Abstract

The strong coupling of THz radiation and material excitations can improve the quantum efficiency of THz emitters. In this paper, we investigate THz polaritons and antipolaritons based on valence band transitions, which allow TE coupling in a simple configuration. The approach can improve the quantum efficiency of THz based devices based on TE mode in the strong coupling regime of THz radiations and intervalence bands transitions in a GaAs/AlGaAs quantum wells. A Nonequilibrium Many Body Approach for the optical response beyond the Hartree-Fock approximation is used as input to the effective dielectric function formalism for the polariton/antipolariton problem. The energy dispersion relations in the THz range are obtained by adjusting the full numerical solutions to simple analytical expressions, which can be used for non specialists in a wide number of new structures and material systems. The combination of manybody and nonparabolicity at high densities leads to dramatic changes in the polariton spectra in a nonequilibrium configuration, which is only possible for intervalence band transitions.

© 2014 Optical Society of America

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  1. P. Uhd Jepsen, D. G. Cooke, and P. H. Siegel, “Introduction to the Special Issue on Terahertz Spectroscopy,” IEEE Trans. Terahertz Sci. Technol. 3(3), 237–238 (2013).
    [Crossref]
  2. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
    [Crossref] [PubMed]
  3. M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
    [Crossref]
  4. R. Houdré, “Early stages of continuous wave experiments on cavity-polaritons,” Phys. Status Solidi, B Basic Res. 242(11), 2167–2196 (2005).
    [Crossref]
  5. D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).
  6. A. Liu, “Rabi splitting of the optical intersubband absorption line of multiple quantum wellsinside a Fabry-Pérot microcavity,” Phys. Rev. B 55(11), 7101–7109 (1997).
    [Crossref]
  7. D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
    [Crossref] [PubMed]
  8. A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
    [Crossref]
  9. M. F. Pereira., “Intersubband antipolaritons: Microscopic approach,” Phys. Rev. B 75(19), 195301 (2007).
    [Crossref]
  10. M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
    [Crossref] [PubMed]
  11. M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
    [Crossref]
  12. M. F. Pereira and H. Wenzel, “Interplay of Coulomb and nonparabolicity effects in the intersubband absorption of electrons and holes in quantum wells,” Phys. Rev. B 70(20), 205331 (2004).
    [Crossref]
  13. M. F. Pereira., “Intervalence transverse-electric mode terahertz lasing without population inversion,” Phys. Rev. B 78(24), 245305 (2008).
    [Crossref]
  14. M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
    [Crossref]
  15. A. Wacker, “Semiconductor Superlattices: A model system for nonlinear transport,” Phys. Rep. 357(1), 1–111 (2002).
    [Crossref]
  16. T. Schmielau and M. F. Pereira., “Nonequilibrium many body theory for quantum transport in terahertz quantum cascade lasers,” Appl. Phys. Lett. 95(23), 231111 (2009).
    [Crossref]
  17. T. Schmielau and M.F. Pereira, “Impact of momentum dependent matrix elements on scattering effects in quantum cascade lasers,” Phys. Status Solidi B 246, 329 (2009).

2013 (3)

P. Uhd Jepsen, D. G. Cooke, and P. H. Siegel, “Introduction to the Special Issue on Terahertz Spectroscopy,” IEEE Trans. Terahertz Sci. Technol. 3(3), 237–238 (2013).
[Crossref]

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

2012 (3)

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

2009 (2)

T. Schmielau and M. F. Pereira., “Nonequilibrium many body theory for quantum transport in terahertz quantum cascade lasers,” Appl. Phys. Lett. 95(23), 231111 (2009).
[Crossref]

T. Schmielau and M.F. Pereira, “Impact of momentum dependent matrix elements on scattering effects in quantum cascade lasers,” Phys. Status Solidi B 246, 329 (2009).

2008 (1)

M. F. Pereira., “Intervalence transverse-electric mode terahertz lasing without population inversion,” Phys. Rev. B 78(24), 245305 (2008).
[Crossref]

2007 (2)

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

M. F. Pereira., “Intersubband antipolaritons: Microscopic approach,” Phys. Rev. B 75(19), 195301 (2007).
[Crossref]

2005 (1)

R. Houdré, “Early stages of continuous wave experiments on cavity-polaritons,” Phys. Status Solidi, B Basic Res. 242(11), 2167–2196 (2005).
[Crossref]

2004 (1)

M. F. Pereira and H. Wenzel, “Interplay of Coulomb and nonparabolicity effects in the intersubband absorption of electrons and holes in quantum wells,” Phys. Rev. B 70(20), 205331 (2004).
[Crossref]

2003 (1)

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

2002 (2)

A. Wacker, “Semiconductor Superlattices: A model system for nonlinear transport,” Phys. Rep. 357(1), 1–111 (2002).
[Crossref]

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[Crossref] [PubMed]

1997 (1)

A. Liu, “Rabi splitting of the optical intersubband absorption line of multiple quantum wellsinside a Fabry-Pérot microcavity,” Phys. Rev. B 55(11), 7101–7109 (1997).
[Crossref]

Anappara, A. A.

