Abstract

Polarization properties of pure four-wave mixing (FWM) and dressed-FWM processes in a two-level system and a cascade three-level atomic system are theoretically and experimentally investigated. The relative intensities and polarization characteristics of the FWM signals in different laser polarization configurations and different level systems are experimentally investigated and compared. Also, the results are theoretically explained by different transition paths combinations. In the dressed-FWM processes, we study the dependence of dressing effect on the incident field’s polarization. The FWM signal generated by a linearly polarized pumping field is suppressed more by the dressing field than the one generated by a circularly polarized pumping field. However, an opposite effect was observed when the probe field’s polarization is changed. The multidressing mechanisms are used to explain these effects. In addition, the interference and polarization dependence of the coexisting FWM signals in the same atomic system are discussed.

© 2009 Optical Society of America

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  1. K. Tsukiyama, “Parametric four-wave mixing in Kr,” J. Phys. B 29, L345-L351 (1996).
    [CrossRef]
  2. L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
    [CrossRef]
  3. J. Ishii, Y. Ogi, Y. Tanaka, and K. Tsukiyama, “Observation of the two-photon resonant parametric four-wave mixing in the NO C2Π(v=0) state,” Opt. Commun. 132, 316-320 (1996).
    [CrossRef]
  4. C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
    [CrossRef]
  5. P. B. Chapple, K. G. H. Baldwin, and H. A. Bachor, “Interference between competing quantum-mechanical pathways for four-wave mixing,” J. Opt. Soc. Am. B 6, 180-183 (1998).
    [CrossRef]
  6. W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, “Four-wave mixing with Rydberg levels in rubidium vapor: Observation of interference fringes,” Phys. Rev. A 63, 063406 (2001).
    [CrossRef]
  7. W. R. Garret and Y. Zhu, “Coherent control of multiphoton driven processes: A laser-induced catalyst,” J. Chem. Phys. 106, 2045-2048 (1997).
    [CrossRef]
  8. Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
    [CrossRef]
  9. H. Ma, A. S. L. Gomes, and Cid B. de Araujo, “All-optical power-controlled switching in wave mixing: application to semiconductor-doped glasses,” Opt. Lett. 18, 414-416 (1993).
    [CrossRef] [PubMed]
  10. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]
  11. T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801(R) (2006).
    [CrossRef]
  12. S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W. R. Tabosa, “Polarization dependence and interference in four-wave mixing with Rydberg levels in rubidium vapor,” Phys. Rev. A 58, 3000-3003 (1998).
    [CrossRef]
  13. Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
    [CrossRef]
  14. H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
    [CrossRef]
  15. Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
    [CrossRef]
  16. S. G. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
    [CrossRef] [PubMed]
  17. S. G. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: Interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
    [CrossRef]
  18. Y. P. Zhang and M. Xiao, Multi-Wave Mixing Processes (Higher Education Press, Beijing and Springer, Berlin, 2009).
    [CrossRef]
  19. Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual induced transparency,” Phys. Rev. Lett. 99, 123603 (2007).
    [CrossRef] [PubMed]
  20. Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
    [CrossRef] [PubMed]

2009 (1)

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

2008 (2)

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

2007 (4)

Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

S. G. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

S. G. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: Interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual induced transparency,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

2006 (1)

T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801(R) (2006).
[CrossRef]

2005 (1)

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

2003 (1)

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

2001 (1)

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, “Four-wave mixing with Rydberg levels in rubidium vapor: Observation of interference fringes,” Phys. Rev. A 63, 063406 (2001).
[CrossRef]

2000 (1)

L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
[CrossRef]

1998 (2)

P. B. Chapple, K. G. H. Baldwin, and H. A. Bachor, “Interference between competing quantum-mechanical pathways for four-wave mixing,” J. Opt. Soc. Am. B 6, 180-183 (1998).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W. R. Tabosa, “Polarization dependence and interference in four-wave mixing with Rydberg levels in rubidium vapor,” Phys. Rev. A 58, 3000-3003 (1998).
[CrossRef]

1997 (1)

W. R. Garret and Y. Zhu, “Coherent control of multiphoton driven processes: A laser-induced catalyst,” J. Chem. Phys. 106, 2045-2048 (1997).
[CrossRef]

1996 (2)

J. Ishii, Y. Ogi, Y. Tanaka, and K. Tsukiyama, “Observation of the two-photon resonant parametric four-wave mixing in the NO C2Π(v=0) state,” Opt. Commun. 132, 316-320 (1996).
[CrossRef]

K. Tsukiyama, “Parametric four-wave mixing in Kr,” J. Phys. B 29, L345-L351 (1996).
[CrossRef]

1993 (1)

Anderson, B.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Bachor, H. A.

Bahder, T. B.

