Abstract

We theoretically demonstrate how the cuprous oxide Cu 2O could be used as a gain medium in a solid-state maser. By taking advantage of radiative microwave transitions between highly excited Rydberg states, one can achieve population inversion and masing in a wide range of wavelengths. In the pulsed emission regime, the considered excitonic system is characterized by intricate and rich dynamics, which are investigated numerically, taking into account several key features of the medium, such as strong Stark shift of energy levels and the presence of the Rydberg blockade effect.

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

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  1. T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
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  2. S. Zielińska-Raczyńska, G. Czajkowski, and D. Ziemkiewicz, "Optical properties of Rydberg excitons and polaritons," Phys. Rev. B 93, 075206 (2016).
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  3. S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Electro-optical properties of Rydberg excitons," Phys. Rev. B 94, 045205 (2016).
    [Crossref]
  4. S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Magneto-optical properties of Rydberg excitons: Center-of-mass quantization approach," Phys. Rev. B 95, 075204 (2017).
    [Crossref]
  5. J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
    [Crossref]
  6. M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
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  7. V. Walther, R. Johne, and T. Pohl, "Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities," Nat. Commun. 9, 1309 (2018).
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  11. Z. Zhang, J. Feng, X. Liu, J. Sheng, Y. Zhang, Y. Zhang, and M. Xiao, "Controllable photonic crystal with periodic Raman gain in a coherent atomic medium," Opt. Lett. 43, 919–921 (2018).
    [Crossref] [PubMed]
  12. D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
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  16. J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).
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    [Crossref]
  25. T. Itoh and S. I. Narita, "Analysis of Wavelength Derivative Spectra of Exciton in Cu 2O," J. Phys. Soc. Jpn. 39, 140–147 (1975).
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  26. D. Fröhlich, A. Nöthe, and K. Reimann, "Observation of the Resonant Optical Stark Effect in a Semiconductor," Phys. Rev. Lett. 55, 1335 (1985).
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  27. T. F. Gallagher, "Rydbeg atoms" (Cambridge University Press, 1994).
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  28. J. H. Hoogenraad and L. D. Noordam, "Rydberg atoms in far-infrared radiation fields. I. Dipole matrix elements of H, Li, and Rb," Phys. Rev. A 57, 4533 (1998).
    [Crossref]
  29. J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
    [Crossref]
  30. I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).
  31. D. M. Strayer, G. J. Dick, and J. E. Mercereau, "Performance of a superconducting cavity stabilized ruby maser oscillator," IEEE Trans. Magn. 23, 1624–1628 (1987).
    [Crossref]
  32. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 674 (1946).
  33. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
    [Crossref] [PubMed]
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  37. S. E. Pourmand, N. Bidin, and H. Bakhtiar, "Effects of temperature and input energy on quasi-three-level emission cross section of Nd 3+:YAG pumped by flashlamp," Chin. Phys. B 21, 094214 (2012).
    [Crossref]

2018 (6)

V. Walther, R. Johne, and T. Pohl, "Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities," Nat. Commun. 9, 1309 (2018).
[Crossref] [PubMed]

V. Walther, S. O. Kruger, S. Scheel, and T. Pohl, "Interactions between Rydberg excitons in Cu 2O," Phys. Rev. B 98, 165201 (2018).
[Crossref]

Z. Zhang, J. Feng, X. Liu, J. Sheng, Y. Zhang, Y. Zhang, and M. Xiao, "Controllable photonic crystal with periodic Raman gain in a coherent atomic medium," Opt. Lett. 43, 919–921 (2018).
[Crossref] [PubMed]

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

D. Ziemkiewicz and S. Zielińska-Raczyńska, "Proposal of tunable Rydberg exciton maser," Opt. Lett. 43, 3742 (2018).
[Crossref] [PubMed]

H. Stolz, F. Schöne, and D. Semkat, "Interaction of Rydberg excitons in cuprous oxide with phonons and photons: optical linewidth and polariton effect," New J. Phys. 20, 023019 (2018).
[Crossref]

2017 (5)

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

T. Kitamura, M. Takahata, and N. Naka, "Quantum number dependence of the photoluminescence broadening of excitonic Rydberg states in cuprous oxide," J. Lumin. 192, 808–813 (2017).
[Crossref]

