Gravitational-Wave Fringes at LIGO: Detecting Compact Dark Matter by
  Gravitational Lensing
  Utilizing gravitational-wave (GW) lensing opens a new way to understand the
small-scale structure of the universe. We show that, in spite of its coarse
angular resolution and short duration of observation, LIGO can detect the GW
lensing induced by compact structures, in particular by compact dark matter
(DM) or primordial black holes of $10 - 10^5 \, M_\odot$, which remain
interesting DM candidates. The lensing is detected through GW frequency
chirping, creating the natural and rapid change of lensing patterns:
\emph{frequency-dependent amplification and modulation} of GW waveforms. As a
highest-frequency GW detector, LIGO is a unique GW lab to probe such light
compact DM. With the design sensitivity of Advanced LIGO, one-year observation
by three detectors can optimistically constrain the compact DM density fraction
$f_{\rm DM}$ to the level of a few percent.
