  Here we present a liquid nitrogen-cooled Ca^+ optical clock with an overall
systematic uncertainty of 3*10^-18. In contrast with the room-temperature Ca^+
optical clock that we have reported previously, the temperature of the
blackbody radiation (BBR) shield in vacuum has been reduced to 82(5) K using
liquid nitrogen. An ion trap with a lower heating rate and improved cooling
lasers were also introduced. This allows cooling the ion temperature to the
Doppler cooling limit during the clock operation, and the systematic
uncertainty due to the ion's secular (thermal) motion is reduced to < 1*10^-18.
The uncertainty due to the probe laser light shift and the servo error are also
reduced to < 1*10^-19 and 4*10^-19 with the hyper-Ramsey method and the
higher-order servo algorithm, respectively. By comparing the output frequency
of the cryogenic clock to that of a room-temperature clock, the differential
BBR shift between the two was measured with a fractional statistical
uncertainty of 7*10^-18. The differential BBR shift was used to calculate the
static differential polarizability, and it was found in excellent agreement
with our previous measurement with a different method. This work suggests that
the BBR shift of optical clocks can be well suppressed in a liquid nitrogen
environment. This is advantageous because conventional liquid-helium cryogenic
systems for optical clocks are more expensive and complicated. Moreover, the
proposed system can be used to suppress the BBR shift significantly in other
types of optical clocks such as Yb^+, Sr^+, Yb, Sr, etc.