M. Khazali, K. Heshami, and C. Simon, "Single-photon source based on Rydberg exciton blockade," J. Phys. B 50, 215301 (2017).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Magneto-optical properties of Rydberg excitons: Center-of-mass quantization approach," Phys. Rev. B 95, 075204 (2017).
[Crossref]

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

2016 (3)

M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
[Crossref]

S. Zielińska-Raczyńska, G. Czajkowski, and D. Ziemkiewicz, "Optical properties of Rydberg excitons and polaritons," Phys. Rev. B 93, 075206 (2016).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Electro-optical properties of Rydberg excitons," Phys. Rev. B 94, 045205 (2016).
[Crossref]

2014 (2)

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

2013 (1)

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

2012 (2)

S. E. Pourmand, N. Bidin, and H. Bakhtiar, "Effects of temperature and input energy on quasi-three-level emission cross section of Nd 3+:YAG pumped by flashlamp," Chin. Phys. B 21, 094214 (2012).
[Crossref]

M. Oxborrow, J. D. Breeze, and N. M. Alford, "Room-temperature solid-state maser," Nature 488, 353–356 (2012).
[Crossref] [PubMed]

2003 (2)

H. Kang, K. Wen, and Y. Zhu, "Normal or anomalous dispersion and gain in a resonant coherent medium," Phys. Rev. A 68, 063806 (2003).
[Crossref]

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

2002 (1)

H. Zhao, S. Wachter, and H. Kalt, "Effect of quantum confinement on exciton-phonon interactions," Phys. Rev. B 66, 085337 (2002).
[Crossref]

1998 (1)

J. H. Hoogenraad and L. D. Noordam, "Rydberg atoms in far-infrared radiation fields. I. Dipole matrix elements of H, Li, and Rb," Phys. Rev. A 57, 4533 (1998).
[Crossref]

1990 (1)

S. Rudin, T. L. Reinecke, and B. Segall, "Temperature-dependent exciton linewidths in semiconductors," Phys. Rev. B 42, 11218 (1990).
[Crossref]

1987 (1)

D. M. Strayer, G. J. Dick, and J. E. Mercereau, "Performance of a superconducting cavity stabilized ruby maser oscillator," IEEE Trans. Magn. 23, 1624–1628 (1987).
[Crossref]

1986 (1)

1985 (1)

D. Fröhlich, A. Nöthe, and K. Reimann, "Observation of the Resonant Optical Stark Effect in a Semiconductor," Phys. Rev. Lett. 55, 1335 (1985).
[Crossref] [PubMed]

1983 (1)

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

1975 (1)

T. Itoh and S. I. Narita, "Analysis of Wavelength Derivative Spectra of Exciton in Cu 2O," J. Phys. Soc. Jpn. 39, 140–147 (1975).
[Crossref]

1965 (1)

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

1946 (1)

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 674 (1946).

Alford, N. M.

M. Oxborrow, J. D. Breeze, and N. M. Alford, "Room-temperature solid-state maser," Nature 488, 353–356 (2012).
[Crossref] [PubMed]

Alford, NMcN.

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

Aslam, N.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Aßmann, M.

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
[Crossref]

Bakhtiar, H.

S. E. Pourmand, N. Bidin, and H. Bakhtiar, "Effects of temperature and input energy on quasi-three-level emission cross section of Nd 3+:YAG pumped by flashlamp," Chin. Phys. B 21, 094214 (2012).
[Crossref]

Bayer, M.

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
[Crossref]

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

Berg, H. C.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Bidin, N.

S. E. Pourmand, N. Bidin, and H. Bakhtiar, "Effects of temperature and input energy on quasi-three-level emission cross section of Nd 3+:YAG pumped by flashlamp," Chin. Phys. B 21, 094214 (2012).
[Crossref]

Breeze, J. D.

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

M. Oxborrow, J. D. Breeze, and N. M. Alford, "Room-temperature solid-state maser," Nature 488, 353–356 (2012).
[Crossref] [PubMed]

Caird, J. A.

Chiao, R.Y.

J.C. Garrison and R.Y. Chiao, "Quantum optics" (Oxford University Press, 2012).

Crampton, S. B.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Czajkowski, G.

