Analog black-white hole solitons in traveling wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements

Abstract

We show that existing traveling wave parametric amplifier (TWPA) setups, using superconducting nonlinear asymmetric inductive elements (SNAILs), admit soliton solutions that act as analog event horizons. The SNAIL-TWPA circuit dynamics are described by the Korteweg-de Vries or modified Korteweg-de Vries equations in the continuum field approximation, depending on the external magnetic flux bias, and validated numerically. The soliton spatially modulates the velocity for weak probes, resulting in the effective realization of analog black hole and white hole event horizon pairs. The SNAIL external magnetic flux bias tunability facilitates a three-wave mixing process, which enhances the prospects for observing Hawking photon radiation.