Abstract

We report phase-sensitive amplification (PSA) of a near-infrared electromagnetic field using room-temperature $^{85}$Rb atoms possessing ground-state coherence. Our novelty is in achieving significant optical PSA by manipulating the intensity and phase of a frequency-separated microwave field. PSA is obtained by inducing a three-wave mixing nonlinear process utilising a three-level cyclic scheme in the D1 manifold. We achieve a near-ideal PSA with a gain of 7 dB over a range of 500 kHz bandwidth with very low pump-field intensities and with low optical depths. Such a hybrid, ground-state-coherence-assisted PSA is the first such demonstration using atomic ensembles.

© 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. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
    [Crossref]
  2. Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
    [Crossref]
  3. V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
    [Crossref]
  4. S. Kim and A. M. Marino, “Generation of $^{87}\textrm {Rb}$87Rb resonant bright two-mode squeezed light with four-wave mixing,” Opt. Express 26(25), 33366–33375 (2018).
    [Crossref]
  5. G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
    [Crossref]
  6. E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lettere al Nuovo Cimento (1971-1985) 17(10), 333–338 (1976).
    [Crossref]
  7. H. R. Gray, R. M. Whitley, and C. R. Stroud, “Coherent trapping of atomic populations,” Opt. Lett. 3(6), 218–220 (1978).
    [Crossref]
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  9. J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67(22), 3062–3065 (1991).
    [Crossref]
  10. M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
    [Crossref]
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    [Crossref]
  12. D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
    [Crossref]
  13. J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
    [Crossref]
  14. J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
    [Crossref]
  15. T. Li, B. E. Anderson, T. Horrom, B. L. Schmittberger, K. M. Jones, and P. D. Lett, “Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier,” Opt. Express 25(18), 21301–21311 (2017).
    [Crossref]
  16. C. Jiang, L. N. Song, and Y. Li, “Directional phase-sensitive amplifier between microwave and optical photons,” Phys. Rev. A 99(2), 023823 (2019).
    [Crossref]
  17. A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent and collimated blue light generated by four-wave mixing in $\textrm {Rb}$Rb vapour,” Opt. Express 17(25), 22861–22870 (2009).
    [Crossref]
  18. N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
    [Crossref]
  19. P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
    [Crossref]
  20. K. V. Adwaith, A. Karigowda, C. Manwatkar, F. Bretenaker, and A. Narayanan, “Coherent microwave-to-optical conversion by three-wave mixing in a room temperature atomic system,” Opt. Lett. 44(1), 33–36 (2019).
    [Crossref]
  21. M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
    [Crossref]
  22. M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
    [Crossref]
  23. S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
    [Crossref]
  24. Y. Zhang, J. Schröder, C. Husko, S. Lefrancois, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Pump-degenerate phase-sensitive amplification in chalcogenide waveguides,” J. Opt. Soc. Am. B 31(4), 780–787 (2014).
    [Crossref]
  25. Y. Zhang, C. Husko, J. Schröder, S. Lefrancois, I. H. Rey, T. F. Krauss, and B. J. Eggleton, “Phase-sensitive amplification in silicon photonic crystal waveguides,” Opt. Lett. 39(2), 363–366 (2014).
    [Crossref]
  26. X. Fu, X. Guo, and S. Chester, “Raman-enhanced phase-sensitive fibre optical parametric amplifier,” Sci. Rep. 6(1), 20180 (2016).
    [Crossref]
  27. H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
    [Crossref]
  28. A. B. Deb and N. Kjaergaard, “Radio-over-fiber using an optical antenna based on rydberg states of atoms,” Appl. Phys. Lett. 112(21), 211106 (2018).
    [Crossref]
  29. G. Wendin, “Quantum information processing with superconducting circuits: a review,” Rep. Prog. Phys. 80(10), 106001 (2017).
    [Crossref]
  30. A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
    [Crossref]

2019 (2)

2018 (3)

S. Kim and A. M. Marino, “Generation of $^{87}\textrm {Rb}$87Rb resonant bright two-mode squeezed light with four-wave mixing,” Opt. Express 26(25), 33366–33375 (2018).
[Crossref]

A. B. Deb and N. Kjaergaard, “Radio-over-fiber using an optical antenna based on rydberg states of atoms,” Appl. Phys. Lett. 112(21), 211106 (2018).
[Crossref]

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

2017 (4)

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

G. Wendin, “Quantum information processing with superconducting circuits: a review,” Rep. Prog. Phys. 80(10), 106001 (2017).
[Crossref]

T. Li, B. E. Anderson, T. Horrom, B. L. Schmittberger, K. M. Jones, and P. D. Lett, “Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier,” Opt. Express 25(18), 21301–21311 (2017).
[Crossref]

2016 (1)

