Dissipative Effects in Transmission Line Analogues of Hawking Radiation

Abstract

Hawking radiation is a fundamental result of quantum field theory in curved spacetime, yet its direct observation remains beyond current experimental capabilities. Circuit quantum electrodynamics provides a practical platform for realizing analogue systems where Hawking-like radiation may be studied under controlled laboratory conditions. In this work, we analyze two superconducting-circuit analogues of Schwarzschild black holes: a tunable dc-SQUID transmission line and a SNAIL-based transmission line supporting solitonic solutions of the KdV equation. We investigate the conditions under which these architectures can generate an observable Hawking temperature and study the impact of dissipation and thermal noise using an open quantum systems approach. To assess the observability of the Hawking signal, we propose complementing particle number measurements with estimates of the Hilbert-Schmidt distance to the thermal bath. Our analysis establishes practical detectability thresholds and shows that Hawking temperatures above approximately 73 mK remain distinguishable under realistic experimental conditions. While the tunable transmission line architecture can reach temperatures of about 113 mK and therefore appears more viable, the solitonic model requires further optimization and more demanding experimental conditions.