Abstract

We study the parametric amplification of electromagnetically induced transparency-assisted Rydberg six- and eight-wave mixing signals through a cascaded nonlinear optical process in a hot rubidium atomic ensemble both theoretically and experimentally. The shift of the resonant frequency (induced by the Rydberg–Rydberg interaction) of parametrically amplified six-wave mixing signal is observed. Moreover, the interplays between the dressing effects and Rydberg–Rydberg interactions in parametrically amplified multiwave mixing signals are investigated. The linear amplification of Rydberg multiwave mixing processes with multichannel nature acts against the suppression caused by Rydberg–Rydberg interaction and dressing effect.

© 2018 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
  38. H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four-and six-wave mixing in an optical ring cavity,” Sci. Rep. 4, 3619 (2014).
    [Crossref]
  39. Y. Li, G. Huang, D. Zhang, Z. Wu, Y. Zhang, J. Che, and Y. Zhang, “Density control of dressed four-wave mixing and super-fluorescence,” IEEE J. Quantum Electron. 50, 25–34 (2014).
    [Crossref]
  40. J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
    [Crossref]
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    [Crossref]

2016 (3)

N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. L. Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
[Crossref]

Z. Bai and G. Huang, “Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction,” Opt. Express 24, 4442–4461 (2016).
[Crossref]

Z. Zhang, H. Tang, I. Ahmed, N. Ahmed, G. Khan, A. Mahesar, and Y. Zhang, “Controlling Rydberg-dressed four-wave mixing via dual electromagnetically induced transparency windows,” J. Opt. Soc. Am. B 33, 1661–1667 (2016).
[Crossref]

2015 (6)

R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2, 393–399 (2015).
[Crossref]

Z. Zhang, J. Che, D. Zhang, Z. Liu, X. Wang, and Y. Zhang, “Eight-wave mixing process in a Rydberg-dressing atomic ensemble,” Opt. Express 23, 13814–13822 (2015).
[Crossref]

Z. Zhang, H. Zheng, X. Yao, Y. Tian, J. Che, X. Wang, D. Zhu, Y. Zhang, and M. Xiao, “Phase modulation in Rydberg dressed multi-wave mixing processes,” Sci. Rep. 5, 10462 (2015).
[Crossref]

Z. Zhang, F. Wen, J. Che, D. Zhang, C. Li, Y. Zhang, and M. Xiao, “Dressed gain from the parametrically amplified four-wave mixing process in an atomic vapor,” Sci. Rep. 5, 15058 (2015).
[Crossref]

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photon. 3, 8–13 (2015).
[Crossref]

J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
[Crossref]

2014 (4)

H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four-and six-wave mixing in an optical ring cavity,” Sci. Rep. 4, 3619 (2014).
[Crossref]

Y. Li, G. Huang, D. Zhang, Z. Wu, Y. Zhang, J. Che, and Y. Zhang, “Density control of dressed four-wave mixing and super-fluorescence,” IEEE J. Quantum Electron. 50, 25–34 (2014).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
[Crossref]

2013 (3)

P. Li, H. Zheng, Y. Zhang, J. Sun, C. Li, G. Huang, Z. Zhang, Y. Li, and Y. Zhang, “Controlling the transition of bright and dark states via scanning dressing field,” Opt. Mater. 35, 1062–1070 (2013).
[Crossref]

H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3, 1885 (2013).
[Crossref]

Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4588 (2013).
[Crossref]

2012 (6)

C. Carr, M. Tanasittikosol, A. Sargsyan, D. Sarkisyan, C. S. Adams, and K. J. Weatherill, “Three-photon electromagnetically induced transparency using Rydberg states,” Opt. Lett. 37, 3858–3860 (2012).
[Crossref]

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

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

A. Kölle, G. Epple, H. Kübler, R. Löw, and T. Pfau, “Four-wave mixing involving Rydberg states in thermal vapor,” Phys. Rev. A 85, 063821 (2012).
[Crossref]

Y. O. Dudin and A. Kuzmich, “Strongly interacting Rydberg excitations of a cold atomic gas,” Science 336, 887–889 (2012).
[Crossref]

