  Position measurements at the quantum level are vital for many applications,
but also challenging. Typically, methods based on optical phase shifts are
used, but these methods are often weak and difficult to apply to many
materials. An important example is graphene, which is an excellent mechanical
resonator due to its small mass and an outstanding platform for
nanotechnologies, but is largely transparent. Here, we present a novel
detection scheme based upon the strong, dispersive vacuum interactions between
a graphene sheet and a quantum emitter. In particular, the mechanical
displacement causes strong changes in the vacuum-induced shifts of the
transition frequency of the emitter, which can be read out via optical fields.
We show that this enables strong quantum squeezing of the graphene position on
time scales short compared to the mechanical period.
