Towards a transportable Ca$^+$ optical clock with a systematic uncertainty of $4.8\times 10^{-18}$

We present a compact, long-term nearly continuous operation of a room-temperature Ca$^+$ optical clock setup towards a transportable clock, achieving an overall systematic uncertainty of $4.8\times 10^{-18}$ and an uptime rate of 97.8% over an 8-day period. The active liquid-cooling scheme is adopted, combined with the precise temperature measurement with 13 temperature sensors both inside and outside the vacuum chamber to ensure the accurate evaluation of the thermal environment for the optical clock. The environmental temperature uncertainty is evaluated as 293.31(0.4) K, corresponding to a blackbody radiation (BBR) frequency shift uncertainty of $4.6\times 10^{-18}$, which is reduced more than two times compared to our previous work. Through the frequency comparison between the room temperature Ca$^+$ optical clock and a cryogenic Ca$^+$ optical clock, the overall uncertainty of the clock comparison is $7.5\times 10^{-18}$, including a statistic uncertainty of $4.9\times 10^{-18}$ and a systematic uncertainty of $5.7\times 10^{-18}$. This work provides a set of feasible implementations for high-precision transportable ion optical clocks.