G. Günter, M. Robert-De-Saint-Vincent, H. Schempp, C. S. Hofmann, S. Whitlock, and M. Weidemüller, “Interaction enhanced imaging of individual Rydberg atoms in dense gases,” Phys. Rev. Lett. 108, 013002 (2012).
[Crossref]

2011 (1)

2010 (1)

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

2009 (1)

Y. 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]

2008 (3)

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

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

E. Brekke, J. O. Day, and T. G. Walker, “Four-wave mixing in ultracold atoms using intermediate Rydberg states,” Phys. Rev. A 78, 063830 (2008).
[Crossref]

2007 (1)

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

2006 (3)

J. M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006).
[Crossref]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74–77 (2006).
[Crossref]

2004 (1)

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[Crossref]

2001 (1)

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

2000 (1)

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[Crossref]

1999 (1)

M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82, 1847–1850 (1999).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[Crossref]

1995 (1)

M. Xiao, Y. Li, S. Jin, and J. Geabanacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[Crossref]

1994 (1)

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref]

1986 (1)

P. P. Herrmann, J. Hoffnagle, N. Schlumpf, V. L. Telegdi, and A. Weis, “Stark spectroscopy of forbidden two-photon transitions: a sensitive probe for the quantitative measurement of small electric fields,” J. Phys. B 19, 1271–1280 (1986).
[Crossref]

Adams, C. S.

Ahmed, I.

Ahmed, N.

Almeida, M. P.

N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. L. Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
[Crossref]

Anderson, B.

Y. 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]

Anton, C.

N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. L. Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
[Crossref]

Auffeves, A.

N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. L. Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
[Crossref]

Bai, Z.

Belic, M.

Boyer, V.

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

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

Brekke, E.

E. Brekke, J. O. Day, and T. G. Walker, “Four-wave mixing in ultracold atoms using intermediate Rydberg states,” Phys. Rev. A 78, 063830 (2008).
[Crossref]

Brown, A. W.

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

Carr, C.

Che, J.

Z. Zhang, J. Che, D. Zhang, Z. Liu, X. Wang, and Y. Zhang, “Eight-wave mixing process in a Rydberg-dressing atomic ensemble,” Opt. Express 23, 13814–13822 (2015).
[Crossref]

J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
[Crossref]

Z. Zhang, H. Zheng, X. Yao, Y. Tian, J. Che, X. Wang, D. Zhu, Y. Zhang, and M. Xiao, “Phase modulation in Rydberg dressed multi-wave mixing processes,” Sci. Rep. 5, 10462 (2015).
[Crossref]

Z. Zhang, F. Wen, J. Che, D. Zhang, C. Li, Y. Zhang, and M. Xiao, “Dressed gain from the parametrically amplified four-wave mixing process in an atomic vapor,” Sci. Rep. 5, 15058 (2015).
[Crossref]

Y. Li, G. Huang, D. Zhang, Z. Wu, Y. Zhang, J. Che, and Y. Zhang, “Density control of dressed four-wave mixing and super-fluorescence,” IEEE J. Quantum Electron. 50, 25–34 (2014).
[Crossref]

Che, J. L.

H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
[Crossref]

Chen, H.

H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four-and six-wave mixing in an optical ring cavity,” Sci. Rep. 4, 3619 (2014).
[Crossref]

H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3, 1885 (2013).
[Crossref]

Chen, H. X.

Cirac, J. I.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

Cote, R.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

Côté, R.

D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
[Crossref]

Day, J. O.

E. Brekke, J. O. Day, and T. G. Walker, “Four-wave mixing in ultracold atoms using intermediate Rydberg states,” Phys. Rev. A 78, 063830 (2008).
[Crossref]

De Santis, L.

N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. L. Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
[Crossref]

Demory, J.