T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801(R) (2006).
[CrossRef]

Baldwin, K. G. H.

Brown, A. W.

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual induced transparency,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Castex, M. C.

L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
[CrossRef]

Chang, H.

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Chapple, P. B.

de Araujo, Cid B.

Du, S. G.

S. G. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

S. G. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: Interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

Eden, J. G.

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

Gao, J.

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

Garret, W. R.

W. R. Garret and Y. Zhu, “Coherent control of multiphoton driven processes: A laser-induced catalyst,” J. Chem. Phys. 106, 2045-2048 (1997).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Gomes, A. S. L.

Ishii, J.

J. Ishii, Y. Ogi, Y. Tanaka, and K. Tsukiyama, “Observation of the two-photon resonant parametric four-wave mixing in the NO C2Π(v=0) state,” Opt. Commun. 132, 316-320 (1996).
[CrossRef]

Khadka, U.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Li, C. B.

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Li, P. Z.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

Lopata, P. A.

T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801(R) (2006).
[CrossRef]

Lu, Z. H.

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

Ma, H.

Magno, W. C.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, “Four-wave mixing with Rydberg levels in rubidium vapor: Observation of interference fringes,” Phys. Rev. A 63, 063406 (2001).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W. R. Tabosa, “Polarization dependence and interference in four-wave mixing with Rydberg levels in rubidium vapor,” Phys. Rev. A 58, 3000-3003 (1998).
[CrossRef]

Museur, L.

L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
[CrossRef]

Nie, Z. Q.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Nussenzveig, P.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, “Four-wave mixing with Rydberg levels in rubidium vapor: Observation of interference fringes,” Phys. Rev. A 63, 063406 (2001).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W. R. Tabosa, “Polarization dependence and interference in four-wave mixing with Rydberg levels in rubidium vapor,” Phys. Rev. A 58, 3000-3003 (1998).
[CrossRef]

Ogi, Y.

J. Ishii, Y. Ogi, Y. Tanaka, and K. Tsukiyama, “Observation of the two-photon resonant parametric four-wave mixing in the NO C2Π(v=0) state,” Opt. Commun. 132, 316-320 (1996).
[CrossRef]

Oh, E.

S. G. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: Interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

Olivero, C.

L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
[CrossRef]

Prandini, R. B.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, “Four-wave mixing with Rydberg levels in rubidium vapor: Observation of interference fringes,” Phys. Rev. A 63, 063406 (2001).
[CrossRef]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Riedel, D.

L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
[CrossRef]

Rubin, M. H.

S. G. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: Interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

S. G. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

Saldana, J.

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Senin, A. A.

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

Song, J. P.

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Tabosa, J. W. R.

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W. R. Tabosa, “Polarization dependence and interference in four-wave mixing with Rydberg levels in rubidium vapor,” Phys. Rev. A 58, 3000-3003 (1998).
[CrossRef]

Tanaka, Y.

J. Ishii, Y. Ogi, Y. Tanaka, and K. Tsukiyama, “Observation of the two-photon resonant parametric four-wave mixing in the NO C2Π(v=0) state,” Opt. Commun. 132, 316-320 (1996).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Tsukiyama, K.

J. Ishii, Y. Ogi, Y. Tanaka, and K. Tsukiyama, “Observation of the two-photon resonant parametric four-wave mixing in the NO C2Π(v=0) state,” Opt. Commun. 132, 316-320 (1996).
[CrossRef]

K. Tsukiyama, “Parametric four-wave mixing in Kr,” J. Phys. B 29, L345-L351 (1996).
[CrossRef]

Vianna, S. S.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, “Four-wave mixing with Rydberg levels in rubidium vapor: Observation of interference fringes,” Phys. Rev. A 63, 063406 (2001).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W. R. Tabosa, “Polarization dependence and interference in four-wave mixing with Rydberg levels in rubidium vapor,” Phys. Rev. A 58, 3000-3003 (1998).
[CrossRef]

Wen, J. M.

S. G. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

S. G. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: Interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

Wu, Y.

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Xiao, M.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual induced transparency,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Y. P. Zhang and M. Xiao, Multi-Wave Mixing Processes (Higher Education Press, Beijing and Springer, Berlin, 2009).
[CrossRef]

Xiao, Y.

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

Yang, Y. M.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

Yin, G. Y.

S. G. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Zhang, Y. P.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual induced transparency,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Y. P. Zhang and M. Xiao, Multi-Wave Mixing Processes (Higher Education Press, Beijing and Springer, Berlin, 2009).
[CrossRef]

Zheng, H. B.

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level folding atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

Zhu, C. J.

