Abstract

We investigate the polarization dependence of eight coexisting four-wave mixing (FWM) signals in a two-level atomic system. The intensities and polarization states of coexisting FWM signals are modulated by the polarization configurations and frequency detunings of the incident fields. The suppression and enhancement due to the dressing effects present different polarization dependences. Both the mutual-dressing effect and the self-dressing effect are considered to explain the observed phenomena.

© 2011 Optical Society of America

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  1. 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 (1989).
    [CrossRef]
  2. 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]
  3. S. W. 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]
  4. S. W. 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]
  5. E. F. McCormack and E. Sarajlic, “Polarization effects in quantum coherences probed by two-color, resonant four-wave mixing in the time domain,” Phys. Rev. A 63, 023406 (2001).
    [CrossRef]
  6. K. Tsukiyama, “Parametric four-wave mixing in Kr,” J. Phys. B 29, L345 (1996).
    [CrossRef]
  7. 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]
  8. 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]
  9. 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]
  10. R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
    [CrossRef]
  11. H. B. Zheng, Y. P. Zhang, U. Khadka, R. M. Wang, C. B. Li, Z. Q. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480(2009).
    [CrossRef] [PubMed]
  12. C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
    [CrossRef]
  13. Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77, 063829 (2008).
    [CrossRef]
  14. Y. P. Zhang and M. Xiao, “Generalized dressed and doubly-dressed multiwave mixing,” Opt. Express 15, 7182–7189 (2007).
    [CrossRef] [PubMed]
  15. C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
    [CrossRef]
  16. C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
    [CrossRef]
  17. Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
    [CrossRef]

2010

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[CrossRef]

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

2009

R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
[CrossRef]

H. B. Zheng, Y. P. Zhang, U. Khadka, R. M. Wang, C. B. Li, Z. Q. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480(2009).
[CrossRef] [PubMed]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

2008

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

2007

S. W. 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. W. 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 and M. Xiao, “Generalized dressed and doubly-dressed multiwave mixing,” Opt. Express 15, 7182–7189 (2007).
[CrossRef] [PubMed]

2005

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]

2001

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]

E. F. McCormack and E. Sarajlic, “Polarization effects in quantum coherences probed by two-color, resonant four-wave mixing in the time domain,” Phys. Rev. A 63, 023406 (2001).
[CrossRef]

2000

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]

1996

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 (1996).
[CrossRef]

1989

Bachor, H. A.

Baldwin, K. G. H.

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.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

Chapple, P. B.

Du, S. W.

S. W. 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. W. 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]

Du, Y. G.

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[CrossRef]

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
[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]

Gan, C. L.

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[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]

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.

Li, C. B.

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[CrossRef]

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

H. B. Zheng, Y. P. Zhang, U. Khadka, R. M. Wang, C. B. Li, Z. Q. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480(2009).
[CrossRef] [PubMed]

R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
[CrossRef]

Li, P. Z.

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

Li, Y. Y.

Lu, K. Q.

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[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]

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]

McCormack, E. F.

E. F. McCormack and E. Sarajlic, “Polarization effects in quantum coherences probed by two-color, resonant four-wave mixing in the time domain,” Phys. Rev. A 63, 023406 (2001).
[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.

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
[CrossRef]

H. B. Zheng, Y. P. Zhang, U. Khadka, R. M. Wang, C. B. Li, Z. Q. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480(2009).
[CrossRef] [PubMed]

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

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. W. 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]

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. W. 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. W. 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]

Sarajlic, E.

E. F. McCormack and E. Sarajlic, “Polarization effects in quantum coherences probed by two-color, resonant four-wave mixing in the time domain,” Phys. Rev. A 63, 023406 (2001).
[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.

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
[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]

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 (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]

Wang, R. M.

Wen, J. M.

S. W. 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. W. 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]

Xiao, M.

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

H. B. Zheng, Y. P. Zhang, U. Khadka, R. M. Wang, C. B. Li, Z. Q. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480(2009).
[CrossRef] [PubMed]

R. M. Wang, Y. G. Du, Y. P. Zhang, H. B. Zheng, Z. Q. Nie, C. B. Li, Y. Y. Li, J. P. Song, and M. Xiao, “Polarization spectroscopy of dressed four-wave mixing in a three-level atomic system,” J. Opt. Soc. Am. B 26, 1710–1719 (2009).
[CrossRef]

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

Y. P. Zhang and M. Xiao, “Generalized dressed and doubly-dressed multiwave mixing,” Opt. Express 15, 7182–7189 (2007).
[CrossRef] [PubMed]

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 multiwave mixing in a five-level atomic system,” Phys. Rev. A 77, 063829 (2008).
[CrossRef]

Yin, G. Y.

S. W. 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]

Zhang, Y. P.

