Abstract

In a spontaneous process, laser-polarized dressings produce characteristic triphoton waveforms regarding the oscillation period and coherence time. Correspondingly, circularly polarized dressings make it have longer oscillation periods compared to the effect of linearly polarized dressings attributed to dispersion relation changes, and shorter coherence times owing to the larger dressing field. Given that the optical response of the polarization state of incident light is the dressing field, we can control the averaged three-photon coincidence count rate by adjusting the polarization of the incident light. By performing quantum tomography, we can obtain W and W-like polarization entanglement states. Accordingly, strong and weak visibilities can be evoked for circularly and linearly polarized dressings.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
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    [Crossref]
  4. H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
    [Crossref]
  5. C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
    [Crossref]
  6. B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98(24), 240502 (2007).
    [Crossref]
  7. L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
    [Crossref]
  8. J. M. Wen, E. Oh, and S. W. Du, “Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state,” J. Opt. Soc. Am. B 27(6), A11–A20 (2010).
    [Crossref]
  9. 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(5), 053601 (2007).
    [Crossref]
  10. D. S. Ding, W. Zhang, S. Shi, Z. Y. Zhou, Y. Li, B. S. Shi, and G. C. Guo, “Experimental generation of tripartite telecom photons by using an atomic ensemble and a nonlinear waveguide,” Optica 2(7), 642–645 (2015).
    [Crossref]
  11. D. Zhang, Y. Q. Zhang, X. H. Li, D. Zhang, L. Cheng, C. B. Li, and Y. P. Zhang, “Generation of high-dimensional energy-time-entangled photon pairs,” Phys. Rev. A 96(5), 053849 (2017).
    [Crossref]
  12. D. Zhang, C. B. Li, Z. Y. Zhang, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media,” Phys. Rev. A 96(4), 043847 (2017).
    [Crossref]
  13. X. H. Li, D. Zhang, D. Zhang, L. Hao, H. X. Chen, Z. G. Wang, and Y. P. Zhang, “Dressing control of biphotons waveform transition,” Phys. Rev. A 97, 053830 (2018).
    [Crossref]
  14. 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(6), 063829 (2008).
    [Crossref]
  15. C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
    [Crossref]
  16. H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
    [Crossref]
  17. Y. Q. Yan, Z. K. Wu, J. H. Si, L. H. Yan, Y. Q. Zhang, C. Z. Yuan, J. Sun, and Y. P. Zhang, “Investigation of odd-order nonlinear susceptibilities in atomic vapors,” Ann. Phys. 333, 307–322 (2013).
    [Crossref]
  18. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
    [Crossref]

2018 (1)

X. H. Li, D. Zhang, D. Zhang, L. Hao, H. X. Chen, Z. G. Wang, and Y. P. Zhang, “Dressing control of biphotons waveform transition,” Phys. Rev. A 97, 053830 (2018).
[Crossref]

2017 (2)

D. Zhang, Y. Q. Zhang, X. H. Li, D. Zhang, L. Cheng, C. B. Li, and Y. P. Zhang, “Generation of high-dimensional energy-time-entangled photon pairs,” Phys. Rev. A 96(5), 053849 (2017).
[Crossref]

D. Zhang, C. B. Li, Z. Y. Zhang, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media,” Phys. Rev. A 96(4), 043847 (2017).
[Crossref]

2016 (1)

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

2015 (2)

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
[Crossref]

D. S. Ding, W. Zhang, S. Shi, Z. Y. Zhou, Y. Li, B. S. Shi, and G. C. Guo, “Experimental generation of tripartite telecom photons by using an atomic ensemble and a nonlinear waveguide,” Optica 2(7), 642–645 (2015).
[Crossref]

2013 (2)

Y. Q. Yan, Z. K. Wu, J. H. Si, L. H. Yan, Y. Q. Zhang, C. Z. Yuan, J. Sun, and Y. P. Zhang, “Investigation of odd-order nonlinear susceptibilities in atomic vapors,” Ann. Phys. 333, 307–322 (2013).
[Crossref]

