Most present-day resonant systems, throughout physics and engineering, are characterized by a strict time-reversal symmetry between the rates of energy coupled in and out of the system, which leads to a trade-off between how long a wave can be stored in the system and the system bandwidth. Any attempt to reduce the losses of the resonant system, and hence store a (mechanical, acoustic, electronic, optical, atomic, or of any other nature) wave for more time, will inevitably also reduce the bandwidth of the system. Until recently, this time-bandwidth limit has been considered fundamental, arising from basic Fourier reciprocity. A recent theory suggested that it might in fact be overcome by breaking Lorentz reciprocity in the resonant system, reinvigorated a debate about whether (or not) this was indeed the case. Here, we report an experimental realization of a cavity where, inducing nonreciprocity by breaking the time invariance, we do overcome the fundamental time-bandwidth limit of ordinary resonant systems by a factor of 30, in full agreement with accompanying numerical simulations. We show that, although in practice experimental constraints limit our scheme, the time bandwidth product can be arbitrarily large, simply dictated by the finesse of the cavity. Our experimental realization uses a simple macroscopic, time-variant, fiber-optic cavity, where we break Lorentz reciprocity by non-adiabatically opening the cavity, injecting a pulse of large bandwidth, and then closing the cavity, storing the pulse which can be released on-demand at a later time. Our results open the path for designing resonant systems, ubiquitous in physics and engineering, that can simultaneously be broadband (i.e., ultrafast) and possessing long storage times, thereby unleashing fundamentally new functionalities in wave physics and wave-matter interactions.
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