Resonant pumping of polaritonic SSH chains

An optical-lattice realization of a Su-Schrieffer-Heeger chain is theoretically investigated. The topological state is controlled by the relative phase of the lasers constructing the lattice. The hopping amplitudes are calculated within the harmonic approximation to the optical potential in the vicinity of its minima. Finally, we examine polaritons loaded into adiabatically shaken optical lattices with damping and pumping and demonstrate that, in the case of resonant pumping, the system manifests different quantitative and qualitative behaviour for topologically trivial and non-trivial phases. 1. Introduction A topological insulator (TI) is a state of matter that behaves as a typical insulator in the bulk but can host midgap states localized at its boundary[1] (the so-called edge states). The minimalistic model demonstrating topological properties was initially suggested by Su, Schrieffer, and Heeger (SSH)[2]. The system can be presented as a dimerized linear chain with each unit cell consinting of two sites with staggered intra-(t1) and inter-cell (t2) hopping amplitudes. Due to the simplicity and rich properties, the SSH model and its different generalizations have been extensively studied during the recent years (in the field of electronics[3, 4] and waveguide photonics[5, 6]). Periodically modulated (Floquet-engineered[7, 8]) SSH chains have been investigated as well with respect to topological properties and phase transitions[9{11]. Floquet engineering is known to be achievable not only in the field of charged particles, but in the field of cold atoms physics as well. There, a possible realization of Floquet engineering is utilization of cyclically modulated (shaken) optical lattices (OL)[12{14]. In this research, we theoretically investigate the resonant pumping of the SSH chain modelled as an adiabatically shaken OL loaded with exciton-polaritons in microcavities. The topology is adjusted by tuning the relative phase of the lasers constructing the optical potential.