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
[Crossref]

2011 (1)

H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
[Crossref]

2010 (2)

J. M. Wen, E. Oh, and S. W. Du, “Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state,” J. Opt. Soc. Am. B 27(6), A11–A20 (2010).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[Crossref]

2008 (2)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[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(6), 063829 (2008).
[Crossref]

2007 (2)

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(5), 053601 (2007).
[Crossref]

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98(24), 240502 (2007).
[Crossref]

2004 (1)

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
[Crossref]

2002 (1)

L. A. Lugiato, A. Gatti, and E. Brambilla, “Quantum image,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

1998 (1)

A. Steane, “Quantum computing,” Rep. Prog. Phys. 61(2), 117–173 (1998).
[Crossref]

Bourennane, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
[Crossref]

Boyer, V.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

Brambilla, E.

L. A. Lugiato, A. Gatti, and E. Brambilla, “Quantum image,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

Chen, H. X.

X. H. Li, D. Zhang, D. Zhang, L. Hao, H. X. Chen, Z. G. Wang, and Y. P. Zhang, “Dressing control of biphotons waveform transition,” Phys. Rev. A 97, 053830 (2018).
[Crossref]

Chen, J. F.

H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
[Crossref]

Chen, P.

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
[Crossref]

Chen, Y. A.

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98(24), 240502 (2007).
[Crossref]

Chen, Z. B.

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98(24), 240502 (2007).
[Crossref]

Cheng, L.

D. Zhang, Y. Q. Zhang, X. H. Li, D. Zhang, L. Cheng, C. B. Li, and Y. P. Zhang, “Generation of high-dimensional energy-time-entangled photon pairs,” Phys. Rev. A 96(5), 053849 (2017).
[Crossref]

Chow, T. K. A.

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Ding, D. S.

Du, S. W.

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
[Crossref]

H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
[Crossref]

J. M. Wen, E. Oh, and S. W. Du, “Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state,” J. Opt. Soc. Am. B 27(6), A11–A20 (2010).
[Crossref]

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(5), 053601 (2007).
[Crossref]

Eibl, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
[Crossref]

Fedrizzi, A.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[Crossref]

Gatti, A.

L. A. Lugiato, A. Gatti, and E. Brambilla, “Quantum image,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

Guo, G. C.

Guo, X. X.

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
[Crossref]

Hamel, D. R.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[Crossref]

Hao, L.

X. H. Li, D. Zhang, D. Zhang, L. Hao, H. X. Chen, Z. G. Wang, and Y. P. Zhang, “Dressing control of biphotons waveform transition,” Phys. Rev. A 97, 053830 (2018).
[Crossref]

Hübel, H.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[Crossref]

Jennewein, T.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[Crossref]

Kiesel, N.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
[Crossref]

Kurtsiefer, C.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
[Crossref]

Lett, P. D.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

Li, C. B.

D. Zhang, Y. Q. Zhang, X. H. Li, D. Zhang, L. Cheng, C. B. Li, and Y. P. Zhang, “Generation of high-dimensional energy-time-entangled photon pairs,” Phys. Rev. A 96(5), 053849 (2017).
[Crossref]

D. Zhang, C. B. Li, Z. Y. Zhang, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media,” Phys. Rev. A 96(4), 043847 (2017).
[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(6), 063829 (2008).
[Crossref]

Li, X. H.

X. H. Li, D. Zhang, D. Zhang, L. Hao, H. X. Chen, Z. G. Wang, and Y. P. Zhang, “Dressing control of biphotons waveform transition,” Phys. Rev. A 97, 053830 (2018).
[Crossref]

D. Zhang, Y. Q. Zhang, X. H. Li, D. Zhang, L. Cheng, C. B. Li, and Y. P. Zhang, “Generation of high-dimensional energy-time-entangled photon pairs,” Phys. Rev. A 96(5), 053849 (2017).
[Crossref]

Li, Y.

Loy, M. M. T.