X. Fu, X. Guo, and S. Chester, “Raman-enhanced phase-sensitive fibre optical parametric amplifier,” Sci. Rep. 6(1), 20180 (2016).
[Crossref]

2015 (1)

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

2014 (4)

Y. Zhang, C. Husko, J. Schröder, S. Lefrancois, I. H. Rey, T. F. Krauss, and B. J. Eggleton, “Phase-sensitive amplification in silicon photonic crystal waveguides,” Opt. Lett. 39(2), 363–366 (2014).
[Crossref]

Y. Zhang, J. Schröder, C. Husko, S. Lefrancois, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Pump-degenerate phase-sensitive amplification in chalcogenide waveguides,” J. Opt. Soc. Am. B 31(4), 780–787 (2014).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

2012 (1)

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

2009 (3)

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

A. M. Akulshin, R. J. McLean, A. I. Sidorov, and P. Hannaford, “Coherent and collimated blue light generated by four-wave mixing in $\textrm {Rb}$Rb vapour,” Opt. Express 17(25), 22861–22870 (2009).
[Crossref]

2008 (1)

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref]

1998 (1)

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
[Crossref]

1993 (2)

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
[Crossref]

1991 (2)

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67(22), 3062–3065 (1991).
[Crossref]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

1986 (1)

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

1978 (1)

1976 (2)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
[Crossref]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lettere al Nuovo Cimento (1971-1985) 17(10), 333–338 (1976).
[Crossref]

Abram, I.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
[Crossref]

Adwaith, K. V.

Akulshin, A. M.

Alotaibi, H. M.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
[Crossref]

Anderson, B. E.

Arcari, M.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Arimondo, E.

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lettere al Nuovo Cimento (1971-1985) 17(10), 333–338 (1976).
[Crossref]

Banerjee, C.

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

Barnett, S. M.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

Boller, K.-J.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Boyer, V.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref]

Bretenaker, F.

K. V. Adwaith, A. Karigowda, C. Manwatkar, F. Bretenaker, and A. Narayanan, “Coherent microwave-to-optical conversion by three-wave mixing in a room temperature atomic system,” Opt. Lett. 44(1), 33–36 (2019).
[Crossref]

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

Brion, E.

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

Buckle, S. J.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

Cao, L.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Chester, S.

X. Fu, X. Guo, and S. Chester, “Raman-enhanced phase-sensitive fibre optical parametric amplifier,” Sci. Rep. 6(1), 20180 (2016).
[Crossref]

Choi, D.-Y.

Corzo, N. V.

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

Deb, A. B.

A. B. Deb and N. Kjaergaard, “Radio-over-fiber using an optical antenna based on rydberg states of atoms,” Appl. Phys. Lett. 112(21), 211106 (2018).
[Crossref]

Eggleton, B. J.

Fayolle, P.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

Field, J. E.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67(22), 3062–3065 (1991).
[Crossref]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Fu, X.

X. Fu, X. Guo, and S. Chester, “Raman-enhanced phase-sensitive fibre optical parametric amplifier,” Sci. Rep. 6(1), 20180 (2016).
[Crossref]

Garreau, J. C.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

Ghosh, M.

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

Goldfarb, F.

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
[Crossref]

Grangier, P.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
[Crossref]

Gray, H. R.

Guo, X.

X. Fu, X. Guo, and S. Chester, “Raman-enhanced phase-sensitive fibre optical parametric amplifier,” Sci. Rep. 6(1), 20180 (2016).
[Crossref]

Hahn, K. H.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67(22), 3062–3065 (1991).
[Crossref]

Hannaford, P.

Hansen, S. L.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Harris, S. E.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67(22), 3062–3065 (1991).
[Crossref]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Hemmer, P. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
[Crossref]

Horrom, T.

Husko, C.

Imamoglu, A.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Javadi, A.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Jayaraman, A.

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

Jiang, C.

C. Jiang, L. N. Song, and Y. Li, “Directional phase-sensitive amplifier between microwave and optical photons,” Phys. Rev. A 99(2), 023823 (2019).
[Crossref]

Jing, J.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Jones, K. M.

T. Li, B. E. Anderson, T. Horrom, B. L. Schmittberger, K. M. Jones, and P. D. Lett, “Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier,” Opt. Express 25(18), 21301–21311 (2017).
[Crossref]

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

Karigowda, A.

K. V. Adwaith, A. Karigowda, C. Manwatkar, F. Bretenaker, and A. Narayanan, “Coherent microwave-to-optical conversion by three-wave mixing in a room temperature atomic system,” Opt. Lett. 44(1), 33–36 (2019).
[Crossref]

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

Kim, S.

Kiršanske, G.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Kjaergaard, N.

A. B. Deb and N. Kjaergaard, “Radio-over-fiber using an optical antenna based on rydberg states of atoms,” Appl. Phys. Lett. 112(21), 211106 (2018).
[Crossref]

Knight, P. L.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

Krauss, T. F.

