  The detection of a secular post-merger gravitational wave (GW) signal in a
binary neutron star (BNS) merger serves as strong evidence for the formation of
a long-lived post-merger neutron star (NS), which can help constrain the
maximum mass of NSs and differentiate NS equation of states. We specifically
focus on the detection of GW emissions from rigidly rotating NSs formed through
BNS mergers, using several kilohertz GW detectors that have been designed. We
simulate the BNS mergers within the detecting limit of LIGO-Virgo-KARGA O4 and
attempt to find out on what fraction the simulated sources may have a
detectable secular post-merger GW signal. For kilohertz detectors designed in
the same configuration of LIGO A+, we find that the design with peak
sensitivity at approximately $2{\rm kHz}$ is most appropriate for such signals.
The fraction of sources that have a detectable secular post-merger GW signal
would be approximately $0.94\% - 11\%$ when the spindowns of the post-merger
rigidly rotating NSs are dominated by GW radiation, while be approximately
$0.46\% - 1.6\%$ when the contribution of electromagnetic (EM) radiation to the
spin-down processes is non-negligible. We also estimate this fraction based on
other well-known proposed kilohertz GW detectors and find that, with advanced
design, it can reach approximately $12\% - 45\%$ for the GW-dominated spindown
case and $4.7\% - 16\%$ when both the GW and EM radiations are considered.
