  In the quantum system under periodical modulation, the particle can be
excited by absorbing the laser photon with the assistance of integer Floquet
photons, so that the Floquet sidebands appear. Here, we experimentally observe
non-integer Floquet sidebands (NIFBs) emerging between the integer ones while
increasing the strength of the probe laser in the optical lattice clock system.
Then, we propose the Floquet channel interference hypothesis (FCIH) which
surprisingly matches quantitatively well with both experimental and numerical
results. With its help, we found both Rabi and Ramsey spectra are very
sensitive to the initial phase and exhibit additional two symmetries. More
importantly, the height of Ramsey NIFBs is comparable to the integer one at
larger $g/\omega_s$ which indicates an exotic phenomenon beyond the
perturbative description. Our work provides new insight into the spectroscopy
of the Floquet system and has potential application in quantum technology.