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Magneto-optical properties of Rydberg excitons: Center-of-mass quantization approach," Phys. Rev. B 95, 075204 (2017).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Electro-optical properties of Rydberg excitons," Phys. Rev. B 94, 045205 (2016).
[Crossref]

S. Zielińska-Raczyńska, G. Czajkowski, and D. Ziemkiewicz, "Optical properties of Rydberg excitons and polaritons," Phys. Rev. B 93, 075206 (2016).
[Crossref]

Dick, G. J.

D. M. Strayer, G. J. Dick, and J. E. Mercereau, "Performance of a superconducting cavity stabilized ruby maser oscillator," IEEE Trans. Magn. 23, 1624–1628 (1987).
[Crossref]

Fabre, C.

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

Feng, J.

Freitag, M.

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

Fröhlich, D.

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
[Crossref]

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

D. Fröhlich, A. Nöthe, and K. Reimann, "Observation of the Resonant Optical Stark Effect in a Semiconductor," Phys. Rev. Lett. 55, 1335 (1985).
[Crossref] [PubMed]

Fröhlich, M.

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

Gallagher, T. F.

T. F. Gallagher, "Rydbeg atoms" (Cambridge University Press, 1994).
[Crossref]

Garrison, J.C.

J.C. Garrison and R.Y. Chiao, "Quantum optics" (Oxford University Press, 2012).

Glazov, M. M.

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

Goy, P.

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

Gross, M.

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

Haroche, S.

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

Heckötter, J.

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

Heshami, K.

M. Khazali, K. Heshami, and C. Simon, "Single-photon source based on Rydberg exciton blockade," J. Phys. B 50, 215301 (2017).
[Crossref]

Hiroyuki, I.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Hoogenraad, J. H.

J. H. Hoogenraad and L. D. Noordam, "Rydberg atoms in far-infrared radiation fields. I. Dipole matrix elements of H, Li, and Rb," Phys. Rev. A 57, 4533 (1998).
[Crossref]

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Itoh, T.

T. Itoh and S. I. Narita, "Analysis of Wavelength Derivative Spectra of Exciton in Cu 2O," J. Phys. Soc. Jpn. 39, 140–147 (1975).
[Crossref]

Jin, L.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Johne, R.

V. Walther, R. Johne, and T. Pohl, "Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities," Nat. Commun. 9, 1309 (2018).
[Crossref] [PubMed]

Jun, U.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Kalt, H.

H. Zhao, S. Wachter, and H. Kalt, "Effect of quantum confinement on exciton-phonon interactions," Phys. Rev. B 66, 085337 (2002).
[Crossref]

Kang, H.

H. Kang, K. Wen, and Y. Zhu, "Normal or anomalous dispersion and gain in a resonant coherent medium," Phys. Rev. A 68, 063806 (2003).
[Crossref]

Kay, C. W. M.

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

Kazimierczuk, T.

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

Ken-ichiro, T.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Kenjiro, M.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Khazali, M.

M. Khazali, K. Heshami, and C. Simon, "Single-photon source based on Rydberg exciton blockade," J. Phys. B 50, 215301 (2017).
[Crossref]

Kitamura, T.

T. Kitamura, M. Takahata, and N. Naka, "Quantum number dependence of the photoluminescence broadening of excitonic Rydberg states in cuprous oxide," J. Lumin. 192, 808–813 (2017).
[Crossref]

Kleppner, D.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Kruger, S. O.

V. Walther, S. O. Kruger, S. Scheel, and T. Pohl, "Interactions between Rydberg excitons in Cu 2O," Phys. Rev. B 98, 165201 (2018).
[Crossref]

Krupke, W. F.

Lalanne, P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Liu, R.-B.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Liu, X.

Maksymov, I. S.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Marion, J. E.

Masahiro, T.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Masaro, U.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Mercereau, J. E.

D. M. Strayer, G. J. Dick, and J. E. Mercereau, "Performance of a superconducting cavity stabilized ruby maser oscillator," IEEE Trans. Magn. 23, 1624–1628 (1987).
[Crossref]

Mizuhiko, H.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Moi, L.

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

Naka, N.

T. Kitamura, M. Takahata, and N. Naka, "Quantum number dependence of the photoluminescence broadening of excitonic Rydberg states in cuprous oxide," J. Lumin. 192, 808–813 (2017).
[Crossref]

Narita, S. I.

