Theory and Analysis of Nonreciprocity for Superconducting Qubits Coupled to a Waveguide

This article delves into the intricacies of nonreciprocity in a system composed of two superconducting qubits operating in a transmon regime and coupled to a 1-D waveguide. Nonreciprocity, characterized by asymmetric signal transmission, is a phenomenon of increasing interest in quantum technologies, as it enables one-way signal propagation and isolation. Our investigation derives the conditions to obtain nonreciprocity in a qubit-loaded waveguide and discusses how common approximations may impact the observed nonreciprocal effects, highlighting crucial factors that must be considered in designing such systems. By employing realistic system parameters, we unveil significant effects on the system dynamics when higher energy levels are included in the transmon regime. This leads to a reduction of nonreciprocity compared to the ideal scenario, with the transmission ratio falling below the two-level approximation limit of
$2/3$
. Additionally, the statistical properties of the system undergo significant changes, particularly in the coherent functions for transmitted and reflected signals. The emergence of additional population transfer channels and the critical role of quantum correlations between qubits underscore the necessity of careful modeling. Our findings have implications for quantum device engineering, offering insights that can enhance the design of more efficient quantum technology and advanced quantum communication systems.