C. J. Zhu, A. A. Senin, Z. H. Lu, J. Gao, Y. Xiao, and J. G. Eden, “Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast (~150-fs) and nanosecond time scale excitation,” Phys. Rev. A 72, 023811 (2005).
[CrossRef]

Zhu, Y.

W. R. Garret and Y. Zhu, “Coherent control of multiphoton driven processes: A laser-induced catalyst,” J. Chem. Phys. 106, 2045-2048 (1997).
[CrossRef]

Zhu, Y. F.

Y. Wu, J. Saldana, and Y. F. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).
[CrossRef]

Appl. Phys. B (1)

L. Museur, C. Olivero, D. Riedel, and M. C. Castex, “Polarization properties of coherent VUV light at 125 nm generated by sum-frequency four-wave mixing in mercury,” Appl. Phys. B 70, 499-503 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

H. B. Zheng, Y. P. Zhang, Z. Q. Nie, C. B. Li, H. Chang, J. P. Song, and M. Xiao, “Interplay among multidressed four-wave mixing processes,” Appl. Phys. Lett. 93, 241101 (2008).
[CrossRef]

Y. P. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

J. Chem. Phys. (1)

W. R. Garret and Y. Zhu, “Coherent control of multiphoton driven processes: A laser-induced catalyst,” J. Chem. Phys. 106, 2045-2048 (1997).
[CrossRef]

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

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Figures (7)

Fig. 1
Fig. 1

Schematic diagrams of the experimental arrangement and the relevant energy levels in the Na atom.

Fig. 2
Fig. 2

Energy level diagrams and transition paths at different laser polarization configurations. (a) and (e) Schematic diagrams of the P-polarization generation in two-level and three-level systems when the waveplates change k p , k d , and k d . (b)–(d) and (f)–(h) Schematic diagrams of S-polarization generation in two-level and three-level systems when the waveplates change k p , k d , and k d , respectively. Dotted, long-dashed, solid, and short-dashed lines are transitions for the probe, coupling, dressing, and FWM signal fields, respectively.

Fig. 3
Fig. 3

Variations of the relative FWM intensities versus the rotation angle of the waveplate. (a) and (b) The FWM signals of the cascade three-level system with the HWP. (c)–(d) The FWM signals of the two-level system with the QWP. The scattered points are the experimental data and the solid curves are the theoretical results.

Fig. 4
Fig. 4

Dependence of the relative NDFWM signal intensity on α for three values of the coupling laser’s ellipticity.

Fig. 5
Fig. 5

Variations of the dressed NDFWM signal intensities versus α. (a) Singly dressed FWM signals when the coupling beam k c is modulated by the QWP. (b) Doubly dressed FWM signals when the coupling beam k c is modulated by the QWP. (c) Variation of the relative FWM intensity versus the rotation angle θ of the QWP.

Fig. 6
Fig. 6

Dependence of the relative NDFWM signal intensity on α for three values of probe laser’s ellipticity. (a) and (b) Pure and singly dressed FWM signals, respectively, of the cascade three-level system as the probe beam is modulated by the QWP.

Fig. 7
Fig. 7

Variations of the DFWM signal intensities versus α (a) Pure FWM signal of the two-level system versus α for several different rotation angles θ of the HWP. (b) Singly dressed and doubly dressed FWM signals when the input beams are all horizontally polarized. (c) The rotation angle α of the polarization analyzer when the maximum intensity is observed. The scattered points are the experimental results, and the solid line represents the case with the polarization analyzer and polarizer rotating the same angle ( α = θ ) .

Tables (3)

Tables Icon

Table 1 Effective Nonlinear Susceptibilities for Different Laser Polarization Configurations

Tables Icon

Table 2 Perturbation Chains of the Two-Level System for Different Laser Polarization Configurations

Tables Icon

Table 3 Perturbation Chains of the Cascade System for Different Laser Polarization Configurations

Equations (15)

