We report high-resolution spectroscopic detection of TiO molecular signature in the day-side spectra of WASP-33 b, the second hottest known hot Jupiter. We used High-Dispersion Spectrograph (HDS; R $sim$ 165,000) in the wavelength range of 0.62 -- 0.88 $mu$m with the Subaru telescope to obtain the day-side spectra of WASP-33 b. We suppress and correct the systematic effects of the instrument, the telluric and stellar lines by using SYSREM algorithm after the selection of good orders based on Barnard star and other M-type stars. We detect a 4.8-$sigma$ signal at an orbital velocity of $K_{p}$= +237.5 $^{+13.0}_{-5.0}$ km s$^{-1}$ and systemic velocity $V_{sys}$= -1.5 $^{+4.0} _{-10.5}$ km s$^{-1}$, which agree with the derived values from the previous analysis of primary transit. Our detection with the temperature inversion model implies the existence of stratosphere in its atmosphere, however, we were unable to constrain the volume-mixing ratio of the detected TiO. We also measure the stellar radial velocity and use it to obtain a more stringent constraint on the orbital velocity, $K_{p} = 239.0^{+2.0}_{-1.0}$ km s$^{-1}$. Our results demonstrate that high-dispersion spectroscopy is a powerful tool to characterize the atmosphere of an exoplanet, even in the optical wavelength range, and show a promising potential in using and developing similar techniques with high-dispersion spectrograph on current 10m-class and future extremely large telescopes.
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