WIDG Seminar: Chitres Guria, Yale University, “Topological structures and dynamics in an optomechanical system with exceptional points”

A system whose time evolution is linear, i.e. dx/dt= -iH.x, shows non-trivial topological structures and dynamics when the effective Hamiltonian H is allowed to be any complex matrix, which includes all Hermitian and non-Hermitian matrices. Previous works have investigated a system of two optomechanically coupled oscillators, described by a non-Hermitian 2x2 effective Hamiltonian H parametrized by two independent control parameters. It showed the existence of a second-order exceptional point (EP2) in the system, and topological energy transfer between the two eigenstates (EP2: where both the complex eigenvalues of H are equal and its two eigenstates coalesce into one eigenstate). In our current experiments, we investigate a system of three optomechanically coupled oscillators, described by a non-Hermitian 3x3 effective Hamiltonian parametrized by four independent control parameters. Firstly, we show that there exists a third-order exceptional point (EP3: where all three complex eigenvalues are equal and all three eigenstates coalesce into one eigenstate). We then demonstrate that the space of EP2 points in a certain neighborhood of the EP3 point form an extended topological structure – a Trefoil knot. Finally, we explore the topological structures formed by the eigenvalues themselves when we parametrically encircle the Trefoil knot. These structures known as braids, form a complete set of generators of the braid group B3. We also report our ongoing efforts to use these braids as an avenue for topological energy transfer between all three eigenmodes.
Zoom link: https://yale.zoom.us/j/754440361