C. B. Li, Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. C. Zuo, Y. G. Du, J. P. Song, K. Q. Lu, and C. L. Gan, “Controlled multi-wave mixing via interacting dark states in a five-level system,” Opt. Commun. 283, 2918–2928 (2010).
[CrossRef]

C. B. Li, Y. P. Zhang, Z. Q. Nie, Y. G. Du, R. M. Wang, J. P. Song, and M. Xiao, “Controlling enhancement and suppression of four-wave mixing via polarized light,” Phys. Rev. A 81, 033801(2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80, 055804 (2009).
[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Schematic of two-level system configuration consisting of Zeeman sublevels. (a) QWP changes field k c , (b) QWP changes field k c , (c) QWP changes both fields k c and k c . Solid lines, the coupling fields k c and k c ; dashed lines, coupling fields k d and k d ; dashed–dotted lines, probe field k p ; dotted lines, probe field k p .

Fig. 3
Fig. 3

Relative intensities of four FWM signals ( k s 1 , k s 2 , k s 3 , k s 4 ) versus Δ 1 with Δ 2 = 0.3 cm 1 . (a) Undressed-FWM signals k s 1 , k s 2 , and k d -dressed k s 1 , k s 2 . (b) Undressed-FWM signals k s 3 , k s 4 , and k d -dressed k s 3 , k s 4 . (c) Coexisting FWM signals k s 1 + k s 2 and k d -dressed k s 1 + k s 2 . (d) Coexisting FWM signals k s 3 + k s 4 and k d -dressed k s 3 + k s 4 .

Fig. 4
Fig. 4

Dependence of the FWM signal intensity on the rotation angle of the HWP put on the path of field k c . (a)–(c) FWM signals when coupling field k c or k d is blocked. Squares, six laser beams are all turned on; circles, k c is blocked; triangles, k d is blocked. (b)–(d) FWM signals when probe field k p or k p is blocked. Squares, six laser beams are all turned on; circles, k p is blocked; triangles, k p is blocked.

Fig. 5
Fig. 5

Dependence of the relative FWM signal intensity on the rotation angle of the polarization analyzer for four values of the ellipticity of field k c . (a)–(c) FWM signals detected by PMT1 and PMT2, respectively. (b)–(d)  FWM signals detected by PMT1 and PMT2 when k d is blocked. Squares, θ = 0 ° (θ is the polarization angle of k c ); circles, θ = 15 ° ; triangles, θ = 30 ° ; asterisks, θ = 45 ° .

Fig. 6
Fig. 6

Polarization dependence of the suppression of FWM signals versus the rotation angle of the QWP. (a) FWM signals when k c is at 45 ° . (b) Field k c is modulated by the QWP. (c) Zeeman sublevel schemes. (d) Fields k c and k c are simultaneously modulated by the QWP.

Fig. 7
Fig. 7

Polarization dependence of the enhancement of FWM signals versus the rotation angle of the QWP. (a) Field k c is modulated by the QWP. (b) Field k c is blocked, and k d is modulated by the QWP. (c) Field k c is modulated by the QWP.

Tables (2)

Tables Icon

Table 1 Wave Vectors and Frequencies of the Generated FWM Signals Detected by PMT1 and PMT2

Tables Icon

Table 2 Perturbation Chains of Horizontally Polarized Components of FWM Signals When Fields k c and k c are Changed by the QWP

Equations (16)

