  We propose the use of a waveguide-like transmission line based on
direct-current superconducting quantum interference devices (dc-SQUID) and
study the sine-Gordon (SG) equation which characterises the dynamical behavior
of the superconducting phase in this transmission line. Guided by the duality
between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in
sine-Gordon field theory, we show how to, in our setup, realize 1 + 1
dimensional black holes as solitons of the sine-Gordon equation. We also study
the analogue Hawking radiation in terms of the quantum soliton evaporation, and
analyze its feasibility within current circuit quantum electrodynamics (cQED)
technology. Our results may not only facilitate experimentally understanding
the relation between Jackiw-Teitelboim dilaton gravity and sine-Gordon field
theory, but also pave a new way, in principle, for the exploration of analogue
quantum gravitational effects.