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

Ballarini, D.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Beck, M.

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

Beere, H. E.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Beltram, F.

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

Biasiol, G.

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

Bramati, A.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Cancellieri, E.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Castellano, F.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

Cingolani, R.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Ciuti, C.

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

Cooke, D. G.

P. Uhd Jepsen, D. G. Cooke, and P. H. Siegel, “Introduction to the Special Issue on Terahertz Spectroscopy,” IEEE Trans. Terahertz Sci. Technol. 3(3), 237–238 (2013).
[Crossref]

De Giorgi, M.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

De Liberato, S.

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

Dini, D.

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

Faist, J.

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[Crossref] [PubMed]

Geiser, M.

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

Giacobino, E.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Gigli, G.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Houdré, R.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

R. Houdré, “Early stages of continuous wave experiments on cavity-polaritons,” Phys. Status Solidi, B Basic Res. 242(11), 2167–2196 (2005).
[Crossref]

Hu, Q.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Iotti, R. C.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Köhler, R.

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

Liu, A.

A. Liu, “Rabi splitting of the optical intersubband absorption line of multiple quantum wellsinside a Fabry-Pérot microcavity,” Phys. Rev. B 55(11), 7101–7109 (1997).
[Crossref]

Mahler, L.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Nevou, L.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

Pereira, M. F.

T. Schmielau and M. F. Pereira., “Nonequilibrium many body theory for quantum transport in terahertz quantum cascade lasers,” Appl. Phys. Lett. 95(23), 231111 (2009).
[Crossref]

M. F. Pereira., “Intervalence transverse-electric mode terahertz lasing without population inversion,” Phys. Rev. B 78(24), 245305 (2008).
[Crossref]

M. F. Pereira., “Intersubband antipolaritons: Microscopic approach,” Phys. Rev. B 75(19), 195301 (2007).
[Crossref]

M. F. Pereira and H. Wenzel, “Interplay of Coulomb and nonparabolicity effects in the intersubband absorption of electrons and holes in quantum wells,” Phys. Rev. B 70(20), 205331 (2004).
[Crossref]

Pereira, M.F.

T. Schmielau and M.F. Pereira, “Impact of momentum dependent matrix elements on scattering effects in quantum cascade lasers,” Phys. Status Solidi B 246, 329 (2009).

Ritchie, D. A.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Rossi, F.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Sanvitto, D.

D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, and D. Sanvitto, “All-optical polariton transistor,” Nat. Commun. 4, 1778 (2013).

Scalari, G.

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

Scamarcio, G.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Schmielau, T.

T. Schmielau and M.F. Pereira, “Impact of momentum dependent matrix elements on scattering effects in quantum cascade lasers,” Phys. Status Solidi B 246, 329 (2009).

T. Schmielau and M. F. Pereira., “Nonequilibrium many body theory for quantum transport in terahertz quantum cascade lasers,” Appl. Phys. Lett. 95(23), 231111 (2009).
[Crossref]

Siegel, P. H.

P. Uhd Jepsen, D. G. Cooke, and P. H. Siegel, “Introduction to the Special Issue on Terahertz Spectroscopy,” IEEE Trans. Terahertz Sci. Technol. 3(3), 237–238 (2013).
[Crossref]

Sorba, L.

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

Terahertz, L. C.

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

Tredicucci, A.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

D. Dini, R. Köhler, A. Tredicucci, G. Biasiol, and L. Sorba, “Microcavity polariton splitting of intersubband transitions,” Phys. Rev. Lett. 90(11), 116401 (2003).
[Crossref] [PubMed]

Uhd Jepsen, P.

P. Uhd Jepsen, D. G. Cooke, and P. H. Siegel, “Introduction to the Special Issue on Terahertz Spectroscopy,” IEEE Trans. Terahertz Sci. Technol. 3(3), 237–238 (2013).
[Crossref]

Vitiello, M. S.

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

Wacker, A.

A. Wacker, “Semiconductor Superlattices: A model system for nonlinear transport,” Phys. Rep. 357(1), 1–111 (2002).
[Crossref]

Walther, C.

