Quantum Simulation of Luttinger Liquids in Josephson Transmission Lines

Here we present the first quantum simulator for an impurity-scattering in interacting 1D wires. The simulator consists of a transmission line made out of more than 30,000 Josephson junctions, serving as a high-impedance media for microwave photons, and a small phase slip Josephson junction, playing the role of a back-scattering impurity. The system can be described by a boundary sine-Gordon model where the interaction strength is defined as g = Z/R_Q with Z being the transmission line impedance and R_Q = 6.5 kOhm the resistance quantum. By measuring scattering amplitudes and a spectrum of inelastically scattered microwave photons we can find the first and higher order correlation functions related to an AC conductance of the impurity. The ability to control the transmission line parameters and the finite size of the system allow us to fabricate lines with impedances exceeding R_Q while keeping the phase slip rate of the line’s junctions very low. It gives us the unique opportunity to test Luttinger liquid physics at both sides of the critical point g = 1.