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
[Crossref]

H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
[Crossref]

Lugiato, L. A.

L. A. Lugiato, A. Gatti, and E. Brambilla, “Quantum image,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

Marino, A. M.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

Nie, Z. Q.

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(6), 063829 (2008).
[Crossref]

Oh, E.

Pan, J. W.

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98(24), 240502 (2007).
[Crossref]

Pooser, R. C.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

Ramelow, S.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[Crossref]

Resch, K. J.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
[Crossref]

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466(7306), 601–603 (2010).
[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(5), 053601 (2007).
[Crossref]

Schmiedmayer, J.

B. Zhao, Z. B. Chen, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Robust creation of entanglement between remote memory qubits,” Phys. Rev. Lett. 98(24), 240502 (2007).
[Crossref]

Shalm, L. K.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
[Crossref]

Shi, B. S.

Shi, S.

Shu, C.

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91(4), 043820 (2015).
[Crossref]

Si, J. H.

Y. Q. Yan, Z. K. Wu, J. H. Si, L. H. Yan, Y. Q. Zhang, C. Z. Yuan, J. Sun, and Y. P. Zhang, “Investigation of odd-order nonlinear susceptibilities in atomic vapors,” Ann. Phys. 333, 307–322 (2013).
[Crossref]

Simon, C.

L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, “Three-photon energy–time entanglement,” Nat. Phys. 9(1), 19–22 (2013).
[Crossref]

Steane, A.

A. Steane, “Quantum computing,” Rep. Prog. Phys. 61(2), 117–173 (1998).
[Crossref]

Sun, J.

Y. Q. Yan, Z. K. Wu, J. H. Si, L. H. Yan, Y. Q. Zhang, C. Z. Yuan, J. Sun, and Y. P. Zhang, “Investigation of odd-order nonlinear susceptibilities in atomic vapors,” Ann. Phys. 333, 307–322 (2013).
[Crossref]

Wang, Z. G.

X. H. Li, D. Zhang, D. Zhang, L. Hao, H. X. Chen, Z. G. Wang, and Y. P. Zhang, “Dressing control of biphotons waveform transition,” Phys. Rev. A 97, 053830 (2018).
[Crossref]

Weinfurter, H.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92(7), 077901 (2004).
[Crossref]

Wen, J. M.

J. M. Wen, E. Oh, and S. W. Du, “Tripartite entanglement generation via four-wave mixings: narrowband triphoton W state,” J. Opt. Soc. Am. B 27(6), A11–A20 (2010).
[Crossref]

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(5), 053601 (2007).
[Crossref]

Wong, G. K. L.

H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
[Crossref]

Wu, Z. K.

Y. Q. Yan, Z. K. Wu, J. H. Si, L. H. Yan, Y. Q. Zhang, C. Z. Yuan, J. Sun, and Y. P. Zhang, “Investigation of odd-order nonlinear susceptibilities in atomic vapors,” Ann. Phys. 333, 307–322 (2013).
[Crossref]

Xiao, M.

D. Zhang, C. B. Li, Z. Y. Zhang, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media,” Phys. Rev. A 96(4), 043847 (2017).
[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(6), 063829 (2008).
[Crossref]

Xiao, Y. H.

C. Shu, P. Chen, T. K. A. Chow, L. B. Zhu, Y. H. Xiao, M. M. T. Loy, and S. W. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Yan, H.

H. Yan, S. C. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106(3), 033601 (2011).
[Crossref]

Yan, L. H.

Y. Q. Yan, Z. K. Wu, J. H. Si, L. H. Yan, Y. Q. Zhang, C. Z. Yuan, J. Sun, and Y. P. Zhang, “Investigation of odd-order nonlinear susceptibilities in atomic vapors,” Ann. Phys. 333, 307–322 (2013).
[Crossref]

Yan, Y. Q.

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[Crossref]

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Zhang, Z. Y.