T. Itoh and S. I. Narita, "Analysis of Wavelength Derivative Spectra of Exciton in Cu 2O," J. Phys. Soc. Jpn. 39, 140–147 (1975).
[Crossref]

Neumann, P.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Noordam, L. D.

J. H. Hoogenraad and L. D. Noordam, "Rydberg atoms in far-infrared radiation fields. I. Dipole matrix elements of H, Li, and Rb," Phys. Rev. A 57, 4533 (1998).
[Crossref]

Nöthe, A.

D. Fröhlich, A. Nöthe, and K. Reimann, "Observation of the Resonant Optical Stark Effect in a Semiconductor," Phys. Rev. Lett. 55, 1335 (1985).
[Crossref] [PubMed]

Oxborrow, M.

M. Oxborrow, J. D. Breeze, and N. M. Alford, "Room-temperature solid-state maser," Nature 488, 353–356 (2012).
[Crossref] [PubMed]

Peters, H. E.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Pfender, M.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Pohl, T.

V. Walther, R. Johne, and T. Pohl, "Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities," Nat. Commun. 9, 1309 (2018).
[Crossref] [PubMed]

V. Walther, S. O. Kruger, S. Scheel, and T. Pohl, "Interactions between Rydberg excitons in Cu 2O," Phys. Rev. B 98, 165201 (2018).
[Crossref]

Pourmand, S. E.

S. E. Pourmand, N. Bidin, and H. Bakhtiar, "Effects of temperature and input energy on quasi-three-level emission cross section of Nd 3+:YAG pumped by flashlamp," Chin. Phys. B 21, 094214 (2012).
[Crossref]

Purcell, E. M.

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 674 (1946).

Raimond, J. M.

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

Ramsey, N. F.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Reimann, K.

D. Fröhlich, A. Nöthe, and K. Reimann, "Observation of the Resonant Optical Stark Effect in a Semiconductor," Phys. Rev. Lett. 55, 1335 (1985).
[Crossref] [PubMed]

Reinecke, T. L.

S. Rudin, T. L. Reinecke, and B. Segall, "Temperature-dependent exciton linewidths in semiconductors," Phys. Rev. B 42, 11218 (1990).
[Crossref]

Renk, K. F.

K. F. Renk, "Basics of Laser Physics" (SpringerInternational Publishing, 2017).

Rudin, S.

S. Rudin, T. L. Reinecke, and B. Segall, "Temperature-dependent exciton linewidths in semiconductors," Phys. Rev. B 42, 11218 (1990).
[Crossref]

Salvadori, E.

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

Sathian, J.

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

Sauvan, C.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Scheel, S.

V. Walther, S. O. Kruger, S. Scheel, and T. Pohl, "Interactions between Rydberg excitons in Cu 2O," Phys. Rev. B 98, 165201 (2018).
[Crossref]

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

Schöne, F.

H. Stolz, F. Schöne, and D. Semkat, "Interaction of Rydberg excitons in cuprous oxide with phonons and photons: optical linewidth and polariton effect," New J. Phys. 20, 023019 (2018).
[Crossref]

Segall, B.

S. Rudin, T. L. Reinecke, and B. Segall, "Temperature-dependent exciton linewidths in semiconductors," Phys. Rev. B 42, 11218 (1990).
[Crossref]

Semina, M. A.

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

Semkat, D.

H. Stolz, F. Schöne, and D. Semkat, "Interaction of Rydberg excitons in cuprous oxide with phonons and photons: optical linewidth and polariton effect," New J. Phys. 20, 023019 (2018).
[Crossref]

Sheng, J.

Shinn, M. D.

Siegman, A.E.

A.E. Siegman, "Microwave Solid-State Masers" (McGraw-Hill,1964).

Simon, C.

M. Khazali, K. Heshami, and C. Simon, "Single-photon source based on Rydberg exciton blockade," J. Phys. B 50, 215301 (2017).
[Crossref]

Stokowski, S. E.

Stolz, H.

H. Stolz, F. Schöne, and D. Semkat, "Interaction of Rydberg excitons in cuprous oxide with phonons and photons: optical linewidth and polariton effect," New J. Phys. 20, 023019 (2018).
[Crossref]

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

Strayer, D. M.