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A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
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J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
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Z. Zhang, F. Wen, J. Che, D. Zhang, C. Li, Y. Zhang, and M. Xiao, “Dressed gain from the parametrically amplified four-wave mixing process in an atomic vapor,” Sci. Rep. 5, 15058 (2015).
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Z. Zhang, H. Zheng, X. Yao, Y. Tian, J. Che, X. Wang, D. Zhu, Y. Zhang, and M. Xiao, “Phase modulation in Rydberg dressed multi-wave mixing processes,” Sci. Rep. 5, 10462 (2015).
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H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four-and six-wave mixing in an optical ring cavity,” Sci. Rep. 4, 3619 (2014).
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H. Chen, Y. Zhang, X. Yao, Z. Wu, X. Zhang, Y. Zhang, and M. Xiao, “Parametrically amplified bright-state polariton of four-and six-wave mixing in an optical ring cavity,” Sci. Rep. 4, 3619 (2014).
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P. Li, H. Zheng, Y. Zhang, J. Sun, C. Li, G. Huang, Z. Zhang, Y. Li, and Y. Zhang, “Controlling the transition of bright and dark states via scanning dressing field,” Opt. Mater. 35, 1062–1070 (2013).
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Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4588 (2013).
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Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4588 (2013).
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Y. P. Zhang, P. Y. Li, H. B. Zheng, Z. G. Wang, H. X. Chen, C. B. Li, R. Zhang, and Y. Zhang, “Observation of Autler-Townes splitting in six-wave mixing,” Opt. Express 19, 7769–7777 (2011).
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Y. 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).
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H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
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Y. P. Zhang, P. Y. Li, H. B. Zheng, Z. G. Wang, H. X. Chen, C. B. Li, R. Zhang, and Y. Zhang, “Observation of Autler-Townes splitting in six-wave mixing,” Opt. Express 19, 7769–7777 (2011).
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Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
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D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. 93, 063001 (2004).
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H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
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J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
[Crossref]

Z. Zhang, J. Che, D. Zhang, Z. Liu, X. Wang, and Y. Zhang, “Eight-wave mixing process in a Rydberg-dressing atomic ensemble,” Opt. Express 23, 13814–13822 (2015).
[Crossref]

Z. Zhang, F. Wen, J. Che, D. Zhang, C. Li, Y. Zhang, and M. Xiao, “Dressed gain from the parametrically amplified four-wave mixing process in an atomic vapor,” Sci. Rep. 5, 15058 (2015).
[Crossref]

Z. Zhang, H. Zheng, X. Yao, Y. Tian, J. Che, X. Wang, D. Zhu, Y. Zhang, and M. Xiao, “Phase modulation in Rydberg dressed multi-wave mixing processes,” Sci. Rep. 5, 10462 (2015).
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P. Li, H. Zheng, Y. Zhang, J. Sun, C. Li, G. Huang, Z. Zhang, Y. Li, and Y. Zhang, “Controlling the transition of bright and dark states via scanning dressing field,” Opt. Mater. 35, 1062–1070 (2013).
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H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3, 1885 (2013).
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H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
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Z. Zhang, H. Zheng, X. Yao, Y. Tian, J. Che, X. Wang, D. Zhu, Y. Zhang, and M. Xiao, “Phase modulation in Rydberg dressed multi-wave mixing processes,” Sci. Rep. 5, 10462 (2015).
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J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
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H. Zheng, X. Zhang, Z. Zhang, Y. Tian, H. Chen, C. Li, and Y. Zhang, “Parametric amplification and cascaded-nonlinearity processes in common atomic system,” Sci. Rep. 3, 1885 (2013).
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P. Li, H. Zheng, Y. Zhang, J. Sun, C. Li, G. Huang, Z. Zhang, Y. Li, and Y. Zhang, “Controlling the transition of bright and dark states via scanning dressing field,” Opt. Mater. 35, 1062–1070 (2013).
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Y. Zhang, M. Belić, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38, 4585–4588 (2013).
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H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
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Y. P. Zhang, P. Y. Li, H. B. Zheng, Z. G. Wang, H. X. Chen, C. B. Li, R. Zhang, and Y. Zhang, “Observation of Autler-Townes splitting in six-wave mixing,” Opt. Express 19, 7769–7777 (2011).
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Z. Zhang, H. Zheng, X. Yao, Y. Tian, J. Che, X. Wang, D. Zhu, Y. Zhang, and M. Xiao, “Phase modulation in Rydberg dressed multi-wave mixing processes,” Sci. Rep. 5, 10462 (2015).
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M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
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ACS Photon. (1)

