## 1 Introduction  
Research on atomic clocks based on optical transitions is making rapid and steady progress. Recent advances in the frequency uncertainties of the state-of-the-art optical clocks have reached a \(10^{-18}\) regime [1], which is deemed as suitable for the redefinition of SI a second in the future [2]. Laboratories around the world are working continually on improving the performance of optical clocks for SI-traceable measurements [3], improved timekeeping and global navigation satellite systems [4], geodesy measurements [1], cold-atom instruments for space applications [5, 6], high precision tests of fundamental laws of physics including violations of relativity [7], and so on. The quest for ever-increasing measurement accuracy requires optical clocks to improve constantly with more elaborate manipulation of atomic systems. Precise manipulation of quantum systems is, at the same time, the preparation and subsequent tool for many quantum experiments, such as quantum sensing, quantum computing, and simulation. Floquet engineering (FE) is a common tool for steering quantum states [8, 9] and has been employed in the optical lattice. In previous work, we have obtained a series of Rabi spectroscopy processes by periodically modulating the lattice trapping potential with a tool of FE [10]. Interference between the two Floquet channels was observed by simultaneously modulating the frequency of the lattice laser and the Rabi frequency [11]. The suppression of broadening of the Rabi spectrum by tunneling effects was also observed in the shallow potential FE lattice [12].  
The \({}^{87}\)Sr optical lattice clock (OLC) based on a highly forbidden \(55^{21}S_{0}\) (\(F=9/2\)) \(\rightarrow\) 5s5p \({}^{3}P_{0}\) (\(F=9/2\)) electric dipole transition is one of the most reported OLC and has realized the systematic uncertainty of 2 \(\times\)\(10^{-18}\) and the best frequency instability of \(2\times 10^{-18}\) (\(\tau/s\))\({}^{-0.5}\)[2]. The dephasing of the Rabi flopping process indicates that the maximum excitation fraction is reduced exponentially with increasing clock laser pulse duration [13]. The dephasing process limits the clock detection time and, thus, affects the instability and uncertainty [14]. It has been observed that the dephasing effect is aggravated by increasing the temperature of the cold ensemble or the atomic density [15, 16]. However,improving the instability requires an increase in the number of atoms in lattice and a reduction in the preparation time of cooled atoms, which contradicts with the lower temperature as a lower temperature needs more time for cooling. Many efforts have been made to settle the contradiction between atomic interaction and clock performance in OLCs, such as by using the three-dimensional optical lattice [17], an atomic-array optical clock [18], and the cavity-enhanced lattice with a larger waist diameter [19]. In addition, dephasing is also one of the major challenges in many quantum sciences, such as quantum communication [20] and quantum information processing [21]. However, there are few reports about the suppression of the dephasing of the Rabi flopping process caused by the atomic thermal distribution over motional quantum states.  
In this paper, we designed a scheme for experimentally verifying the suppression of dephasing in the OLC by the FE. We apply the FE to a dynamically driving many-body system and study experimentally the effect of FE on the excitation fraction of clock transition spectroscopy. We measure the excitation fraction of the Rabi spectrum as a function of clock pulse duration at different atomic densities and temperatures, with and without FE.