M. Geiser, G. Scalari, M. Beck, C. Walther, J. Faist, and L. C. Terahertz, “Terahertz LC microcavities: from quantum cascade lasers to ultrastrong light-matter coupling,” J. Infrared Millimeter Terahertz Waves 34(5–6), 393–404 (2013).
[Crossref]

Wenzel, H.

M. F. Pereira and H. Wenzel, “Interplay of Coulomb and nonparabolicity effects in the intersubband absorption of electrons and holes in quantum wells,” Phys. Rev. B 70(20), 205331 (2004).
[Crossref]

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

A. A. Anappara, A. Tredicucci, F. Beltram, G. Biasiol, L. Sorba, S. De Liberato, and C. Ciuti, “Cavity polaritons from excited-subband transitions,” Appl. Phys. Lett. 91(23), 231118 (2007).
[Crossref]

M. Geiser, G. Scalari, F. Castellano, M. Beck, and J. Faist, “Room temperature terahertz polariton emitter,” Appl. Phys. Lett. 101(14), 141118 (2012).
[Crossref]

M. S. Vitiello, R. C. Iotti, F. Rossi, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, Q. Hu, and G. Scamarcio, “Non-equilibrium longitudinal and transverse optical phonons in terahertz quantum cascade lasers,” Appl. Phys. Lett. 100(9), 091101 (2012).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Diagram of the microcavity geometry, showing the directions of incident light and polarized electric field. The cavity core contains a series of (GaAs/Al0.33Ga0.67As) QWs surrounded by lower refractive index with a GaAs cap and bottom GaAs as substrate. The coupling prism can be made by e.g. etching or cleaving a high refractive index material that can be e.g. GaAs. This is simpler to realize than growing the sample over a prism [7].

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Fig. 2
Fig. 2 Combined optical susceptibility for all relevant transitions (solid, black) and each individual contribution (2-1) blue, dashed gain; (2-3) green, dot-dashed absorption and (2-4) double-dotted-dash absorption for a nonequilibrium configuration in which the second subband is occupied with N=1.0× 10 12 cm −2 and all other subbands are empty.

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Fig. 3
Fig. 3 THz valence band polaritons/antipolaritons corresponding to the transitions: (a) 2-1; (b) 2-3, (c) 2-4 and all together (d). In all cases the carriers are assumed to be thermalized at 300 K in subband 2 with a density N=1.0× 10 12 cm −2 and all other subbands are empty.

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Fig. 4
Fig. 4 Combination of band structure and manybody effects in a single transition leading to a split in the optical susceptibility (solid-blue) of the (2,3) transition at high densities in contrast to the free carrier case (dashed-red) leading to extra structures in the polariton spectra for a nonequilibrium configuration in which the first subband is occupied with N=1.0× 10 12 cm −2 and all other subbands are empty. Only the transition between subbands (2,3) is considered here.

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Fig. 5
Fig. 5 Comparison of optical susceptibilities with different models for the (2,3) transition with the lowest subband (μ=2) occupied with N=1.0× 10 12 cm −2 and the upper subband (ν=3) empty. The free carrier case (dashed-red) has only one peak. The combination of band structure and manybody effects in a single transition leads to a split in the optical susceptibility (solid-black) and thus to extra structures in the polariton spectra for a nonequilibrium configuration as seen in Fig. 4. If the strongly k-dependent transition dipole moment shown in the inset is replaced by a constant - here taken as its maximum value, the dot-dashed (blue) curve is obtained in which the camel-back structure that leads to three branches when coupled with photons in a microcavity disappears.

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Equations (7)

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ℏ( ∂ ∂t +i( e υ − e μ ) ) G νμ < ( k,t )+( G μμ < ( k,t )− G νν < ( k,t ) )× { ℘ → νμ ⋅ E → ( t )+ ∑ k → ' G νμ < ( k',t )  V ˜ ( νμ k → − k' → ) }= I νμ ( k,t ).
I μν (k,t)= ∑ λ ∫ −∞ t dt'[ Σ νλ < (k,tt') G λμ > (k,tt')+ Σ νλ > (k,tt') G λμ < (k,tt')−( >⇔< ) ] .
χ( ω )=− 1 4π ∑ μ≠ν { Λ μν ω− ω μν +i γ μν − Λ μν ω+ ω μν +i γ μν },
ε( ω )= ε b +4πλχ( ω ),
ΔE( ω )+ ω 2 c 2 ε( ω )E( ω )=0
  k y 2 + k z 2 = ω 2 c 2 ε( ω ).
sinθ=  ε b ε cap ( 1−4πλℜ{ χ( ω )/ ε b }−  ω c 2 / ω 2 ) .

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