  Integrated frequency combs promise transformation of lab-based metrology into
disruptive real-world applications. These microcombs are, however, sensitive to
stochastic thermal fluctuations of the integrated cavity refractive index, with
its impact becoming more significant as the cavity size becomes smaller. This
tradeoff between microcomb noise performance and footprint stands as a
prominent obstacle to realizing applications beyond a controlled lab
environment. Here, we demonstrate that small footprint and low noise become
compatible through the all-optical Kerr-induced synchronization (KIS) method.
Our study unveils that the phase-locking nature of the synchronization between
the cavity soliton and the injected reference pump laser enables the microcomb
to no longer be limited by internal noise sources. Instead, the microcomb noise
is mostly limited by external sources, namely, the frequency noise of the two
pumps that doubly pin the microcomb. First, we theoretically and experimentally
show that the individual comb tooth linewidths of an octave-spanning microcomb
remain within the same order-of-magnitude as the pump lasers, contrary to the
single-pumped case that exhibits a more than two order-of-magnitude increase
from the pump to the comb edge. Second, we theoretically show that intrinsic
noise sources such as thermorefractive noise in KIS are quenched at the cavity
decay rate, greatly decreasing its impact. Experimentally, we show that even
with free-running lasers, the KIS microcomb can exhibit better repetition rate
noise performance than the predicted thermorefractive noise limitation in
absence of KIS.
