Stabilizing topological transport in a non-Hermitian system

When the dynamical matrix (or “Hamiltonian”) of a non-Hermitian system is tuned around a closed loop in the vicinity of an exceptional point (EP), the system’s complex eigenvalues trace out a braid. The particular braid traced out is a topological property of the loop, determined only by how the loop encloses EP₂, the space of doubly degenerate EPs. While in principle adiabatic loops in parameter space could be used to execute braid operations to exponential accuracy in the loop time, the dynamics at long times is dominated by gain-loss effects and adiabatic evolution breaks down. We discuss schemes for shortcuts to adiabaticity, a class of techniques for generating control sequences that emulate adiabatic evolution on finite timescales, with the goal of dynamically executing braids by encircling exceptional points. We also discuss progress experimentally implementing these control sequences on a set of nearly degenerate vibrational modes of a SiN membrane optomechanically coupled to an optical resonator, and strategies for tailoring control sequences to account for experimental limitations.