  It is challenging for observing superbunching effect with true chaotic light,
here we propose and demonstrate a method to achieve superbunching effect of the
degree of second-order coherence is 2.42 with broadband stationary chaotic
light based on a cascaded Michelson interferometer (CMI), exceeding the
theoretical upper limit of 2 for the two-photon bunching effect of chaotic
light. The superbunching correlation peak is measured with an ultrafast
two-photon absorption detector which the full width at half maximum reaches
about 95 fs. Two-photon superbunching theory in a CMI is developed to interpret
the effect and is in agreement with experimental results. The theory also
predicts that the degree of second-order coherence can be much greater than $2$
if chaotic light propagates $N$ times in a CMI. Finally, a new type of weak
signals detection setup which employs broadband chaotic light circulating in a
CMI is proposed. Theoretically, it can increase the detection sensitivity of
weak signals 79 times after the chaotic light circulating 100 times in the CMI.
