Abstract

In cavity quantum electrodynamics, strong light–matter coupling is normally observed between a photon mode and a discrete optically active transition. In the present work we demonstrate that strong coupling can also be achieved using ionizing, intrinsically continuum, transitions. This leads to the appearance of novel discrete polaritonic resonances, corresponding to dressed bound exciton states, kept together by the exchange of virtual cavity photons. We apply our theory to the case of intersubband transitions in doped quantum wells, where Coulomb-bound excitons are absent. In considering quantum wells with a single bound electronic subband, in which all transitions involve states in the continuum, we find that the novel bound excitons predicted by our theory are observable within present-day, realistic parameters. Our work shows how strong light–matter coupling can be used as a novel gauge to tune both optical and electronic properties of semiconductor heterostructures beyond those permitted by mere crystal properties.

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  55. M. Załużny and C. Nalewajko, “Coupling of infrared radiation to intersubband transitions in multiple quantum wells: the effective-medium approach,” Phys. Rev. B 59, 13043–13053 (1999).
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    [Crossref]
  57. G. Scalari, N. Hoyler, M. Giovannini, and J. Faist, “Terahertz bound-to-continuum quantum-cascade lasers based on optical-phonon scattering extraction,” Appl. Phys. Lett. 86, 181101 (2005).
    [Crossref]

2019 (1)

G. L. Paravicini-Bagliani, F. Appugliese, E. Richter, F. Valmorra, J. Keller, M. Beck, N. Bartolo, C. Rössler, T. Ihn, K. Ensslin, C. Ciuti, G. Scalari, and J. Faist, “Magneto-transport controlled by Landau polariton states,” Nat. Phys. 15, 186–190 (2019).
[Crossref]

2018 (6)

D. Hagenmüller, S. Schütz, J. Schachenmayer, C. Genes, and G. Pupillo, “Cavity-assisted mesoscopic transport of fermions: coherent and dissipative dynamics,” Phys. Rev. B 97, 205303 (2018).
[Crossref]

L. A. Martínez-Martínez, M. Du, R. F. Ribeiro, S. Kéna-Cohen, and J. Yuen-Zhou, “Polariton-assisted singlet fission in acene aggregates,” J. Phys. Chem. Lett. 9, 1951–1957 (2018).
[Crossref]

J.-M. Manceau, N.-L. Tran, G. Biasiol, T. Laurent, I. Sagnes, G. Beaudoin, S. De Liberato, I. Carusotto, and R. Colombelli, “Resonant intersubband polariton-LO phonon scattering in an optically pumped polaritonic device,” Appl. Phys. Lett. 112, 191106 (2018).
[Crossref]

N. C. Passler, C. R. Gubbin, T. G. Folland, I. Razdolski, D. S. Katzer, D. F. Storm, M. Wolf, S. De Liberato, J. D. Caldwell, and A. Paarmann, “Strong coupling of epsilon-near-zero phonon polaritons in polar dielectric heterostructures,” Nano Lett. 18, 4285–4292 (2018).
[Crossref]

J. Keeling and P. G. Kirton, “Orientational alignment in cavity quantum electrodynamics,” Phys. Rev. A 97, 053863 (2018).
[Crossref]

D. De Bernardis, P. Pilar, T. Jaako, S. De Liberato, and P. Rabl, “Breakdown of gauge invariance in ultrastrong-coupling cavity QED,” Phys. Rev. A 98, 053819 (2018).
[Crossref]

2017 (11)

C. R. Gubbin, S. A. Maier, and S. De Liberato, “Theoretical investigation of phonon polaritons in SiC micropillar resonators,” Phys. Rev. B 95, 035313 (2017).
[Crossref]

J.-M. Manceau, G. Biasiol, N. L. Tran, I. Carusotto, and R. Colombelli, “Immunity of intersubband polaritons to inhomogeneous broadening,” Phys. Rev. B 96, 235301 (2017).
[Crossref]

N. Shammah, N. Lambert, F. Nori, and S. De Liberato, “Superradiance with local phase-breaking effects,” Phys. Rev. A 96, 023863 (2017).
[Crossref]