D. Zhang, C. B. Li, Z. Y. Zhang, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media,” Phys. Rev. A 96(4), 043847 (2017).
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[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(6), 063829 (2008).
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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic diagrams of the experimental arrangement in the ${}^{85}Rb$ atomic vapor. EOP is omitted in (c)–(f). (b)–(f) Zeeman energy level diagrams and transition paths at different laser polarized configurations in four-level systems along with (b)–(e) schematic diagrams of single processes and (f) the schematic diagram of the entire set of processes.
Fig. 2.
Fig. 2. Resonances in the fifth-order nonlinear susceptibility |χS3(5)| (a) with a linear polarization dressing field, (b) with dressing field |G1|2 (without polarization dressing), and (c) with a circular polarization dressing field. (a2), (b2), and (c2), are resonances in the dimension of δ3 from (a1), (b1), and (c1), respectively. Similarly, (a3), (b3), and (c3), are resonances in the dimension of δ1 from (a1), (b1), and (c1), respectively.
Fig. 3.
Fig. 3. Multimode triphoton coincidence counting rate in the τ12=t1-t2 and τ13=t1-t3 directions for the damped Rabi oscillation regime. (a) Without polarized dressing, (b) with linearly polarized dressing, and (c) with circularly polarized dressing fields.
Fig. 4.
Fig. 4. Reduced density matrix. (a) Input of HHH (W-like state, heights = 1/4). (b) Input of HHV, HVH, or VHH (W-states, heights = 1/3). (c) Input of VVV (W-like state, heights = 1/4). (d) Input of VVH, VHV, or HVV (W-states, heights = 1/3).
Fig. 5.
Fig. 5. Interference of normal coincidence counts. (a) With circular polarization, and (b) without polarized dressing. (c) With linear polarization dressing. Dashed lines and solid lines exhibit π phase differences.

Tables (1)

Tables Icon

Table 1. Dressing Perturbation chains of the four-level system for linear and circular polarization configurations for the laser

Equations (30)

