  The Aubry transition between sliding and pinned phases, driven by the
competition between two incommensurate length scales, represents a paradigm
that is applicable to a large variety of microscopically distinct systems.
Despite previous theoretical studies, it remains an open question to what
extent quantum effects modify the transition, or are experimentally observable.
An experimental platform that can potentially reach the quantum regime has
recently become available in the form of trapped laser-cooled ions subject to a
periodic optical potential [A. Bylinskii, D. Gangloff, I. Counts, and V.
Vuletic, Nature Materials 15, 717 (2016)]. Using Path-Integral Monte Carlo
(PIMC) simulation methods, we analyze the impact of quantum tunneling on the
sliding-to-pinned transition in this system, and determine the phase diagram in
terms of incommensuration and potential strength. We propose new signatures of
the quantum Aubry transition that are robust against thermal and finite-size
effects, and that can be observed in future experiments.
