An improved optomechanical system for measuring the trefoil knot of degeneracies near a triple exceptional point

When the N×N dynamical matrix (or “Hamiltonian”) of an N mode 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. It has recently been experimentally demonstrated that, in a three-mode system (consisting of three vibrational modes of a SiN membrane optomechanically coupled to an optical resonator), the space of double exceptional points (EP₂’s) in the vicinity of a triple exceptional point (EP₃) forms a trefoil knot, and that the braid traced out by the eigenvalues depends on how the loop encloses this knot. However, experimentally verifying this structure involves the time-intensive process of measuring eigenvalue spectra throughout a 4-dimensional control space. In this talk we discuss an improved experimental setup in which this process can be made substantially faster. We discuss the prospects for using this device to efficiently raster over the 4-dimensional control space, and for carrying out real time operations in this space.