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H I = ε 0 V d 3 z χ ( 5 ) E 1 ( + ) E 2 ( + ) E 3 ( + ) E S 3 ( ) E S 2 ( ) E S 1 ( ) + H . c .
E 1 ( + ) = E 1 e i ( k 1 z ω 1 t ) , E 2 ( + ) = E 2 e i ( k 2 z ω 2 t ) , E 3 ( + ) = E 3 e i ( k 3 z ω 3 t ) ,
E S 1 ( + ) ( z , t ) = 1 2 π d ω 2 ϖ S 1 c ε 0 A a ^ S 1 ( ω ) e i [ k S 1 z ω t ] ,
E S 2 ( + ) ( z , t ) = 1 2 π d ω 2 ϖ S 2 c ε 0 A a ^ S 2 ( ω ) e i [ k S 2 z + ω t ] ,
E S 3 ( + ) ( z , t ) = 1 2 π d ω 2 ϖ S 3 c ε 0 A a ^ S 3 ( ω ) e i [ k S 3 z ω t ] ,
H I = W 1 d ω S 1 d ω S 2 d ω S 3 κ sin c ( Δ k L 2 ) a ^ S 1 a ^ S 2 a ^ S 3 e i Δ ω t + H . c . ,
| ψ = i + d t H I | 0 .
| ψ = d ω S 1 d ω S 2 d ω S 3 κ sin c ( Δ k L 2 ) a ^ S 1 a ^ S 2 a ^ S 3 δ ( Δ ω ) | 0 = d ω S 1 d ω S 2 d ω S 3 κ ( ω i ) sin c ( Δ k L 2 ) a ^ S 1 a ^ S 2 a ^ S 3 | 0 .
R c c = lim T 1 T 0 T d t S 1 0 T d t S 2 0 T d t S 3 G ( 3 ) M 1 ( t S 2 t S 1 ) M 2 ( t S 3 t S 1 ) ,
G ( 3 ) = | Ψ | E S 1 ( ) E S 2 ( ) E S 3 ( ) E S 3 ( + ) E S 2 ( + ) E S 1 ( + ) | Ψ | = | 0 | E S 3 ( + ) E S 2 ( + ) E S 1 ( + ) | Ψ | 2 = | B ( τ S 1 , τ S 2 , τ S 3 ) | 2 ,
B ( τ S 1 , τ S 2 , τ S 3 ) = W 2 d ω S 1 d ω S 2 d ω S 3 κ ( ω i ) Φ ( Δ k L ) e i ( ω S 1 τ S 1 + ω S 2 τ S 2 + ω S 3 τ S 3 ) ,
3 x x x x x x   =   ( x x x x y y +   x x x y y x +   x x y y x x +   x y y x x x +   y y x x x x +   y x y x x x +   y x x y x x +   y x x x y x +   y x x x x y +   x y x y x x +   x y x x y x +   x y x x x y +   x x y x y x +   x x y x x y +   x x x y x y ) ,
χ S 3 ( 5 )  =  N 0 d 31 d 21 d d 41 d 11 d d 41  =  N 0 ε 0 ( Γ 20  +  i Δ 2 ) P 3 ( δ 2 , δ 3 ) ,
χ s 3 = N 1 μ 14 2 d ¨ 41 ,
R c c 3 = W 2 [ Ω e 1 2 e 2 ( Γ 10 Γ e 1 ) τ 12 + Ω e 1 2 2 e 2 Γ e 1 τ 12 ( 1 cos ( Ω e 1 τ 12 ) ) Ω e 1 ( Γ 10 Γ e 1 ) sin ( Ω e 1 τ 12 ) + Ω e 1 ( Γ 10 Γ e 1 ) sin ( ( Ω e 1 2 + Δ 1 2 ) τ 12 ) ( Ω e 1 2 2 + ( Δ 1 2 ) e ( Γ 10 Γ e 1 ) τ 12 ) cos ( ( Ω e 1 2 + Δ 1 2 ) τ 12 ) + Ω e 1 ( Γ 10 Γ e 1 ) sin ( ( Ω e 1 2 Δ 1 2 ) τ 12 ) ( Ω e 1 2 2 ( Δ 1 2 ) e ( Γ 10 Γ e 1 ) τ 12 ) cos ( ( Ω e 1 2 Δ 1 2 ) τ 12 ) ] e 2 ( Γ e 1 τ 12 + Γ e 2 τ 13 ) , [ Ω e 2 2 e 2 ( Γ 30 Γ e 2 ) τ 13 + Ω e 2 2 2 e 2 Γ e 2 τ 13 ( 1 cos ( Ω e 2 τ 13 ) ) Ω e 2 ( Γ 30 Γ e 2 ) sin ( Ω e 2 τ 13 ) + Ω e 2 ( Γ 30 Γ e 2 ) sin ( ( Ω e 2 2 Δ 1 2 Δ 3 ) τ 13 ) ( Ω e 2 2 2 + ( Δ 1 2 Δ 3 ) e ( Γ 30 Γ e 2 ) τ 13 ) cos ( ( Ω e 2 2 Δ 1 2 Δ 3 ) τ 13 ) + Ω e 2 ( Γ 30 Γ e 2 ) sin ( ( Ω e 2 2 + Δ 1 2 + Δ 3 ) τ 13 ) ( Ω e 2 2 2 ( Δ 1 2 Δ 3 ) e ( Γ 30 Γ e 2 ) τ 13 ) cos ( ( Ω e 2 2 + Δ 1 2 + Δ 3 ) τ 13 ) ]
