Exciton-Polariton Gap Solitons in Two-Dimensional Lattices

Abstract

We report on the two-dimensional gap-soliton nature of exciton-polariton macroscopic coherent phases (PMCP) in a square lattice with a tunable amplitude. The resonantly excited PMCP forms close to the negative mass M point of the lattice band structure with energy within the lattice band gap and its wave function localized within a few lattice periods. The PMCPs are well described as gap solitons resulting from the interplay between repulsive polariton-polariton interactions and effective attractive forces due to the negative mass. The solitonic nature accounts for the reduction of the PMCP coherence length and optical excitation threshold with increasing lattice amplitude. DOI: 10.1103/PhysRevLett.111.146401 PACS numbers: 71.36.+c, 42.65.Yj, 63.20.kk, 73.21.Cd The periodic spatial modulation of a medium creates an artificial band structure with energy gaps and anomalous (i.e., negative) dispersion. In the presence of nonlinearity, spatially self-localized states may appear within the energy gaps as the result of the interplay between the anomalous dispersion and interparticle interactions. This takes place when the kinetic energy contribution [E K ¼ À 2 @ 2 =ð2m b 2 Þ] due to localization of particles with a negative mass Àm b within a radius compensates the repulsive interparticle interaction energy E I . These states, known as gap solitons (GSs), are metastable solutions of the Gross-Pitaevskii equation [1]. GSs have been explored in optical fibers [2], nonlinear photonic crystals [3-6], atomic Bose Einstein condensates (BECs) in optical lattices [7,8], and, very recently, also in the hybrid lightmatter polariton system [9]. Polaritons result from the strong coupling of photons and quantum well (QW) excitons in a semiconductor microcavity (MC). Being bosonic light-matter quasiparticles, they advantageously combine features from both species. Namely, the small mass arising from the photonic component allows them to form polariton macroscopic coherent phases (PMCPs) at low densities and high temperatures, while the interexcitonic interactions provide a nonlinearity several orders of magnitude stronger than in purely photonic systems [10]. While GSs in one-dimensional (1D) potentials have been extensively studied [2,3,5,[7][8][9], GSs in 2D lattices have so far only been reported for purely photonic systems [4,6]. GSs in 2D potentials are qualitatively different from their 1D counterparts, for example, opening the way to the realization of novel topological phases [6,11].In this Letter, we demonstrate the formation and manipulation of GSs of PMCPs in a 2D tunable lattice. The studies were carried out in PMCPs resonantly excited in a tunable square lattice created by surface acoustic waves (SAWs). While PMCPs in a homogeneous MC normally appear at the lowest energy state with zero in-plane momentum, PMCPs in a shallow (i.e., low amplitude) lattice have a GS character and are excited via the accumulation of particles at critical points of negative mass and energy above the ground state [12]. The PMCP forms clo...

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