Figure 1

Illustration of microcavity structure with polaritonic condensate (green) and 2D electron gas (blue). The photons are confined between dielectric Bragg mirrors and strongly interact with excitonic transition in the QW placed where the electric field of the cavity mode has a maximum. Strong coupling between photons and excitons leads to the formation of cavity polaritons. Free electrons are situated in the QW parallel to the QW with excitons and interact with them, which leads to the coupling of electronic and polaritonic systems.Reuse & Permissions

Figure 2

Feynman diagrams for the matrix element of the effective polariton-polariton interaction. Index 1 corresponds to electrons, and index 2 to the exciton-polaritons. The arrows show the spin projection. Black circles correspond to the polariton BEC.Reuse & Permissions

Figure 3

The interaction of the exciton and free carrier accompanied by exchange of the electrons. In the configuration where the spins of the exchanged electrons are antiparallel the process leads to the transition of the exciton toward a dark state, which becomes inefficient due to the huge Rabi splitting between polariton and dark exciton modes.Reuse & Permissions

Figure 4

Momentum dependence of the matrix element of the polariton-electron interaction. Black and blue thick lines correspond to direct and exchange matrix elements for well separation of $\Delta =4$ nm, respectively. Green and red lines show exchange interaction for well separations of $\Delta =6$ nm and 8 nm, respectively. Inset: The confinement in the hybrid system of separated quantum wells with width $L=2$ nm. The characteristic decay length $L_0$ was estimated as $2.3$ nm. The filled area under the curves demonstrates the wave function overlap.Reuse & Permissions

Figure 5

Linear dispersion of the elementary excitations of the condensate in the region of small momentum. $\Delta =4,6$ nm (large and medium dashed lines, respectively). Solid lines represent bare upper (blue) and lower (green) BEC dispersion branches. Red solid and dashed lines correspond to initial and modified plasmon modes. Inset: Dispersion of plasmon mode in a single quantum well with 2DEG (red line). The blue filling indicates the electron-hole excitation continuum.Reuse & Permissions

Figure 6

Dispersion of the elementary excitations of the hybrid spinor polariton-electron system created in a GaAs/AlAs heterostructure ($n_{el}=5\times {10}^{12}$ cm${}^{-2}$). Solid blue and green lines correspond to unperturbed upper and lower Bogoliubov branches when separation between QWs is large ($>10$ nm). With decreasing distance the co-polarized lower branch becomes modified by the electronic system ($\Delta =4.1$ nm, small-dashed line) and for certain separation a roton minimum appears ($\Delta =4$ nm, medium-dashed line). For very closely situated wells the polariton-electron interaction strongly increases, which leads to destruction of the condensate ($\Delta =3.7$ nm, large-dashed line).Reuse & Permissions

Figure 7

The dispersion of the co-polarized Bogoliubov branch for different detunings of the cavity mode ($\Delta =4$ nm). While for this separation one has a roton minimum for zero detuning (medium-dashed line), it disappears for large negative detuning ($\delta =-5$ meV, red large-dashed line) due to the decreasing polariton-electron interaction. For positive detuning ($\delta =5$ meV, blue small-dashed line) increasing interaction leads to condensate instability.Reuse & Permissions

Figure 8

Polariton condensate velocities as a function of separation distance between quantum wells. The blue solid line shows the corresponding velocity of the upper branch, while the green curve shows the dependence of the lower branch velocity. The inset shows how the presence of the roton minimum affects the critical velocity of the superfluid flow which is now determined by the slope $tg\Phi$.Reuse & Permissions

Figure 9

The effective interaction constants ${\tilde{V}}_{22}^{\uparrow \uparrow ,\uparrow \downarrow }$ as functions of momentum and frequency ($\Delta =4$ nm, $n_{el}=5\times {10}^{12}$ cm${}^{-2}$). While for the static case the constants are strongly modified by the polariton-electron interaction (gray region, $V_{22}^{\uparrow \uparrow ,\uparrow \downarrow }\approx \left|0.05\right|$ meV), for the high-frequency region retardation effects play a role and effective constants correspond to initial ones.Reuse & Permissions

Figure 10

The spectrum of elementary excitations for various concentrations of electron gas for separation $\Delta =4$ nm. For high electron concentrations ($n_{el}=5\times {10}^{12}$ cm${}^{-2}$) in the interesting region of $q$ distinct plasmon and polariton branches exist (red dashed lines), while for small concentration of electron gas ($n_{el}={10}^9$ cm${}^{-2}$) the bogolon branch corresponds to that of the uncoupled system (solid green line). In the range of medium concentration ($n_{el}=8\times {10}^{11}$ cm${}^{-2}$) the plasmonic and polaritonic modes are strongly coupled (orange solid lines) and reveal anticrossing behavior, as shown in the inset of the figure. The inset shows characteristic mode anticrossing for plasmon and polariton dispersion branches (where the black dashed lines correspond to the spectrum of excitations in uncoupled systems).Reuse & Permissions

Figure 11

The double-barrier structure for obtaining the strongly coupled exciton-electron system. (a) Unbiased system, when there is a difference between the energy levels in right and left QWs and electron (blue) and exciton (green, red) wave functions overlap only weakly. (b) The application of the gate voltage $V_g$ changes the distance between the energy levels in right and left quantum wells and can lead to the tunneling resonance when these energies become equal. At resonance, the electron wave functions will be spread between both wells whereas the left quantum well hole remains strongly confined. As a result, the exciton acquires a significant dipole moment and overlap between wave functions of free electron and exciton increases, thus increasing the exchange interaction between them.Reuse & Permissions