χ S 3 M ( 5 ) = M = ± 1 , ± 2 , ± 3 2 N μ 6 ε 0 × 1 ( Γ 20 M + i Δ 2 ) ( Γ 10 M i δ 1 i δ 3 + C G 2 G 1 M 2 ( cos 4 θ + sin 4 θ ) Γ 30 M i δ 1 i δ 3 i Δ 1 ) ( Γ 30 M i δ 1 i δ 3 + i Δ 1 ) ( Γ 00 M i δ 3 + C G 2 G 1 2 ( cos 4 θ + sin 4 θ ) Γ 11 M i δ 3 i Δ 1 ) ( Γ 30 M i δ 3 + i Δ 3 )
Ω e 1 = [ Δ 1 2 + 4 ( ( cos 4 θ + sin 4 θ ) ( C G l i n G 1 ) 2 + Γ 10 Γ 30 ) ] ,
Ω e 2 = [ Δ 1 2 + 4 ( ( cos 4 θ + sin 4 θ ) ( C G l i n G 1 ) 2 + Γ 00 Γ 11 ) ] .
χ S 3 M ( 5 ) = M = ± 1 , ± 2 , ± 3 2 N μ 6 ε 0 × 1 ( Γ 20 M + i Δ 2 ) ( Γ 10 M i δ 1 i δ 3 + C G 2 G 1 M 2 ( 2 cos 2 θ sin 2 θ ) Γ 30 M i δ 1 i δ 3 i Δ 1 ) ( Γ 30 M i δ 3 + i Δ 3 ) ( Γ 30 M i δ 1 i δ 3 + i Δ 1 ) ( Γ 00 M i δ 3 + C G 2 G 1 2 ( 2 cos 2 θ sin 2 θ ) Γ 11 M i δ 3 i Δ 1 )
Ω e 1 = [ Δ 1 2 + 4 ( ( 2 cos 2 θ sin 2 θ ) ( C G c i r G 1 ) 2 + Γ 10 Γ 30 ) ] Ω e 2 = [ Δ 1 2 + 4 ( ( 2 cos 2 θ sin 2 θ ) ( C G c i r G 1 ) 2 + Γ 00 Γ 11 ) ] .
| ψ p r o j ( 3 ) = | ψ p r o j ( 1 ) ( h 1 , q 1 ) | ψ p r o j ( 1 ) ( h 2 , q 2 ) | ψ p r o j ( 1 ) ( h 3 , q 3 ) = a ( h 1 , q 1 ) a ( h 2 , q 2 ) a ( h 3 , q 3 ) | H H H + a ( h 1 , q 1 ) a ( h 2 , q 2 ) b ( h 3 , q 3 ) | H H V + a ( h 1 , q 1 ) b ( h 2 , q 2 ) a ( h 3 , q 3 ) | H V H + b ( h 1 , q 1 ) a ( h 2 , q 2 ) a ( h 3 , q 3 ) | V H H + b ( h 1 , q 1 ) b ( h 2 , q 2 ) a ( h 3 , q 3 ) | V V H + a ( h 1 , q 1 ) b ( h 2 , q 2 ) b ( h 3 , q 3 ) | H V V + b ( h 1 , q 1 ) a ( h 2 , q 2 ) b ( h 3 , q 3 ) | V H V + b ( h 1 , q 1 ) b ( h 2 , q 2 ) b ( h 3 , q 3 ) | V V V .
n v , l i n = N l i n ψ v | ρ ^ | ψ v | χ S 3 M ( 5 ) | 4 θ = 0 .
n v , c i r = N c i r ψ v | ρ ^ | ψ v | χ S 3 M ( 5 ) | 4 θ = π 4 .
| W 11 = 1 2 ( | H H H + | V V H + | H V V + | V H V )
| W 12 = 1 3 ( | H H V + | H V H + | V H H )
| W 21 = 1 2 ( | V V V + | H H V + | V H H + | H V H )
| W 22 = 1 3 ( | V V H + | V H V + | H V V )
P = 1 2 + 1 2 R c c 1 d τ 12 d τ 13 R c c 3 d τ 12 d τ 13 cos ( φ 1 + φ 2 + φ 3 )
P l i n = 1 2 + 1 2 R c c 2 d τ 12 d τ 13 R c c 3 d τ 12 d τ 13 cos ( φ 1 + φ 2 + φ 3 )
P c i r = 1 2 + 1 2 cos ( φ 1 + φ 2 + φ 3 )