S. Brodbeck, S. De Liberato, M. Amthor, M. Klaas, M. Kamp, L. Worschech, C. Schneider, and S. Höfling, “Experimental verification of the very strong coupling regime in a GaAs quantum well microcavity,” Phys. Rev. Lett. 119, 027401 (2017).
[Crossref]

E. Cortese, P. G. Lagoudakis, and S. De Liberato, “Collective optomechanical effects in cavity quantum electrodynamics,” Phys. Rev. Lett. 119, 043604 (2017).
[Crossref]

H. L. Luk, J. Feist, J. J. Toppari, and G. Froenhof, “Multiscale molecular dynamics simulations of polaritonic chemistry,” J. Chem. Theory Comput. 13, 4324–4335 (2017).
[Crossref]

J. Flick, H. Appel, M. Ruggenthaler, and A. Rubio, “Cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon systems,” J. Chem. Theory Comput. 13, 1616–1625 (2017).
[Crossref]

A. Bayer, M. Pozimski, S. Schambeck, D. Schuh, R. Huber, D. Bougeard, and C. Lange, “Terahertz light-matter interaction beyond unity coupling strength,” Nano Lett. 17, 6340–6344 (2017).
[Crossref]

L. Garziano, A. Ridolfo, S. De Liberato, and S. Savasta, “Cavity QED beyond rotating wave approximation: photon bunching from the emission of individual dressed qubits,” ACS Photon. 4, 2345–2351 (2017).
[Crossref]

C. Gubbin and S. De Liberato, “Theory of nonlinear polaritonics: X(2) scattering on a β-SiC surface,” ACS Photon. 4, 1381–1388 (2017).
[Crossref]

J. Flick, M. Ruggenthaler, H. Appel, and A. Rubio, “Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry,” Proc. Natl. Acad. Sci. USA 114, 3026–3034 (2017).

2016 (3)

F. Herrera and F. C. Spano, “Cavity-controlled chemistry in molecular ensembles,” Phys. Rev. Lett. 116, 238301 (2016).
[Crossref]

A. Le Boité, M.-J. Hwang, H. Nha, and M. B. Plenio, “Fate of photon blockade in the deep strong-coupling regime,” Phys. Rev. A 94, 033827 (2016).
[Crossref]

J. A. Cwik, P. Kirton, S. De Liberato, and J. Keeling, “Self-consistent molecular adaptation induced by strong coupling,” Phys. Rev. A 93, 033840 (2016).
[Crossref]

2015 (5)

E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, and T. W. Ebbesen, “Conductivity in organic semiconductors hybridized with the vacuum field,” Nat. Mater. 14, 1123–1129 (2015).
[Crossref]

J. Feist and F. J. Garcia-Vidal, “Extraordinary exciton conductance induced by strong coupling,” Phys. Rev. Lett. 114, 196402 (2015).
[Crossref]

J. Galego, F. J. Garcia-Vidal, and J. Feist, “Cavity-induced modifications of molecular structure in the strong coupling regime,” Phys. Rev. X 5, 041022 (2015).
[Crossref]

R. Colombelli and J.-M. Manceau, “Perspectives for intersubband polariton lasers,” Phys. Rev. X 5, 011031 (2015).
[Crossref]

Y. Todorov, “Dipolar quantum electrodynamics of the two-dimensional electron gas,” Phys. Rev. B 91, 125409 (2015).
[Crossref]

2014 (3)

M. Ruggenthaler, J. Flick, C. Pellegrini, H. Appel, I. V. Tokatly, and A. Rubio, “Quantum-electrodynamical density-functional theory: bridging quantum optics and electronic-structure theory,” Phys. Rev. A 90, 012508 (2014).
[Crossref]

C. S. Muñoz, E. del Valle, A. G. Tudela, K. Müller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. J. Finley, and F. P. Laussy, “Emitters of N-photon bundles,” Nat. Photonics 8, 550–555 (2014).
[Crossref]

