Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling

Abstract

We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to repulsive excitonic nonlinearity such states are encountered in finite gaps in the spectrum of the periodic array. Spin-orbit coupling between two polarization components stemming from TE-TM energy splitting of the cavity photons acting together with Zeeman splitting lifts the degeneracy between vortex solitons with opposite topological charges and makes their density profiles different for a fixed energy. This results in formation of four distinct families of vortex solitons with topological charges 1 m = , all of which can be stable. At the same time, only two stable families of fundamental gap solitons characterized by domination of different polarization components are encountered.Formation of stable nonlinear excitations in the external periodic potentials is a problem attracting considerable attention in diverse areas of physics, including photonics and matter wave optics. Periodic potential may qualitatively change spatial dispersion, so that excitation of bright lattice solitons with unconventional shapes becomes possible under conditions where bright solitons simply do not exist without the potential. The properties of lattice solitons are well-studied in nonlinear optical settings, where peri- One of the most distinctive features of polariton condensate is the possibility to realize in it sufficiently strong spin-orbit coupling originating in the cavity-induced TE-TM splitting of the polariton energy levels, see, e.g. [6,8,13] and references therein. Among other effects, such a coupling mediates formation of unidirectional polaritonic edge states in truncated honeycomb potentials [8,21]. Nevertheless, the impact of spin-orbit coupling on formation of gap polariton solitons in periodic potentials was not considered yet. At the same time, it is known that in Bose-Einstein condensates spinorbit coupling (of completely different physical origin [22]) may drastically affect stability and symmetries of available nonlinear excitations in periodic potentials [23,24].The aim of this Letter is twofold. First, we introduce vortex polariton solitons in periodic potentials. Second, we study the impact of spin-orbit interactions, specific for polariton condensates, on all gap soliton states, including fundamental and vortex ones. In order to do this we use continuous conservative model describing evolution of exciton-polariton condensates in a square array of microcavity pillars and accounting for spin-dependent interactions and Zeeman splitting in the external magnetic field. We found that in this system the properties of vortex solitons depend on the sign of their topological charge and that four distinct stable vortex soliton families can co-exist for the same energy.We describe the evolution of polariton condensate in periodic potential by a system of dimensionless Gross-Pitaevskii equations for the spin-positive and spin-negativ...

Spin–orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

“…Adding trapping or lattice potentials to the nonlinear SOC systems is a very active direction of the current research, see, e.g., Refs. [21][22][23]. In the polariton microcavities, which are the subject of the present work, a variety of practical methods have been developed to secure high quality of the engineered trapping landscapes [23].…”

Stationary structures of spin-orbit coupled polariton condensates in the Bessel lattices

“…由于极化激元具有有限寿命以及极化激元之间存在散射，因此极化激元凝聚是非平衡 系统 [27] ， 其动力学通常用由于衰减和泵浦引起的非厄米平均场近似理论描述 [28] . 但是, 如果 极化激元凝聚达到稳定状态, 其中的泵浦和衰减达到动态平衡, 可以看成是准保守系统 [16] .…”

“…在原子 BEC 中, SOC 会极大地影响周期势场中可用非线性激发的稳定性和对称性 [15] . 基于此, 文 献 [16] 研究了双组分旋量极化激元凝聚中, 周期势场中 SOC 对能隙极化激元基本孤立子 和涡旋孤立子形成的影响, 给出了四个不同族, 拓扑荷数为 m = ±1 的稳定的涡旋孤立子.…”

Topological edge solitons in polaritonic lattice

“…Recently, the focus of attention in the study of the effects of non-trivial topology has shifted towards systems with nonlinearity [19,20,21,22,16,23,24,25,26,27,29,30], where exciton-polaritons, due to their unique properties, play a special role. Among these works are studies of self-localized states [19,20], self-induced topological transitions [21], topological Bogoliubov excitations [16], suppression of topological phases [22], vortices in lattices [23], spin-Meissner states in ring resonators [24], solitons in lattices [25,26,27,28], dimer chains [29], dark solitons in kagome lattice [31]. In the present work we present our results for propagation of solitons formed from topological edge states of polaritonic kagome lattice.…”