  We design and test a low-loss interface between superconducting 3-dimensional
microwave cavities and 2-dimensional circuits, where the coupling rate is
highly tunable. This interface seamlessly integrates a loop antenna and a
Josephson junction-based coupling element. We demonstrate that the loss added
by connecting this interface to the cavity is 1.28 kHz, corresponding to an
inverse quality factor of $1/(4.5 \times 10^6)$. Furthermore, we show that the
cavity's external coupling rate to a 50 $\Omega$ transmission line can be tuned
from negligibly small to over 3 orders of magnitude larger than its internal
loss rate in a characteristic time of 3.2 ns. This switching speed does not
impose additional limits on the coupling rate because it is much faster than
the coupling rate. Moreover, the coupler can be controlled by low frequency
signals to avoid interference with microwave signals near the cavity or qubit
frequencies. Finally, the coupling element introduces a 0.04 Hz/photon
self-Kerr nonlinearity to the cavity, remaining linear in high photon number
operations.