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ρ P ( PMT 1 ) k 1 , k 1 = i M = ± 1 / 2 [ | G c M 0 | 2 Γ a M a M d 1 ( G p M 0 d 1 + G p M 0 d 2 ) + ( G c M 0 ) * G d M 0 d 3 d 2 ( G p M 0 d 2 + G p M 0 d 4 ) ] i M = ± 1 / 2 1 Γ a M a M ( ( G c M ) * G c M d 11 + ( G c M + ) * G c M + d 12 ) ( G p M 0 d 1 + G p M 0 d 2 ) ,
ρ s ( PMT 1 ) k 1 , k 1 = i M = ± 1 / 2 [ G c M 0 ( G c M ± ) * Γ a M a M d 1 ( G p M 0 d 14 + G p M 0 d 13 ) + G d M 0 ( G c M ± ) * d 7 d 2 ( G p M 0 d 14 + G p M 0 d 8 ) ] ,
ρ P ( PMT 2 ) k 1 , k 1 = i M = ± 1 / 2 [ | G d M 0 | 2 Γ a M a M d 2 ( G p M 0 d 1 + G p M 0 d 2 ) + G c M 0 ( G d M 0 ) * d 5 d 1 ( G p M 0 d 6 + G p M 0 d 1 ) ] ,
ρ s ( PMT 2 ) k 1 , k 1 = i M = ± 1 / 2 [ G c M ( G c M 0 ) * Γ a M a M d 13 ( G p M 0 d 13 + G p M 0 d 14 ) + G c M ( G d M 0 ) * d 9 d 13 ( G p M 0 d 10 + G p M 0 d 13 ) ] ,
ρ P ( PMT 1 ) k 1 , k 1 = i M = ± 1 / 2 [ | G c M 0 | 2 Γ a M a M ( d 1 + | G d M 0 | 2 d 3 ) ( G p M 0 d 1 + G p M 0 d 2 ) + ( G c M 0 ) * G d M 0 d 3 ( d 2 + | ( G d M 0 ) * | 2 Γ a M a M + | G c M 0 | 2 d 5 ) ( G p M 0 d 2 + G p M 0 d 4 ) ] ,
ρ P ( PMT 2 ) k 1 , k 1 = i M = ± 1 / 2 [ | G d M 0 | 2 Γ a M a M ( d 2 + | G c M 0 | 2 d 5 ) ( G p M 0 d 1 + G p M 0 d 2 ) + G c M 0 ( G d M 0 ) * d 5 ( d 1 + | ( G c M 0 ) * | 2 Γ a M a M + | G d M 0 | 2 d 5 ) ( G p M 0 d 6 + G p M 0 d 1 ) ] .
ρ P ( PMT 1 ) k 1 , k 1 = i M = ± 1 / 2 [ | G c M 0 | 2 Γ a M a M ( d 1 + | G d M 0 | 2 d 3 ) ( G p M 0 d 1 + G p M 0 d 2 ) + ( G c M 0 ) * G d M 0 d 3 ( d 2 + | ( G d M 0 ) * | 2 Γ a M a M + | G c M | 2 + | G c M + | 2 d 3 ) × ( G p M 0 d 2 + G p M 0 d 4 ) ] i M = ± 1 / 2 1 Γ a M a M ( ( G c M ) * G c M d 13 + | G d M 0 | 2 d 3 + ( G c M + ) * G c M + d 12 + | G d M 0 | 2 d 3 ) ( G p M 0 d 1 + G p M 0 d 2 ) ,
ρ P ( PMT 2 ) k 1 , k 1 = i M = ± 1 / 2 | G d M 0 | 2 Γ a M a M ( d 2 + | G c M | 2 + | G c M + | 2 d 5 ) ( G p M 0 d 1 + G p M 0 d 2 ) i M = ± 1 / 2 G c M 0 ( G d M 0 ) * d 5 ( d 1 + | ( G c M ) * | 2 + | ( G c M + ) * | 2 Γ a M a M + | G d M 0 | 2 d 5 ) ( G p M 0 d 6 + G p M 0 d 1 ) .
| a 1 / 2 G c 2 0 | b 1 / 2 G c 2 0 | a 1 / 2 G p 2 0 | b 1 / 2 ( G F 2 0 ) * | a 1 / 2 ,
| a 1 / 2 G c 1 0 | b 1 / 2 G c 1 0 | a 1 / 2 G p 1 0 | b 1 / 2 ( G F 1 0 ) * | a 1 / 2 ,
ρ 1 k 1 = i G p 2 0 G c 2 0 ( G c 2 0 ) * Γ a 1 / 2 a 1 / 2 ( i Δ 1 + Γ b 1 / 2 a 1 / 2 + | G d 2 0 | 2 i ( Δ 1 Δ 2 ) + Γ a 1 / 2 a 1 / 2 ) ( i Δ 1 + Γ b 1 / 2 a 1 / 2 ) .
| a 1 / 2 G c 1 + | b 1 / 2 G c 2 0 | a 1 / 2 G p 2 0 | b 1 / 2 ( G F 2 + ) * | a 1 / 2 ,
| a 1 / 2 G c 2 | b 1 / 2 G c 1 0 | a 1 / 2 G p 1 0 | b 1 / 2 ( G F 1 ) * | a 1 / 2 .
ρ 5 k 1 = i G p 2 0 G c 1 + ( G c 2 0 ) * Γ a 1 / 2 a 1 / 2 ( i Δ 1 + Γ b 1 / 2 a 1 / 2 + | G d 2 0 | 2 i ( Δ 1 Δ 2 ) + Γ a 1 / 2 a 1 / 2 ) 2 .
ρ 1 k 1 = i G p 2 0 G c 2 0 ( G c 2 0 ) * Γ a 1 / 2 a 1 / 2 ( i Δ 1 + Γ b 1 / 2 a 1 / 2 + | G d 2 0 | 2 i ( Δ 1 Δ 2 ) + Γ a 1 / 2 a 1 / 2 + | G c 2 0 | 2 Γ a 1 / 2 a 1 / 2 ) ( i Δ 1 + Γ b 1 / 2 a 1 / 2 ) ,
ρ 5 k 1 = i G p 2 0 G c 1 + ( G c 2 0 ) * Γ a 1 / 2 a 1 / 2 ( i Δ 1 + Γ b 1 / 2 a 1 / 2 + | G c 1 0 | 2 Γ a 1 / 2 a 1 / 2 + | ( G c 1 0 ) + | 2 Γ a 1 / 2 a 1 / 2 + | G d 2 0 | 2 i ( Δ 2 ) + Γ a 1 / 2 b 1 / 2 + | G d 2 0 | 2 i ( Δ 1 Δ 2 ) + Γ a 1 / 2 a 1 / 2 ) 2 .

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