  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.
