  We have fabricated and characterized asymmetric gap-engineered junctions and
transmon devices. To create Josephson junctions with asymmetric gaps, Ti was
used to proximitize and lower the superconducting gap of the Al
counter-electrode. DC IV measurements of these small, proximitized Josephson
junctions show a reduced gap and larger excess current for voltage biases below
the superconducting gap when compared to standard Al/AlOx/Al junctions. The
energy relaxation time constant for an Al/AlOx/Al/Ti 3D transmon was T1 = 1
{\mu}s, over two orders of magnitude shorter than the measured T1 = 134 {\mu}s
of a standard Al/AlOx/Al 3D transmon. Intentionally adding disorder between the
Al and Ti layers reduces the proximity effect and subgap current while
increasing the relaxation time to T1 = 32 {\mu}s.