Lauder, M. A.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

Lee, E.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Lefrancois, S.

Lett, P. D.

T. Li, B. E. Anderson, T. Horrom, B. L. Schmittberger, K. M. Jones, and P. D. Lett, “Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier,” Opt. Express 25(18), 21301–21311 (2017).
[Crossref]

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref]

Levenson, J. A.

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
[Crossref]

Li, H.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Li, T.

Li, Y.

C. Jiang, L. N. Song, and Y. Li, “Directional phase-sensitive amplifier between microwave and optical photons,” Phys. Rev. A 99(2), 023823 (2019).
[Crossref]

Liu, C.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Lodahl, P.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Löffler, M.

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
[Crossref]

Lugani, J.

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

Lukin, M. D.

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
[Crossref]

Luther-Davies, B.

Madden, S.

Mahmoodian, S.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Manjappa, M.

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

Manwatkar, C.

Marino, A. M.

S. Kim and A. M. Marino, “Generation of $^{87}\textrm {Rb}$87Rb resonant bright two-mode squeezed light with four-wave mixing,” Opt. Express 26(25), 33366–33375 (2018).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref]

McLean, R. J.

Midolo, L.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
[Crossref]

Narayanan, A.

K. V. Adwaith, A. Karigowda, C. Manwatkar, F. Bretenaker, and A. Narayanan, “Coherent microwave-to-optical conversion by three-wave mixing in a room temperature atomic system,” Opt. Lett. 44(1), 33–36 (2019).
[Crossref]

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

Neveu, P.

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
[Crossref]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lettere al Nuovo Cimento (1971-1985) 17(10), 333–338 (1976).
[Crossref]

Pegg, D. T.

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

Pooser, R. C.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

Pregnolato, T.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Qin, Z.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Rey, I. H.

Rivera, T.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

Rostovtsev, Y. V.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Sanders, B. C.

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

Sautenkov, V. A.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Schmittberger, B. L.

Schröder, J.

Scully, M. O.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
[Crossref]

Sidorov, A. I.

Söllner, I.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Song, J.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Song, L. N.

C. Jiang, L. N. Song, and Y. Li, “Directional phase-sensitive amplifier between microwave and optical photons,” Phys. Rev. A 99(2), 023823 (2019).
[Crossref]

Stobbe, S.

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

Stroud, C. R.

Undurti, S. S.

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

Wang, D.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Wang, H.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Wang, L.-G.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Welch, G. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Wendin, G.

G. Wendin, “Quantum information processing with superconducting circuits: a review,” Rep. Prog. Phys. 80(10), 106001 (2017).
[Crossref]

Whitley, R. M.

Xiao, C.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Zhang, J.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Zhang, W.

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Zhang, Y.

Zhu, S.

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

Appl. Phys. Lett. (1)

A. B. Deb and N. Kjaergaard, “Radio-over-fiber using an optical antenna based on rydberg states of atoms,” Appl. Phys. Lett. 112(21), 211106 (2018).
[Crossref]

Il Nuovo Cimento B (1971-1996) (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented na vapour,” Il Nuovo Cimento B (1971-1996) 36(1), 5–20 (1976).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50(16), 165502 (2017).
[Crossref]

Lettere al Nuovo Cimento (1971-1985) (1)

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lettere al Nuovo Cimento (1971-1985) 17(10), 333–338 (1976).
[Crossref]

Nat. Commun. (1)

A. Javadi, I. Söllner, M. Arcari, S. L. Hansen, L. Midolo, S. Mahmoodian, G. Kiršanskė, T. Pregnolato, E. Lee, J. Song, S. Stobbe, P. Lodahl, and J. Song, “Single-photon non-linear optics with a quantum dot in a waveguide,” Nat. Commun. 6(1), 8655 (2015).
[Crossref]

New J. Phys. (1)

P. Neveu, C. Banerjee, J. Lugani, F. Bretenaker, E. Brion, and F. Goldfarb, “Phase sensitive amplification enabled by coherent population trapping,” New J. Phys. 20(8), 083043 (2018).
[Crossref]

Opt. Acta (1)

S. J. Buckle, S. M. Barnett, P. L. Knight, M. A. Lauder, and D. T. Pegg, “Atomic interferometers,” Opt. Acta 33(9), 1129–1140 (1986).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (3)

M. Manjappa, S. S. Undurti, A. Karigowda, A. Narayanan, and B. C. Sanders, “Effects of temperature and ground-state coherence decay on enhancement and amplification in a $ {\Delta }$Δ atomic system,” Phys. Rev. A 90(4), 043859 (2014).
[Crossref]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

C. Jiang, L. N. Song, and Y. Li, “Directional phase-sensitive amplifier between microwave and optical photons,” Phys. Rev. A 99(2), 023823 (2019).
[Crossref]

