Exceeding the classical time-bandwidth product in nonlinear time-invariant systems

The classical “time-bandwidth” limit for linear time-invariant (LTI) devices in physics and engineering asserts that it is impossible to store broadband propagating waves (large $${\Delta }\omega$$ ’s) long times ?t’s). For standing (non-propagating) waves, i.e., vibrations, particular, this takes on a simple form, }t \,{\Delta }\omega = 1$$ , where the bandwidth over which localization (energy storage) occurs, }t$$ storage time. This related well-known result dynamics, namely one can achieve high Q-factor (narrowband resonance) low damping, or small (broadband but not simultaneously both. It thus remains fundamental challenge wave vibration try find ways overcome limit, least because would allow storing times, achieving resonance damping. Recent theoretical studies have suggested such feat might be possible LTI terminated unidirectional waveguides topological “rainbow trapping” devices, although an experimental confirmation of either concept still lacking. In work, we consider nonlinear mechanical system demonstrate experimentally its time-bandwidth product exceed values both above below unity, energy-tunable way. Our proposed structure consists single-degree-of-freedom oscillator, rigidly coupled nondispersive waveguide. Upon developing full framework class systems, show how may control flow energy frequency domain, thereby managing disproportionately decrease (increase) time resonator, as compared with increase (decrease) system’s . results pave way toward conceiving harnessing hitherto unattainable low-loss wave-storage nonlinear, host key applications engineering.