  Laser interferometric gravitational-wave detectors implement Fabry-Perot
cavities to increase their peak sensitivity. However, this is at cost of
reducing their detection bandwidth, which origins from the propagation phase
delay of the light. The "white-light-cavity" idea, first proposed by Wicht et
al. [Optics Communications 134, 431 (1997)], is to circumvent this limitation
by introducing anomalous dispersion, using double-pumped gain medium, to
compensate for such phase delay. In this article, starting from the Hamiltonian
of atom-light interaction, we apply the input-output formalism to evaluate the
quantum noise of the system. We find that apart from the additional noise
associated with the parametric amplification process noticed by others, the
stability condition for the entire system poses an additional constraint.
Through surveying the parameter regimes where the gain medium remains stable
(not lasing) and stationary, we find that there is no net enhancement of the
shot-noise limited sensitivity. Therefore, other gain mediums or different
parameter regimes shall be explored for realizing the white light cavity.
