  The exotic physics emerging in non-Hermitian systems with balanced
distributions of gain and loss has drawn a great deal of attention in recent
years. These systems exhibit phase transitions and exceptional point
singularities in their spectra, at which eigen-values and eigen-modes coalesce
and the overall dimensionality is reduced. Among several peculiar phenomena
observed at exceptional points, an especially intriguing property, with
relevant practical potential, consists in the inherently enhanced sensitivity
to small-scale perturbations. So far, however, these principles have been
implemented at the expenses of precise fabrication and tuning requirements,
involving tailored nano-structured devices with controlled distributions of
optical gain and loss. In this work, anti-parity-time symmetric phase
transitions and exceptional point singularities are demonstrated in a single
strand of standard single-mode telecommunication fibre, using a setup
consisting of entirely of off-the-shelf components. Two propagating signals are
amplified and coupled through stimulated Brillouin scattering, which makes the
process non-Hermitian and enables exquisite control over gain and loss.
Singular response to small variations around the exceptional point and
topological features arising around this singularity are experimentally
demonstrated with large precision, enabling robustly enhanced spectral response
to small-scale changes in the Brillouin frequency shift. Our findings open
exciting opportunities for the exploration of non-Hermitian phenomena over a
table-top setup, with straightforward extensions to higher-order Hamiltonians
and applications in quantum optics, nanophotonics and sensing.
