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. Microcavity polaritons are composite particles arising from strong exciton-photon coupling in semiconductor microresonators. Due to their excitonic component, polariton-polariton interactions are very strong, enabling the observation of stimulated polariton-polariton scattering, 1,2 nonequilibrium-polariton Bose-Einstein condensation (BEC), 3-5 superfluidity, 6 and polariton solitons. 7,8 Polaritonpolariton interactions also define the size of vortices formed in polariton condensates 9 and modify the excitation spectrum of the condensates, leading to a diffusive Goldstone mode. 4,5,10 Recently, investigation of exciton-polaritons in a periodic potential became a topic in its own right. Study of the spatial coherence of nonequilibrium-polariton condensates arising from optical parametric oscillation (OPO) and condensate transport using surface acoustic wave (SAW) have been reported.11 Polariton condensation into p and d states under incoherent excitation has been observed in microcavities where weak one-dimensional (1D) and two-dimensional (2D) periodic potentials are created by metal patterning on the surface of microcavity.12,13 Furthermore, the formation of bright polariton solitons 14 in spatially modulated microcavity wires has been reported. 15 As well as exciton-polaritons, transport of indirect excitons in semiconductor quantum wells using SAWs 16 and electrode conveyor belts were also demonstrated. 17 We note that investigation of equilibrium cold atom condensates in periodic lattices has also been very productive with observation of superfluid-to-Mott insulator transition, 18 particle number squeezing, and bright gap solitons.
19Without the periodic potential, polariton-polariton interactions have been shown to determine the excitation spectrum of a condensate, which is a diffusive Goldstone mode 4,5,10,20 approaching a sound like Bogoliubov dispersion at higher k-vectors. Bogoliu...