Nonlinear mode competition and symmetry-protected power oscillations in topological lasers

Abstract

Topological photonics started out as a pursuit to engineer systems that mimic fermionic single-particle Hamiltonians with symmetry-protected modes, whose number can only change in spectral phase transitions such as band inversions. The paradigm of topological lasing, realized in three recent experiments, offers entirely new interpretations of these states, as they can be selectively amplified by distributed gain and loss. A key question is whether such topological mode selection persists when one accounts for the nonlinearities that stabilize these systems at their working point. Here we show that topological defect lasers can indeed stably operate in genuinely topological states. These comprise direct analogues of zero modes from the linear setting, as well as a novel class of states displaying symmetry-protected power oscillations, which appear in a spectral phase transition when the gain is increased. These effects show a remarkable practical resilience against imperfections, even if these break the underlying symmetries, and pave the way to harness the power of topological protection in nonlinear quantum devices.

Parity anomaly laser

“…Hokmabadi et al exploited mode pairing via SUSY [4][5][6][7][8], weakly coupling two SUSY partner lattices together and pumping one of them to achieve lasing in the zero mode. Finally, lasing in 1D arrays with topologically protected midgap states has been observed in a few recent experiments [9][10][11][12][13][14][15], where again pumping one of the subsystems (sublattices in this case) induces single mode lasing robust against coupling disorder. While these examples may seem unrelated, they are all ultimately mediated by the parity anomaly.…”

Nonlinear non-Hermitian higher-order topological laser

“…A topological laser based on the SSH model has been discussed 12,13,[48][49][50][51][52][53] . We consider the case where the hopping matrix is governed by the SSH matrix in Eq.…”

“…A topological laser is a prominent application of topological physics 12,13,[46][47][48][49][50][51][52][53][54] . It utilizes topological edge states for the coherent laser emission.…”

Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model

“…Topological gap solitons are also found in a mechanical SSH model with on-site cubic nonlinearity [19] and a photonic SSH model with on-site saturable nonlinearity [20]. Other nonlinearities also find prominent applications including topological lasers [21,22] and topological circuits [23,24] among others.…”