D. M. Strayer, G. J. Dick, and J. E. Mercereau, "Performance of a superconducting cavity stabilized ruby maser oscillator," IEEE Trans. Magn. 23, 1624–1628 (1987).
[Crossref]

Takahata, M.

T. Kitamura, M. Takahata, and N. Naka, "Quantum number dependence of the photoluminescence broadening of excitonic Rydberg states in cuprous oxide," J. Lumin. 192, 808–813 (2017).
[Crossref]

Takao, M.

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Thewes, J.

M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
[Crossref]

Vanier, J.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Vessot, R. F. C.

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

Wachter, S.

H. Zhao, S. Wachter, and H. Kalt, "Effect of quantum confinement on exciton-phonon interactions," Phys. Rev. B 66, 085337 (2002).
[Crossref]

Walther, V.

V. Walther, R. Johne, and T. Pohl, "Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities," Nat. Commun. 9, 1309 (2018).
[Crossref] [PubMed]

V. Walther, S. O. Kruger, S. Scheel, and T. Pohl, "Interactions between Rydberg excitons in Cu 2O," Phys. Rev. B 98, 165201 (2018).
[Crossref]

Weissbluth, M.

M. Weissbluth, "Atoms and Molecules" (Academic Press, 1978).

Wen, K.

H. Kang, K. Wen, and Y. Zhu, "Normal or anomalous dispersion and gain in a resonant coherent medium," Phys. Rev. A 68, 063806 (2003).
[Crossref]

Wrachtrup, J.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Xiao, M.

Yang, S.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Zhang, Y.

Zhang, Z.

Zhao, H.

H. Zhao, S. Wachter, and H. Kalt, "Effect of quantum confinement on exciton-phonon interactions," Phys. Rev. B 66, 085337 (2002).
[Crossref]

Zhu, Y.

H. Kang, K. Wen, and Y. Zhu, "Normal or anomalous dispersion and gain in a resonant coherent medium," Phys. Rev. A 68, 063806 (2003).
[Crossref]

Zielinska-Raczynska, S.

D. Ziemkiewicz and S. Zielińska-Raczyńska, "Proposal of tunable Rydberg exciton maser," Opt. Lett. 43, 3742 (2018).
[Crossref] [PubMed]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Magneto-optical properties of Rydberg excitons: Center-of-mass quantization approach," Phys. Rev. B 95, 075204 (2017).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Electro-optical properties of Rydberg excitons," Phys. Rev. B 94, 045205 (2016).
[Crossref]

S. Zielińska-Raczyńska, G. Czajkowski, and D. Ziemkiewicz, "Optical properties of Rydberg excitons and polaritons," Phys. Rev. B 93, 075206 (2016).
[Crossref]

Ziemkiewicz, D.

D. Ziemkiewicz and S. Zielińska-Raczyńska, "Proposal of tunable Rydberg exciton maser," Opt. Lett. 43, 3742 (2018).
[Crossref] [PubMed]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Magneto-optical properties of Rydberg excitons: Center-of-mass quantization approach," Phys. Rev. B 95, 075204 (2017).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Electro-optical properties of Rydberg excitons," Phys. Rev. B 94, 045205 (2016).
[Crossref]

S. Zielińska-Raczyńska, G. Czajkowski, and D. Ziemkiewicz, "Optical properties of Rydberg excitons and polaritons," Phys. Rev. B 93, 075206 (2016).
[Crossref]

Chin. Phys. B (1)

S. E. Pourmand, N. Bidin, and H. Bakhtiar, "Effects of temperature and input energy on quasi-three-level emission cross section of Nd 3+:YAG pumped by flashlamp," Chin. Phys. B 21, 094214 (2012).
[Crossref]

IEEE Trans. Magn. (1)

D. M. Strayer, G. J. Dick, and J. E. Mercereau, "Performance of a superconducting cavity stabilized ruby maser oscillator," IEEE Trans. Magn. 23, 1624–1628 (1987).
[Crossref]

J. Lumin. (1)

T. Kitamura, M. Takahata, and N. Naka, "Quantum number dependence of the photoluminescence broadening of excitonic Rydberg states in cuprous oxide," J. Lumin. 192, 808–813 (2017).
[Crossref]

