Analogue Hawking Radiation and Sine-Gordon Soliton in a Superconducting Circuit

TL;DR

This paper proposes a superconducting circuit setup to realize 1+1 dimensional black holes as sine-Gordon solitons, enabling the study of analogue Hawking radiation and quantum gravitational effects within current technology.

Contribution

It introduces a novel superconducting transmission line based on dc-SQUIDs to realize sine-Gordon solitons and explores their connection to black hole analogues and Hawking radiation.

Findings

Feasibility of realizing sine-Gordon solitons in superconducting circuits.

Potential to observe analogue Hawking radiation via quantum soliton evaporation.

Connection between superconducting circuits, sine-Gordon theory, and quantum gravity analogues.

Abstract

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.