Non-Abelian effects in dissipative photonic topological lattices

Abstract

Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

Topological Dissipative Photonics and Topological Insulator Lasers in Synthetic Time‐Frequency Dimensions

“…AM1 in the main cavity not only simply connects the sites in the frequency dimension, but also plays a crucial role as exchanging energy between the system and the external reservoir, which distinguishes our work from previous works. [ 21,50,61 ] Besides, the dissipative couplings in frequency dimension from AM also differentiate our model from non‐Hermitian models based on either on‐site gain/loss [ 62 ] or direction‐dependent gain/loss coupling. [ 63 ] Although the proposed dissipative topological photonics may also be implemented using pulses in the time‐multiplexed network, [ 50 ] our proposal in synthetic time‐frequency dimensions carries several possible advantages, summarized in the following.…”