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

J. Phys. B (1)

M. Khazali, K. Heshami, and C. Simon, "Single-photon source based on Rydberg exciton blockade," J. Phys. B 50, 215301 (2017).
[Crossref]

J. Phys. Soc. Jpn. (1)

T. Itoh and S. I. Narita, "Analysis of Wavelength Derivative Spectra of Exciton in Cu 2O," J. Phys. Soc. Jpn. 39, 140–147 (1975).
[Crossref]

Journ. Natl. Inst. Inf. Commun. Technol. (1)

I. Hiroyuki, H. Mizuhiko, U. Jun, M. Takao, T. Masahiro, T. Ken-ichiro, U. Masaro, and M. Kenjiro, "Hydrogen Maser," Journ. Natl. Inst. Inf. Commun. Technol. 50, 85 (2003).

Nat. Commun. (2)

V. Walther, R. Johne, and T. Pohl, "Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities," Nat. Commun. 9, 1309 (2018).
[Crossref] [PubMed]

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, "Proposal for a room-temperature diamond maser," Nat. Commun. 6, 8251 (2014).
[Crossref]

Nature (3)

J. D. Breeze, E. Salvadori, J. Sathian, NMcN. Alford, and C. W. M. Kay, "Continuous-wave room-temperature diamond maser," Nature 493, 25970 (2018).

M. Oxborrow, J. D. Breeze, and N. M. Alford, "Room-temperature solid-state maser," Nature 488, 353–356 (2012).
[Crossref] [PubMed]

T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, "Giant Rydberg excitons in the copper oxide Cu 2O," Nature 514, 343 (2014).
[Crossref] [PubMed]

Nature Materials (1)

M. Aßmann, J. Thewes, D. Fröhlich, and M. Bayer, "Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons," Nature Materials 15, 741–745 (2016).
[Crossref]

New J. Phys. (1)

H. Stolz, F. Schöne, and D. Semkat, "Interaction of Rydberg excitons in cuprous oxide with phonons and photons: optical linewidth and polariton effect," New J. Phys. 20, 023019 (2018).
[Crossref]

Opt. Lett. (2)

Phys. Rev. (2)

D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey, R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser Principles and Techniques," Phys. Rev. 138, A972–A983 (1965).
[Crossref]

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 674 (1946).

Phys. Rev. A (3)

J. H. Hoogenraad and L. D. Noordam, "Rydberg atoms in far-infrared radiation fields. I. Dipole matrix elements of H, Li, and Rb," Phys. Rev. A 57, 4533 (1998).
[Crossref]

L. Moi, P. Goy, M. Gross, J. M. Raimond, C. Fabre, and S. Haroche, "Rydberg-atom masers. I. A theoretical and experimental study of super-radiant systems in the millimeter-wave domain," Phys. Rev. A 27, 4, 2043–2064 (1983).
[Crossref]

H. Kang, K. Wen, and Y. Zhu, "Normal or anomalous dispersion and gain in a resonant coherent medium," Phys. Rev. A 68, 063806 (2003).
[Crossref]

Phys. Rev. B (8)

V. Walther, S. O. Kruger, S. Scheel, and T. Pohl, "Interactions between Rydberg excitons in Cu 2O," Phys. Rev. B 98, 165201 (2018).
[Crossref]

S. Zielińska-Raczyńska, G. Czajkowski, and D. Ziemkiewicz, "Optical properties of Rydberg excitons and polaritons," Phys. Rev. B 93, 075206 (2016).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Electro-optical properties of Rydberg excitons," Phys. Rev. B 94, 045205 (2016).
[Crossref]

S. Zielińska-Raczyńska, D. Ziemkiewicz, and G. Czajkowski, "Magneto-optical properties of Rydberg excitons: Center-of-mass quantization approach," Phys. Rev. B 95, 075204 (2017).
[Crossref]

J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "Scaling laws of Rydberg excitons," Phys. Rev. B 96, 125142 (2017).
[Crossref]

H. Zhao, S. Wachter, and H. Kalt, "Effect of quantum confinement on exciton-phonon interactions," Phys. Rev. B 66, 085337 (2002).
[Crossref]

S. Rudin, T. L. Reinecke, and B. Segall, "Temperature-dependent exciton linewidths in semiconductors," Phys. Rev. B 42, 11218 (1990).
[Crossref]

