Title: Dynamically encircling an exceptional point for asymmetric mode switching
Abstract: A two-mode waveguide is designed to realize a dynamical encircling of an exceptional point at which two resonances coincide in their frequency and their rate of decay; as a result the waveguide transmits only into a unique mode at either one of its two output ports. In physical systems with gain and loss modes, unusual behaviour can arise at so-called exceptional points where such modes coalesce. In previous work on optical systems, exceptional points have been harnessed to realize effects such as unidirectional light transmission and lasing suppression and revival. It is further predicted that slowly encircling exceptional points in parameter space induces non-reciprocal transitions between two states. This intriguing fundamental effect has now been demonstrated experimentally by two independent teams. Jack Harris and colleagues observe energy transfer between two vibrational modes in an optomechanical resonator, and Stefan Rotter and colleagues measure asymmetric mode switching in a microwave transmission line. These studies pave the way for further experimental and fundamental exploration of physical phenomena around exceptional points. Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition1,2,3,4,5,6. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly7,8, such as a state-flip or the accumulation of a geometric phase9,10. The topological structure of exceptional points has been experimentally explored11,12,13, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity14,15,16,17,18,19,20,21 have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.