  In-vacuo cryogenic environments are ideal for applications requiring both low
temperatures and extremely low particle densities. This enables reaching long
storage and coherence times for example in ion traps, essential requirements
for experiments with highly charged ions, quantum computation, and optical
clocks. We have developed a novel cryostat continuously refrigerated with a
pulse-tube cryocooler and providing the lowest vibration level reported for
such a closed-cycle system with 1 W cooling power for a <5 K experiment. A
decoupling system suppresses vibrations from the cryocooler by three orders of
magnitude down to a level of 10 nm peak amplitudes in the horizontal plane.
Heat loads of about 40 W (at 45 K) and 1 W (at 4 K) are transferred from an
experimental chamber, mounted on an optical table, to the cryocooler through a
vacuum-insulated massive 120 kg inertial copper pendulum. The 1.4 m long
pendulum allows installation of the cryocooler in a separate, acoustically
isolated machine room. In the laser laboratory, we measured the residual
vibrations using an interferometric setup. The positioning of the 4 K elements
is reproduced to better than a few micrometer after a full thermal cycle to
room temperature. Extreme high vacuum on the $10^{-15}$ mbar level is achieved.
In collaboration with the Max-Planck-Intitut f\"ur Kernphysik (MPIK), such a
setup is now in operation at the Physikalisch-Technische Bundesanstalt (PTB)
for a next-generation optical clock experiment using highly charged ions.