J. Heckötter, M. Freitag, M. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, "High-resolution study of the yellow excitons in Cu 2O subject to an electric field," Phys. Rev. B 95, 035210 (2017).
[Crossref]

Phys. Rev. Lett. (2)

D. Fröhlich, A. Nöthe, and K. Reimann, "Observation of the Resonant Optical Stark Effect in a Semiconductor," Phys. Rev. Lett. 55, 1335 (1985).
[Crossref] [PubMed]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, "Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators," Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Other (6)

K. F. Renk, "Basics of Laser Physics" (SpringerInternational Publishing, 2017).

J.C. Garrison and R.Y. Chiao, "Quantum optics" (Oxford University Press, 2012).

T. F. Gallagher, "Rydbeg atoms" (Cambridge University Press, 1994).
[Crossref]

M. Weissbluth, "Atoms and Molecules" (Academic Press, 1978).

A.E. Siegman, "Microwave Solid-State Masers" (McGraw-Hill,1964).

D. Ziemkiewicz and S. Zielińska-Raczyńska, "Dynamically Steered Maser Action of Rydberg Excitons in Cu 2O," Phys. Status Solidi B, https://onlinelibrary.wiley.com/doi/abs/10.1002/pssb.201800503 (2019).

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Figures (6)

Fig. 1
Fig. 1 Schematic depiction of the proposed system and excitonic energy level scheme.

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Fig. 2
Fig. 2 Emission power in 3-level system, as a function of wavelength for T=10K and T=100K. The principal numbers n1, n2 are given in the brackets.

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Fig. 3
Fig. 3 (a) State populations and blockade volume occupied by excitons in maser system based on [3, 5] levels. (b) Emission power and transition detuning from the cavity caused by Stark shift. (c) Total absorbed and emitted energy.

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Fig. 4
Fig. 4 (a) State populations and blockade volume occupied by excitons in maser system based on [7, 8] levels. (b) Emission power and transition detuning from the cavity caused by Stark shift. (c) Total absorbed and emitted energy.

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Fig. 5
Fig. 5 Emission power in 4-level system, as a function of wavelength for T = 10K and T = 100K. The principal numbers n1, n2, n3 are given in the brackets. For any set of n1 and n2, the combinations with lowest and highest n3 are shown.

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Fig. 6
Fig. 6 (a) State populations and blockade volume occupied by excitons in maser system based on [2–4] levels. (b) Emission power and transition detuning from the cavity caused by Stark shift. (c) Total absorbed and emitted energy.

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Tables (1)

Tables Icon

Table 1. Transition dipole moments d n 1 n 2 between n 1 S (rows) and n 2 P (columns) states given in units of e a B.

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Equations (9)

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〈 r n 〉 = 1 2 a B [ 3 n 2 − l ( l + 1 ) ]
V b l o c k a d e = 3 ⋅ 10 − 16 n 7 [ mm 3 ] .
γ 0 P ( n ) = 24  meV 1 + 0.01 n 2 n 3
γ P ( n ) = γ 0 P ( n ) + γ A C T + γ L O [ exp  ( ℏ ω L O / k B T ) − 1 ] − 1 .
γ i j ≈ γ i ω i j 3 ω i 3 .
E = E g − R y ( n − δ p ) 2 ,
Δ E = − 2.4 ⋅ 10 − 6 n [ 4.2 − ( n 8.452 ) 2 + ( n 35.16 ) 3 ] F ( 1 + 2.2 / n ) [ eV ] ,
∂ N 3 ± i ∂ t = b P r − γ 3 ± i N 3 ± i − γ ′ 3 ± i , 2 N 3 ± i ∂ N 2 ∂ t = γ ′ 3 ± i , 2 N 3 ± i i − γ 2 N 2 − γ ′ 2 , 1 N 2 − ( N 2 − N 1 ) B W ∂ N 1 ∂ t = γ ′ 2 , 1 N 2 + ( N 2 − N 1 ) B W − γ 1 N 1 ∂ W ∂ t = ℏ ω ( N 2 − N 1 ) B W − 2 γ c 1 W
b = 1 − ∑ i V b l o c k a d e ( n i ) V t o t a l

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