue) with Ω̃C2 positive, leads to EIA and partial EIT. The sharp peaks and dips at the two-photon resonance are magnified in the insets. The parameters are θ = 0, for Case-2 ε1 = ε2 = 0° and for Case-4 ε1 = 23.5°, ε2 = 0° with Ω32 = Ω42, Ω31 = −0.41Ω42 and Ω41 = 1.05Ω42.

Fig. 5
Fig. 5

Enhanced refractive index (point A) accompanied with zero absorption (point B) experienced by a weak component ω1,σ keeping θ = π 4, ε1 = 40°, ε2 = 0° with Ω 32 = Ω 42 *, Ω31 = −0.07(1 − i42 and Ω41 = 0.8(1 − i42.

Fig. 6
Fig. 6

The atomic response for D1 transition of a room temperature doppler broadened atomic vapour of Rb87. The probe field couples the |4〉 ↔ |2〉 transition and, (a) exhibits Case-1 (EIT) ; (b) Case-2 (No quantum interference) with the inset depicting the atomic lineshape with and without doppler broadening, the doppler broadened lineshape is multiplied by a factor of 10 for graphical clarity; (c) red line for Case-3 (AWI) and blue line for Case-4 (EIA); (d) depicts the Case-5 refractive index enhancement. The parameters in (a) and (b) are same as earlier, for (c) and (d) see text for the imbalance in the field polarization.

Equations (22)

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E = E 1 + E 2 ,
E 1 = E 1 [ sin ( ψ 1 ) σ ^ + cos ( ψ 1 ) σ ^ ] e i ω 1 t + c . c ,
E 2 = E 2 [ e i θ sin ( ψ 2 ) σ ^ + e i θ cos ( ψ 2 ) σ ^ ] e i ω 2 t + c . c ,
| D ± = Ω i 1 | 2 Ω i 2 | 1 | Ω i 1 | 2 + | Ω i 2 | 2 , | B ± = Ω i 2 * | 2 + Ω i 1 * | 1 | Ω i 1 | 2 + | Ω i 2 | 2 ,
| N i = Ω 3 i * | 4 Ω 4 i * | 3 | Ω 3 i | 2 + | Ω 4 i | 2 , | C i = Ω 4 i | 4 + Ω 3 i | 3 | Ω 3 i | 2 + | Ω 4 i | 2 ,
Ω C 1 = | Ω 41 | 2 + | Ω 31 | 2 Ω ,
Ω C 2 = Ω 42 Ω 41 * + Ω 32 Ω 31 * Ω ,
Ω N 2 = Ω 42 Ω 31 Ω 32 Ω 41 Ω .
ρ 4 i = Ω 41 ρ C i + Ω 31 * ρ N i Ω , ρ 3 i = Ω 31 ρ C i Ω 41 * ρ N i Ω .
Ω 42 Ω 32 = Ω 41 Ω 31 .
h ¯ Ω i j = e i | r . E | j .
h ¯ Ω i j = d i j C F j , m j , 1 , ± 1 F i , m i E j σ ± ,
C F 1 , m 1 , 1 , 1 F 3 , m 3 C F 1 , m 1 , 1 , + 1 F 4 , m 4 C F 2 , m 2 , 1 , + 1 F 4 , m 4 C F 2 , m 2 , 1 , 1 F 3 , m 3 = E 1 σ + E 1 σ E 2 σ E 2 σ + .
1 + F m 1 + F + m = e 2 i θ tan ( ε 1 + π 4 ) tan ( ε 2 + π 4 ) .
θ = π 2 , 1 + F m 1 + F + m = tan ( ε 1 + π 4 ) tan ( ε 2 + π 4 ) ,
Ω 42 Ω 32 = Ω 31 * Ω 41 * ,
( C F 1 , m 1 , 1 , 1 F 3 , m 3 C F 1 , m 1 , 1 , + 1 F 4 , m 4 ) * ( C F 2 , m 2 , 1 , 1 F 3 , m 3 C F 2 , m 2 , 1 , + 1 F 4 , m 4 ) = E 1 σ + E 1 σ E 2 σ + E 2 σ ,
θ = 0 , 2 + F m 2 + F + m = tan ( ε 1 + π 4 ) tan ( ε 2 + π 4 ) for F e = F + 1 ,
θ = 0 , F + m F m = tan ( ε 1 + π 4 ) tan ( ε 2 + π 4 ) for F e = F .
χ i j ( ω ) = n Ω i j * ε 0 | E i j | 2 ρ i j ,
ρ ˜ 42 = 1 Ω [ ( Ω 41 Ω 42 * Ω C 2 * ) ρ ˜ C 2 + ( Ω 31 * Ω 42 * Ω N 2 * ) ρ ˜ N 2 ] ,
ρ ˜ 32 = 1 Ω [ ( Ω 31 Ω 32 * Ω C 2 * ) ρ ˜ C 2 ( Ω 41 * Ω 32 * Ω N 2 * ) ρ ˜ N 2 ] .

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