Simulating sine-Gordon model with time dependent parameters using Josephson junction arrays.

Superconducting quantum circuits provide a promising path to simulate interesting physical phenomena, such as non trivial effects in quantum field theories, topological phases etc. Recently, there has been a surge in the study and simulation of many-body Hamiltonians with time-dependent interaction strengths, as they exhibit novel dynamical phenomena that are beyond the scope of the Hamiltonians with constant interaction strengths. In this work we propose a superconducting quantum circuit, which consists of Josephson Junction arrays and SQUIDS, that simulates the time-dependent sine-Gordon model. This model is characterized by the Luttinger parameter and the coefficient of the cosine potential, which are functions of time. We show that for specific functions of these parameters, the system is integrable in the sense of the generalized Bethe ansatz framework. For these integrable cases, we obtain the exact many-body wavefunction and discuss the dynamics.