S. De Liberato, “Light-matter decoupling in the deep strong coupling regime: the breakdown of the Purcell effect,” Phys. Rev. Lett. 112, 016401 (2014).
[Crossref]

2013 (4)

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

S. De Liberato, C. Ciuti, and C. C. Phillips, “Terahertz lasing from intersubband polariton-polariton scattering in asymmetric quantum wells,” Phys. Rev. B 87, 241304 (2013).
[Crossref]

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref]

J. D. Caldwell, O. J. Glembocki, Y. Francescato, N. Sharac, V. Giannini, F. J. Bezares, J. P. Long, J. C. Owrutsky, I. Vurgaftman, J. G. Tischler, V. D. Wheeler, N. D. Bassim, L. M. Shirey, R. Kasica, and S. A. Maier, “Low-loss, extreme subdiffraction photon confinement via silicon carbide localized surface phonon polariton resonators,” Nano Lett. 13, 3690–3697 (2013).
[Crossref]

2012 (3)

S. De Liberato and C. Ciuti, “Quantum theory of intersubband polarons,” Phys. Rev. B 85, 125302 (2012).
[Crossref]

Y. Todorov and C. Sirtori, “Intersubband polaritons in the electrical dipole gauge,” Phys. Rev. B 85, 045304 (2012).
[Crossref]

J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, “Modifying chemical landscapes by coupling to vacuum fields,” Angew. Chem. 124, 1624–1628 (2012).
[Crossref]

2010 (1)

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

2009 (4)

S. De Liberato and C. Ciuti, “Stimulated scattering and lasing of intersubband cavity polaritons,” Phys. Rev. Lett. 102, 136403 (2009).
[Crossref]

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of light-matter excitations in the ultra-strong coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

G. Guenter, A. A. Anappara, J. Hees, G. Biasiol, L. Sorba, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, and R. Hubert, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458, 178–181 (2009).
[Crossref]

S. De Liberato and C. Ciuti, “Quantum theory of electron tunneling into intersubband cavity polariton states,” Phys. Rev. B 79, 075317 (2009).
[Crossref]

2005 (4)

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

G. Scalari, N. Hoyler, M. Giovannini, and J. Faist, “Terahertz bound-to-continuum quantum-cascade lasers based on optical-phonon scattering extraction,” Appl. Phys. Lett. 86, 181101 (2005).
[Crossref]

A. A. Anappara and A. Tredicucci, “Electrical control of polariton coupling in intersubband microcavities,” Appl. Phys. Lett. 87, 051105 (2005).
[Crossref]

S. Savasta, O. Di Stefano, V. Savona, and W. Langbein, “Quantum complementarity of microcavity polaritons,” Phys. Rev. Lett. 94, 246401 (2005).
[Crossref]

2004 (1)

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307 (2004).
[Crossref]

2003 (2)

D. S. Citrin and J. B. Khurgin, “Microcavity effect on the electron-hole relative motion in semiconductor quantum wells,” Phys. Rev. B 68, 205325 (2003).
[Crossref]

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

2001 (2)

J. B. Khurgin, “Excitonic radius in the cavity polariton in the regime of very strong coupling,” Solid State Commun. 117, 307–310 (2001).
[Crossref]

J. Faist, M. Beck, and T. Aellen, “Quantum-cascade lasers based on a bound-to-continuum transition,” Appl. Phys. Lett. 78, 147–149 (2001).
[Crossref]

1999 (1)

M. Załużny and C. Nalewajko, “Coupling of infrared radiation to intersubband transitions in multiple quantum wells: the effective-medium approach,” Phys. Rev. B 59, 13043–13053 (1999).
[Crossref]

1996 (1)

R. Houdré, R. P. Stanley, and M. Ilegems, “Vacuum-field Rabi splitting in the presence of inhomogeneous broadening: resolution of a homogeneous linewidth in an inhomogeneously broadened system,” Phys. Rev. A 53, 2711–2715 (1996).
[Crossref]

1992 (1)

F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S.-N. G. Chu, and A. Y. Cho, “Observation of an electronic bound state above a potential well,” Nature 358, 565–567 (1992).
[Crossref]

1991 (1)

M. Załużny, “Bound-free intraband absorption line shape in quantum-well structures,” Solid State Commun. 79, 1013–1016 (1991).
[Crossref]

1956 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1956).
[Crossref]

Aellen, T.

