Lasing in topological edge states of a one-dimensional lattice

Abstract

Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. This feature offers new opportunities for robust trapping of light in nanoand micro-meter scale systems subject to fabrication imperfections and to environmentally induced deformations. Here we show lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear topological photonics.Topological phase transitions in condensed matter have been extensively studied over the last decade. A key manifestation of these transitions is the emergence, at the frontier between materials exhibiting distinct topological phases, of localized states that are unaffected by disorder. One example of this topological protection is provided by chiral edge states at the surface of topological insulators that allow unidirectional transport immune to backscattering 1 .Initially proposed by Haldane and Raghu 2 , the idea of extending these topological arguments to the realm of photonics has recently triggered considerable efforts to engineer optical devices that are unaffected by local perturbations and fabrication defects 3 . For example, topological properties have been used to create polarizationdependent unidirectional waveguides 4 , optical delay lines with enhanced transport properties 5 , backscatteringimmune chiral edge states 6-9 , and protected bound states in parity-time-symmetric crystals 10,11 .The emergence of edge states at the boundary between materials with distinct topological invariants provides an efficient way to create localized photonic modes whose existence is protected by topology 9 . Lasing in these kind of modes would then be robust against fabrication defects, local deformations caused by temperature or other unstable ambient conditions, and long term degradation, all of which would eventually result in the modification of the local optical potential 12 . The main difficulty that has prevented the observation of lasing in topological modes is the need to implement topological lattices in media exhibiting optical gain. In this sense, microcavity polaritons, mixed quasiparticules formed from the strong coupling between cavity photons and quantum well excitons 13 , provide a unique platform: they allow for low-threshold lasing 14,15 , even at room temperature 16,17 , and the engineering of topological properties in lattices of resonators 18,19 .In this work we report lasing in topological edge states of a 1D lattice of coupled semiconductor micropillars. The lattice implements an orbital version of the Su-Schrieff...

Nonlinear topological states in the Su–Schrieffer–Heeger model

“…In the latter case, α m denotes electric field amplitude in m th cavity. Such correspondence allows one to investigate the physics of the SSH model in fully classical setups, including electronic [11,12], photonic [13][14][15][16][17][18][19], plasmonic [20][21][22][23], polaritonic [24] and mechanical [25] systems. The bulk energy spectrum of the SSH model is found from Eqs.…”

“…Possibly the simplest model of the topological states in one-dimensional systems is provided by the wellcelebrated Su-Schrieffer-Heeger model (SSH) [11,12], which was investigated and realized in various contexts including electronic [11,12], photonic [13][14][15][16][17][18][19], plasmonic [20][21][22][23], polaritonic [24] and mechanical [25] systems. Though initially the SSH model was applied to explain charge transfer in polymer molecules, it can be also used for describing the physics of artificial photonic and plasmonic structures.…”

Topological characterization of chiral models through their long time dynamics

“…The driven SSH 4 discussed in section 4 may be implemented by periodical modulation of the separation between the waveguides along the propagation direction [43,45], and long-ranged tunnelings may be obtained by letting the waveguides propagate out of the plane, as possible in 3D-photonic chips [46,47]. Finally, the SSH 4 model may be implemented in exciton-polariton experiments, by a slight modification of the approach used by the group of Amo in [48].…”

“…The driven SSH 4 discussed in section 4 may be implemented by periodical modulation of the separation between the waveguides along the propagation direction [43,45], and long-ranged tunnelings may be obtained by letting the waveguides propagate out of the plane, as possible in 3D-photonic chips [46,47]. Finally, the SSH 4 model may be implemented in exciton-polariton experiments, by a slight modification of the approach used by the group of Amo in [48].Summarizing, in this work we have generalized the notion of mean chiral displacement to chiral systems with any internal dimension , showing that when 2  > the winding number is encoded in the long-time limit of the trace of the mean chiral displacement over a localized basis of the internal space. We analyzed three chiral models having internal dimension 4  = , i.e.…”

Topological Plasmonic Chain with Retardation and Radiative Effects

“…12−23 Topological photonics shows exciting potential for unidirectional plasmonic waveguides, 24 lasing, 25 and field enhancing hotspots with robust topological protection, which could prove useful for nanoparticle arrays on flexible substrates. 26 Plasmonic and photonic systems provide a powerful platform to examine topological insulators without the complication of interacting particles and with interesting additional properties like non-Hermiticity.…”