Observation of slowly decaying eigenmodes without exceptional points in Floquet dissipative synthetic circuits

Abstrct Passive parity-time symmetry breaking transitions, where long-lived eigenmodes emerge in a locally dissipative system, have been extensively studied in recent years. Conventional wisdom says that they occur at exceptional points. Here we report the observation of multiple transitions showing the emergence of slowly decaying eigenmodes in a dissipative, Floquet electronic system with synthetic components. Remarkably, in our system, the modes emerge without exceptional points. Our setup uses an electrical oscillator inductively coupled to a dissipative oscillator, where the time-periodic inductive coupling and resistive-heating losses are independently controlled. With a Floquet dissipation, slowly-decaying eigenmodes emerge at vanishingly small dissipation strength in the weak coupling limit. With a moderate Floquet coupling, multiple instances of their emergence and disappearance are observed. With an asymmetric dimer model, we show that these transitions, driven by avoided-level-crossing in purely dissipative systems, are generically present in static and Floquet domains.