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photon. 3, 8–13 (2015).
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Europhys. Lett. (1)

J. Che, J. Ma, H. Zheng, Z. Zhang, X. Yao, Y. Zhang, and Y. Zhang, “Rydberg six-wave mixing process,” Europhys. Lett. 109, 33001 (2015).
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IEEE J. Quantum Electron. (1)

Y. Li, G. Huang, D. Zhang, Z. Wu, Y. Zhang, J. Che, and Y. Zhang, “Density control of dressed four-wave mixing and super-fluorescence,” IEEE J. Quantum Electron. 50, 25–34 (2014).
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J. Opt. Soc. Am. B (1)

J. Phys. B (1)

P. P. Herrmann, J. Hoffnagle, N. Schlumpf, V. L. Telegdi, and A. Weis, “Stark spectroscopy of forbidden two-photon transitions: a sensitive probe for the quantitative measurement of small electric fields,” J. Phys. B 19, 1271–1280 (1986).
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Laser Phys. (1)

H. B. Zheng, X. Yao, Z. Y. Zhang, J. L. Che, Y. Q. Zhang, Y. P. Zhang, and M. Xiao, “Blockaded six- and eight-wave mixing processes tailored by electromagnetically induced transparency scissors,” Laser Phys. 24, 045404 (2014).
[Crossref]

Nat. Commun. (1)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
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Nat. Photonics (1)

N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. L. Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345 (2016).
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Nat. Phys. (1)

J. A. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8, 819–824 (2012).
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Nature (2)

T. Peyronel, O. Firstenberg, Q. Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
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Opt. Express (3)

Opt. Lett. (2)

Opt. Mater. (1)

P. Li, H. Zheng, Y. Zhang, J. Sun, C. Li, G. Huang, Z. Zhang, Y. Li, and Y. Zhang, “Controlling the transition of bright and dark states via scanning dressing field,” Opt. Mater. 35, 1062–1070 (2013).
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Optica (1)

Phys. Rev. A (5)

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Figures (4)

Fig. 1.
Fig. 1. (a) Five-level K -type energy level diagram depicting the generation of the MWM process in the Rb 85 atomic system. (b) Experimental setup. D, photodetector; L, lens; PBS, polarized beam splitter at corresponding wavelength; FD, frequency doubler; HR, high-reflectivity mirror; HW, half-wave plate at corresponding wavelength. Transverse double-headed arrows and filled dots indicate the horizontal polarization and vertical polarization of incident beams, respectively. Five beams derived from the four laser systems are coupled into the 10 mm long Rb cell wrapped with μ-metal sheets. The transition | 0 | 1 is coupled by the beam E 1 (780.2 nm). Rydberg transition | 1 | 2 is coupled by beam E 2 (480 nm), which counterpropagates with beam E 1 . | 1 | 3 is connected by beams E 3 and E 3 (780.2 nm), which are derived from the same ECDL, and | 1 | 4 is coupled by beam E 4 (775.9 nm). The EIT signal and MWM spectrum signals are received by D1 and D2, respectively. (c1) Energy schematic diagram for SP-FWM process; (c2) phase-matching condition of SP-FWM process.
Fig. 2.
Fig. 2. (a1) Phase-matching diagram of the OPA process with E SWM 1 injected into the Stokes port. (a2) Measured Stokes field E St and (a3) anti-Stokes field E ASt versus Δ 1 ; (b1) and (b2) intensity of PA-SWM2 signals transited from n D 5 / 2 versus Δ 1 at different Δ 2 for n = 37 and n = 54 , respectively; (c1) and (c2) intensity of PA-SWM2 signals transited from fine structure of energy level n D 3 / 2 versus Δ 1 at different Δ 2 for n = 37 and n = 54 , respectively; (d1) PA-SWM1 signals (denoted as blue triangles) versus Δ 1 at different Δ 4 ( Δ 1 + Δ 4 = 0 ); (d2) PA-SWM2 signals transited from 37 D 5 / 2 (denoted as black squares) and 54 D 3 / 2 (denoted as red circles) versus Δ 1 at different Δ 2 ( Δ 1 + Δ 2 + ϵ = 0 ).
Fig. 3.
Fig. 3. (a1) Measured PA-SWM2 signals versus Δ 2 by increasing P 2 for n = 37 ; (a2) intensity dependence of the PA-SWM2 signals corresponding to (a1) on P 2 ; (b1) measured PA-SWM2 signals versus Δ 2 by changing the temperature for n = 37 ; (b2) intensity dependence of the PA-SWM2 signals corresponding to (b1) on resonant condition on temperature; (b3) theoretically simulated PA-SWM2 signals to (b1). The dots indicate the experimental data, and the solid curve represents the theoretical simulation. The dashed lines are a guide for the eyes.
Fig. 4.
Fig. 4. (a1) AT splitting in the five-level atomic system induced by E 2 and E 4 ; (a2) phase-matching diagram of OPA injected with E SWM 1 , E SWM 2 , and E EWM into the Stokes port. (b) Measured MWM versus Δ 2 with discrete Δ 4 for n = 37 ; the range of Δ 4 is from 150 to 150 MHz. (c) Measured MWM signals versus Δ 2 with increasing P 4 for n = 37 ; the range of P 4 is from 10 to 18 mW.

