  We study how tidal streams from globular clusters may be used to constrain
the mass of ultra-light dark matter particles, called `fuzzy' dark matter
(FDM). A general feature of FDM models is the presence of ubiquitous density
fluctuations in bound, virialized dark matter structures, on the scale of the
de Broglie wavelength, arising from wave interference in the evolving dark
matter distribution. These time-varying fluctuations can disturb the motions of
stars, leading to potentially observable signatures in cold thin tidal streams
in our own Galaxy. The study of this effect has been hindered by the difficulty
in simulating the FDM wavefunction in Milky Way-sized systems. We present a
simple method to evolve realistic wavefunctions in nearly static potentials,
that should provide an accurate estimate of this granulation effect. We
quantify the impact of FDM perturbations on tidal streams, and show that
initially, while stream perturbations are small in amplitude, their power
spectra exhibit a sharp cutoff corresponding to the de Broglie wavelength of
the FDM potential fluctuations. Eventually, when stream perturbations become
nonlinear, fold caustics generically arise that lead to density fluctuations
with universal behavior. This erases the signature of the de Broglie wavelength
in the stream density power spectrum, but we show that it will still be
possible to determine the FDM mass in this regime, by considering the
fluctuations in quantities like angular momenta or actions.
