Simulations of Chiral Waveguide Quantum Electrodynamics: The Emergence of Localized Two-body Correlation

We theoretically study a driven-dissipative system consisting of a chain of transmons chirally coupled to a one-dimensional waveguide. The numerical results report the emergence of localized two-body correlation in the steady state when only the leftmost transmon is incoherently pumped. As a comparison, we also coherently drive the leftmost transmon and observe an alternative pattern in the steady-state observables. The correlation length is very sensitive to the chirality, coupling efficiency to the waveguide, and whether the leftmost transmon is incoherently pumped or coherently driven. In the weak pumping (or driving) limit, we derive the expressions to the steady-state moments up to the second order, which explains the localization of the two-body correlation in the incoherent pumping case and the alternative pattern in the coherent driving case.