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J. Keeling and P. G. Kirton, “Orientational alignment in cavity quantum electrodynamics,” Phys. Rev. A 97, 053863 (2018).
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C. S. Muñoz, E. del Valle, A. G. Tudela, K. Müller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. J. Finley, and F. P. Laussy, “Emitters of N-photon bundles,” Nat. Photonics 8, 550–555 (2014).
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I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307 (2004).
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C. S. Muñoz, E. del Valle, A. G. Tudela, K. Müller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. J. Finley, and F. P. Laussy, “Emitters of N-photon bundles,” Nat. Photonics 8, 550–555 (2014).
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A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
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H. L. Luk, J. Feist, J. J. Toppari, and G. Froenhof, “Multiscale molecular dynamics simulations of polaritonic chemistry,” J. Chem. Theory Comput. 13, 4324–4335 (2017).
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C. R. Gubbin, S. A. Maier, and S. De Liberato, “Theoretical investigation of phonon polaritons in SiC micropillar resonators,” Phys. Rev. B 95, 035313 (2017).
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J.-M. Manceau, N.-L. Tran, G. Biasiol, T. Laurent, I. Sagnes, G. Beaudoin, S. De Liberato, I. Carusotto, and R. Colombelli, “Resonant intersubband polariton-LO phonon scattering in an optically pumped polaritonic device,” Appl. Phys. Lett. 112, 191106 (2018).
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A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
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C. S. Muñoz, E. del Valle, A. G. Tudela, K. Müller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. J. Finley, and F. P. Laussy, “Emitters of N-photon bundles,” Nat. Photonics 8, 550–555 (2014).
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C. S. Muñoz, E. del Valle, A. G. Tudela, K. Müller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. J. Finley, and F. P. Laussy, “Emitters of N-photon bundles,” Nat. Photonics 8, 550–555 (2014).
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N. Shammah, N. Lambert, F. Nori, and S. De Liberato, “Superradiance with local phase-breaking effects,” Phys. Rev. A 96, 023863 (2017).
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E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, and T. W. Ebbesen, “Conductivity in organic semiconductors hybridized with the vacuum field,” Nat. Mater. 14, 1123–1129 (2015).
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N. C. Passler, C. R. Gubbin, T. G. Folland, I. Razdolski, D. S. Katzer, D. F. Storm, M. Wolf, S. De Liberato, J. D. Caldwell, and A. Paarmann, “Strong coupling of epsilon-near-zero phonon polaritons in polar dielectric heterostructures,” Nano Lett. 18, 4285–4292 (2018).
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G. L. Paravicini-Bagliani, F. Appugliese, E. Richter, F. Valmorra, J. Keller, M. Beck, N. Bartolo, C. Rössler, T. Ihn, K. Ensslin, C. Ciuti, G. Scalari, and J. Faist, “Magneto-transport controlled by Landau polariton states,” Nat. Phys. 15, 186–190 (2019).
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N. C. Passler, C. R. Gubbin, T. G. Folland, I. Razdolski, D. S. Katzer, D. F. Storm, M. Wolf, S. De Liberato, J. D. Caldwell, and A. Paarmann, “Strong coupling of epsilon-near-zero phonon polaritons in polar dielectric heterostructures,” Nano Lett. 18, 4285–4292 (2018).
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Supplementary Material (1)

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» Supplement 1       The supplemental document includes explicit derivations of the theoretical results presented in the main article.

