  Since the true ground state of the hadrons may be strange quark matter (SQM),
pulsars may actually be strange stars rather than neutron stars. According to
this SQM hypothesis, strange planets can also stably exist. The density of
normal matter planets can hardly be higher than 30 g cm$^{-3}$. As a result,
they will be tidally disrupted when its orbital radius is less than $\sim
5.6\times10^{10} \rm \, cm $, or when the orbital period ($P_{\rm orb}$) is
less than $ \sim \rm 6100\, s $. On the contrary, a strange planet can safely
survive even when it is very close to the host, due to its high density. The
feature can help us identify SQM objects. In this study, we have tried to
search for SQM objects among close-in exoplanets orbiting around pulsars.
Encouragingly, it is found that four pulsar planets (XTE J1807-294 b, XTE
J1751-305 b, PSR 0636 b, PSR J1807-2459A b) completely meet the criteria of
$P_{\rm orb} < \rm 6100\, s $, and are thus good candidates for SQM planets.
The orbital periods of two other planets (PSR J1719+14 b and PSR J2051-0827 b)
are only slightly higher than the criteria. They could be regarded as potential
candidates. Additionally, we find that the periods of five white dwarf planets
(GP Com b, V396 Hya b, J1433 b, WD 0137-349 b, and SDSS J1411+2009 b) are less
than 0.1 days. We argue that they might also be SQM planets. It is further
found that the persistent gravitational wave emissions from at least three of
these close-in planetary systems are detectable to LISA. More encouragingly,
the advanced LIGO and Einstein Telescope are able to detect the gravitational
wave bursts produced by the merger events of such SQM planetary systems, which
will provide a unique test for the SQM hypothesis.
