Effect of polariton-polariton interactions on the excitation spectrum of a nonequilibrium condensate in a periodic potential

Polariton condensates are investigated in periodical potentials created by surface acoustic waves (SAWs) using both coherent and incoherent optical excitation. Under coherent resonant pumping, condensates are formed due to polariton-parametric scattering from the pump. In this case, the excitation spectrum of the condensate shows a strong reduction of the energy gap arising from the acoustic modulation, indicating efficient screening of the SAW potential by spatial modulation of the polariton density. The observed results are in good agreement with a model based on generalized Gross-Pitaveskii equations, with account taken of the spatial dependence of the exciton energy landscape. In the case of incoherent pumping, coexisting nonequilibrium condensates with $s$- and $p$-type wavefunctions are observed, which have different energies, symmetry, and spatial coherence. The energy splitting between these condensate states is also reduced with respect to the gap of the one particle spectrum below threshold, but the screening effect is less pronounced than in the case of coherently pumped system due to weaker modulation of the pump state.

Figure 1

(a) Schematic of microcavity device with interdigitated transducer on top of the sample generating SAW along [010]. (b) Calculated single-particle polariton spectrum in periodic potential. $s$ denotes the polariton ground state, whereas $s$′, $p$ denote states of the first and the second bands at the MBZ boundary, respectively. (c) Unmodulated polariton dispersion versus $k_x$ and $k_y$. Pump-excitation conditions for optical parametric oscillation ($P_{\mathrm{OPO}}$) and nonequilibrium polariton BEC ($P_{\mathrm{BEC}}$) are shown.

Figure 2

Polariton-emission spectra versus energy and $k_y$ taken at $k_x$ $=$ 0 below (a) and above (b–d) condensation threshold of the OPO. Data in (b) are measured without SAW. (c, d) Condensation with applied SAWs.

Figure 3

Intensity of first-order diffraction replica of the pump versus pump power (a) and SAW amplitude (b) at fixed $u$ $=$ 2.8 mW${}^{0.5}$ and $I_L$ ∼ 800 W/cm${}^2$, respectively.

Figure 4

Calculated PL spectrum under a nearly zero pump power (a) and slightly above the threshold of parametric generation (b).

Figure 5

(a) Model dependences of the SAW-induced LP potential ($\Delta E_{\mathrm{SAW}}$), LP blue shift induced by the polariton-polariton interaction at a pump power 1.5 times above the threshold ($\Delta E_{\mathrm{shift}}$), the effective polariton energy, and the sum of the previous two contributions ($\Delta E_{\mathrm{eff}}$). (b) Intensities of the driven mode ($k_y=0$) and diffracted pump replicas ($k_y=\pm k_{\mathrm{SAW}}$) versus pump power expressed in units of its threshold magnitude.

Figure 6

Polariton emission versus energy and $k_y$ recorded at an optical power 1.5 to 2 times above the BEC condensation threshold $I_{\mathrm{BECth}}=2.2\times {10}^4$ W/cm${}^2$ in the absence (a) and presence (b) of a SAW ($u$ $=$ 3.3 mW${}^{0.5}$), respectively. The first-order spatial correlation function $g^{\left(1\right)}(y,-y)$ of the $s$ and $p$ states, respectively, is shown in (c) and (d).

Figure 7

Energy splitting between $s$ and $p$ states of nonequilibrium BEC condensate versus SAW amplitude is shown by red triangles. Polariton energy gap at the edge of the first MBZ at $k_{\mathrm{SAW}}/2$ below condensation threshold is shown by blue circles.