Phys. Rev. Lett. (9)

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless optical amplifier operating on hundreds of spatial modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

J. A. Levenson, I. Abram, T. Rivera, P. Fayolle, J. C. Garreau, and P. Grangier, “Quantum optical cloning amplifier,” Phys. Rev. Lett. 70(3), 267–270 (1993).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental generation of multiple quantum correlated beams from hot rubidium vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100(14), 143601 (2008).
[Crossref]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. 67(22), 3062–3065 (1991).
[Crossref]

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998).
[Crossref]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Rep. Prog. Phys. (1)

G. Wendin, “Quantum information processing with superconducting circuits: a review,” Rep. Prog. Phys. 80(10), 106001 (2017).
[Crossref]

Sci. Rep. (2)

X. Fu, X. Guo, and S. Chester, “Raman-enhanced phase-sensitive fibre optical parametric amplifier,” Sci. Rep. 6(1), 20180 (2016).
[Crossref]

D. Wang, C. Liu, C. Xiao, J. Zhang, H. M. Alotaibi, B. C. Sanders, L.-G. Wang, and S. Zhu, “Strong coherent light amplification with double electromagnetically induced transparency coherences,” Sci. Rep. 7(1), 5796 (2017).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. A $\Delta$ configuration with hyperfine levels of $^{85}$Rb D1 manifold formed by interaction with two optical fields, coupling ($\omega _{\textrm{c}}$), probe ($\omega _{\textrm{p}}$) and a microwave field ($\omega _\mu$).
Fig. 2.
Fig. 2. Schematic of our experimental set up. Here ECDL —External Cavity Diode Laser, $\lambda /2$ —half-wave plate, $\lambda /4$ —quarter-wave plate, GP —glass plate, SAS —saturated absorption spectroscopy, PBS —polarising beam-splitter, BS —beam-splitter, M —Mirror, EOM —Electro Optic Modulator, AOM —Acousto-Optic Modulator, MS —Microwave Source, P —power splitter, PS —phase shifter, SA —Spectrum Analyser, PD —Photo-Diode.
Fig. 3.
Fig. 3. Probe gain as a function of relative phase of all the three fields ($\Delta \Phi$). The phase is changed continuously using a microwave digital phase shifter. The dots are results for Gain obtained from our numerical modeling.
Fig. 4.
Fig. 4. Variation of maximum PSA gain ($G_{\textrm{max}}$, blue square) and minimum PSA gain ($G_{\textrm{min}}$, red circle) as a function of microwave intensity. For an ideal PSA $1/G_{\textrm{max}}$ (black diamond) is equal to $G_{\textrm{min}}$. The star points are results from our numerical calculation.
Fig. 5.
Fig. 5. Variation of $G_{\textrm{max}}$ (blue square), $G_{\textrm{min}}$ (red circle), $1/G_{\textrm{max}}$ (black diamond) and C (green star) as a function of two photon detuning for a microwave intensity of 1.2 mW/cm$^2$.
Fig. 6.
Fig. 6. Extinction ratio (ER) which is the difference between the $G_{\textrm{min}}$ and $G_{\textrm{max}}$ values is plotted as a function of microwave intensity.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Δ Φ ( z ) = z ( k p k c ) + ϕ μ .
C := G min 1 G max G max G min
E p, c ( r ) cos ( ω p, c t k p, c z + ϕ p, c )
E μ ( r ) cos ( ω μ t + ϕ μ ) .
H ^ ( r , v ) = δ p ( v ) | 3 3 | + ( δ p ( v ) δ c ( v ) ) | 2 2 | Ω μ ( r ) | 1 2 | Ω p ( r ) | 1 3 | Ω c ( r ) | 2 3 | + h.c.
δ p ( v ) := δ p k p v , δ c ( v ) := δ c k c v
Ω c ( r ) = d 23 E c ( r ) , Ω p ( r ) = d 13 E p ( r ) , Ω μ ( r ) = μ 12 B μ ( r ) e i ( ω μ + ω c ω p ) t + i ( k p k c ) z + i ( ϕ c ϕ p + ϕ μ ) .
σ ˙ ( v , z ) = i [ H ^ ( v , z ) , σ ( v , z ) ] + k = 1 5 L ( a ^ k ) σ ( v , z )
L ( a ^ ) σ = a ^ σ a ^ 1 2 { σ , a ^ a ^ }
a ^ 1 = ( n ¯ + 1 ) Γ 12 | 1 2 | , a ^ 2 = n ¯ Γ 12 | 2 1 | , a ^ 3 = Γ 13 | 1 3 | , a ^ 4 = Γ 23 | 2 3 | , a ^ 5 = Γ μ ( | 1 1 | | 2 2 | )
Ω p z = i η σ ¯ 31 .

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