Equations (15)

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ρ 10 ( 3 ) = i G 1 | G 3 | 2 e i k FWM · r ( d 1 + | G 1 | 2 / Γ 00 ) 2 d 3 ,
ρ 10 ( 5 ) = i G 1 | G 3 | 2 | G 4 | 2 e i k SWM 1 · r ( d 1 + | G 1 | 2 / Γ 00 + | G 4 | 2 / d 4 ) 3 d 3 d 4 ,
ρ 10 ( 5 ) = i G 1 0.2 ( | G 2 | / n 11 ) 0.4 | G 3 | 0.4 e i k SWM 2 · r [ d 1 + | G 1 | 0.4 / Γ 00 + ( | G 2 | / n 11 ) 0.4 / d 2 ) ] 3 d 2 d 3 ,
ρ 10 ( 7 ) = i G 1 0.2 ( | G 2 | / n 11 ) 0.4 | G 3 | 0.4 | G 4 | 2 e i k EWM · r ( d 1 + | G 1 | 0.4 Γ 00 + ( | G 2 | / n 11 ) 0.4 d 2 + | G 4 | 2 d 4 ) 4 d 2 d 3 d 4 ,
ρ 20 ( St ) ( 3 ) = i | G 1 | 2 G ASt * d 1 d 00 d 10 ,
ρ 20 ( ASt ) ( 3 ) = i | G 1 | 2 G St * d 1 d 00 d 10 ,
a ^ out + a ^ out = g a ^ in + a ^ in + ( g 1 ) ,
b ^ out + b ^ out = ( g 1 ) a ^ in + a ^ in + ( g 1 ) ,
d ϵ d P 2 = 2 C μ 12 2 ρ 0 0.2 G 2 1.6 5 ϵ 0 c A 2 n 0.44 ( G 1 2 Γ 10 + G 2 2 / Γ 20 + G 3 2 Γ 30 ) 0.8 × ( G 3 2 Γ 30 G 1 2 2 Γ 10 + G 2 2 / Γ 20 + Γ 10 2 Γ 20 / G 2 2 + G 1 2 Γ 10 + G 2 2 / Γ 20 ) ,
d ϵ d ρ = 0.2 C ρ 0 0.8 ( | G 2 | n 11 ) 0.4 ( | G 1 | 2 Γ 10 + G 2 2 / Γ 20 + | G 3 | 2 Γ 30 ) 0.2 .
ϵ = ρ 2 V U ( r r ) d 3 r ,
i d d t c g = G 2 2 e i β t 2 c e ,
i d d t c e = ϵ ( r , t ) c e + G 2 2 e i β t 2 c g ,
ρ 2 = C ρ 1 0.2 ( | G 2 | n 11 ) 0.4 ,
ρ 1 = ρ 0 2 [ | G 1 | 2 Re ( d 1 + | G 2 | 2 / d 2 + | G 4 | 2 / d 4 ) + | G 3 | 2 Re ( d 3 ) ] ,

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