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Figures (7)

Fig. 1.
Fig. 1. Schematic representation of the electronic structure of a quantum well of width LQW, with a single bound state below the continuum (shaded in gray). (a) Electronic density envelope functions of the different single-particle eigenmodes, shifted by their energy. The potential profile is plotted in red, with the first ionization energy χ and the conduction band discontinuity V explicitly marked. The figure has been obtained using the parameters of the structure described in Section 3.A. For sake of clarity, only one continuum mode in every 10 is shown, with its density multiplied by 10. (b) In-plane dispersion of the different subbands in momentum space. The single bound state is filled with electrons (in red), up to the Fermi energy EF (dashed yellow line). The dashed–dotted blue arrows represent a collective bound-to-continuum transition.
Fig. 2.
Fig. 2. Simulation of a single quantum well of width LQW=4nm in a bulk of total width T=1μm, with effective cavity length Lc=25nm and cavity energy ωqa=185meV, smaller than the first ionization χ=188.4meV. (a) Polaritonic spectrum as a function of the doping. The yellow line marks the cavity energy. (b) Colormap of the excited electron density |ψsqe(z)|2 for the lowest lying polaritonic mode as a function of doping. Yellow dashed lines mark the boundaries of the quantum well. (c)–(g) Plots of |ψsqe(z)|2 for all the polaritonic modes (all the s up to the cutoff) relative to the five values of doping marked by dotted vertical gray lines in panels (a) and (b). The lowest lying mode represented in panel (b) is plotted in blue; all the other modes in the continuum are instead in red, forming the thin homogeneous red band of density T1 visible at the bottom of each panel. Note that, due to the different scale, the node in the localized excited electronic density visible in panel (b) is not clearly resolved in panels (c)–(g).
Fig. 3.
Fig. 3. Same as in Fig. 2, but with cavity energy ωqa=195meV, larger than the first ionization χ=188.4meV.
Fig. 4.
Fig. 4. Same as in Fig. 2, but with cavity energy ωqa=205meV, larger than the first ionization χ=188.4meV.
Fig. 5.
Fig. 5. (a) Ground (blue solid line) and excited (red dashed line) electronic densities corresponding to the lowest eigenmode in Fig. 3(g). The shaded region corresponds to the quantum well. (b) Weight of the matter component Psq for the lowest-lying polaritonic mode as a function of doping for ωqa=185meV (blue solid line), ωqa=195meV (red dashed line), and ωqa=205meV (yellow dashed–dotted line). Other parameters as in Fig. 2.
Fig. 6.
Fig. 6. Simulation of nQW=20 quantum wells of width LQW=4nm in a bulk of total width T=0.5μm embedded in a planar microcavity. The TM0 mode of the microcavity is chosen to have energy ωqa=195meV, larger than the first ionization energy χ=192meV. (a) Polaritonic spectrum as a function of the doping. The yellow line marks the cavity energy. (b), (c) Plots of the excited electron density |ψsqe(z)|2 for the lowest-lying polaritonic mode, for values of doping equal, respectively, to N2DEG=0 and 3×1016cm2, marked by arrows in panel (a). Shaded regions correspond to the locations of the quantum wells.
Fig. 7.
Fig. 7. (a) Reflectivity map for the same structure studied in Fig. 6, calculated considering an electronic linewidth of 4 meV. The horizontal dashed–dotted red line marks the first ionization energy. The solid black and dashed white lines mark instead the dispersion of the lowest polariton mode obtained using the Hopfield approach, respectively without and with the effective medium approximation. (b) A vertical cut of panel (a) for N2DEG=3×1012cm2.

Equations (9)

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Ψk(z)=nϕn(z)cnk,
b(nm)q=1Nkcnk+qcmk.
[bαq,bβq]=δαβδ(qq).
(bαq+bαq)=βhαβ(pβq+pβq).
H=q[ωqaaqaq+αωαppαqpαq+αΞαq2(aq+aq)(pαq+pαq)],
dsq=xsqaq+zsqaq+α[ysαqpαq+wsαqpαq].
ωqaωqa2ωsqd2α|Ξαq|2ωαpωαp2ωsqd2=1.
N(z)=kΨk(z)Ψk(z),
ΔNsq(z)=G|dsqN(z)dsq|GG|N(z)|G=Psq[|ψsqe(z)|2|ψsqg(z)|2],

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