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P i ( 3 ) ( ω s ) = ϵ 0 j k l χ i j k l ( 3 ) ( ω s ; ω c , ω c , ω p ) E c j ( ω c ) E c k * ( ω c ) E p l ( ω p ) ,
I x = cos 2 2 α | E x | 2 + | E y | 2 sin 2 2 α + | E x | | E y | sin 4 α cos δ ,
I y = sin 2 2 α | E x | 2 + | E y | 2 cos 2 2 α | E x | | E y | sin 4 α cos δ ,
ρ ̃ p ( 3 ) = i M = ± 1 2 | G d M 0 | 2 G p M 0 ( 1 ( i Δ p + Γ b M a M ) 2 + 1 Δ p 2 + Γ b M a M 2 ) ( 1 Γ a M a M + 1 Γ b M b M ) .
ρ ̃ s 1 ( 3 ) = [ i G p 1 2 | G d 1 2 0 | 2 ( i Δ p + Γ b 1 2 a 1 2 ) 2 Γ a 1 2 a 1 2 + i G p 1 2 + | G d 1 2 0 | 2 ( i Δ p + Γ b 1 2 a 1 2 ) 2 Γ a 1 2 a 1 2 ] M = ± 1 2 2 Γ b M a M | G d M 0 | 2 Γ a M a M ( Δ p 2 + Γ b M a M 2 ) [ i G p M + ( i Δ p + Γ b M + 1 a M ) + i G p M ( i Δ p + Γ b M 1 a M ) ] .
ρ ̃ s 2 ( r ) = i G p 1 2 0 G d 1 2 + ( G d 1 2 0 ) * Γ a 1 2 a 1 2 ( i Δ p + Γ b 1 2 a 1 2 ) ( i Δ p + Γ b 1 2 a 1 2 ) i G p 1 2 0 G d 1 2 ( G d 1 2 0 ) * Γ a 1 2 a 1 2 ( i Δ p + Γ b 1 2 a 1 2 ) ( i Δ p + Γ b 1 2 a 1 2 ) M = ± 1 2 i G p M 0 ( G d M 0 ) * Γ a M a M ( i Δ p + Γ b M a M ) [ G d M ( i Δ p + Γ b M 1 a M ) + G d M + ( i Δ p + Γ b M + 1 a M ) ] .
ρ ̃ s 3 ( 3 ) = 4 i G p 1 2 0 G d 1 2 0 ( G d 1 2 ) * Γ a 1 2 a 1 2 ( i Δ p + Γ b 1 2 a 1 2 ) ( i Δ p + Γ b 1 2 a 1 2 ) .
ρ p ( 3 ) = M = ± 1 2 i G p M 0 i G c M ( G c M 0 ) * ( i Δ p + Γ b M a M ) 2 [ i ( Δ c + Δ p ) + Γ c M a M ] ,
ρ s 1 ( 3 ) = M = ± 1 2 i G p M | G c M 0 | 2 ( i Δ p + Γ b M 1 a M ) 2 ( [ i ( Δ c + Δ p ) + Γ c M 1 a M ] ) M = ± 1 2 i G p M + | G c M 0 | 2 ( i Δ p + Γ b M + 1 a M ) 2 [ i ( Δ c + Δ p ) + Γ c M + 1 a M ] ,
ρ s 2 ( 3 ) = M = ± 1 2 i G p M 0 ( G c M 0 ) * ( i Δ p + Γ b M a M ) × [ i G c M + ( i Δ p + Γ b M + 1 a M ) [ i ( Δ c + Δ p ) + Γ c M + 1 a M ] + i G c M ( i Δ p + Γ b M 1 a M ) [ i ( Δ c + Δ p ) + Γ c M 1 a M ] ] ,
ρ s 3 ( 3 ) = M = ± 1 2 i G p M 0 G c M 0 ( i Δ p + Γ b M a M ) [ i ( Δ c + Δ p ) + Γ c M a M ] ( ( G c M ) * i Δ p + Γ b M 1 a M + ( G c M + ) * i Δ p + Γ b M + 1 a M ) .
ρ b M a M ( 3 ) = i G p M 0 | G c M 0 | 2 ( i ( Δ c + Δ p ) + Γ c M a M ) × 1 ( i Δ p + Γ b M a M + | G d M | 2 i ( Δ p Δ d ) + Γ a M a M + | G p M 0 | 2 Γ a M a M + | G c M 0 | 2 i ( Δ c + Δ p ) + Γ c M a M ) 2 , ( M = ± 1 2 ) .
ρ b M a M ( 3 ) = i G p M 0 | G c M 0 | 2 i ( Δ c + Δ p ) + Γ c M a M × 1 ( i Δ p + Γ b M a M + 2 | G d M | 2 i ( Δ p Δ d ) + Γ a M a M + | G p M 0 | 2 Γ a M a M + | G c M 0 | 2 i ( Δ c + Δ p ) + Γ c M a M ) 2 , ( M = ± 1 2 ) .
I x = χ x x x x 2 ( cos 4 θ + sin 4 θ ) cos 2 2 α + χ y y x x 2 ( 2 sin 2 θ cos 2 θ ) sin 2 2 α + χ x x x x χ y y x x ( cos 4 θ + sin 4 θ ) ( 2 sin 2 θ cos 2 θ ) sin 4 α cos δ ,
I y = χ x x x x 2 ( cos 4 θ + sin 4 θ ) sin 2 2 α + χ y y x x 2 ( 2 sin 2 θ cos 2 θ ) cos 2 2 α χ x x x x χ y y x x ( cos 4 θ + sin 4 θ ) ( 2 sin 2 θ cos 2 θ ) sin 4 α cos δ .

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