Modeling of simple bandpass filters: bandwidth broadening of Josephson parametric devices due to non-Markovian coupling to dressed transmission-line modes

TL;DR

This paper develops a non-Markovian circuit analysis for Josephson parametric devices, revealing how frequency-dependent coupling broadens bandwidth beyond traditional Markovian models, aiding device optimization.

Contribution

It introduces a non-perturbative, non-Markovian framework for modeling Josephson devices coupled via bandpass filters, improving understanding of bandwidth broadening effects.

Findings

Bandwidth broadening occurs in both resonant and off-resonant regimes.

Exact self-energies significantly modify gain profiles compared to Markovian models.

The analysis provides insights for bandwidth engineering in superconducting quantum devices.

Abstract

Josephson parametric devices are widely used in superconducting quantum computing research but suffer from an inherent gain-bandwidth trade-off. This limitation is partly overcome by coupling the device to its input/output transmission line via a bandpass filter, leading to wider bandwidth at undiminished gain. Here we perform a non-perturbative circuit analysis in terms of dressed transmission-line modes for representative resonant coupling circuits, going beyond the weak-coupling treatment. The strong frequency dependence of the resulting coupling coefficients implies that the Markov approximation commonly employed in cQED analysis is inadequate. By retaining the full frequency dependence of the coupling, we arrive at a non-Markovian form of the quantum Langevin equation with the frequency-dependent complex-valued self-energy of the coupling in place of a single damping parameter. We also consistently generalize the input-output relations and unitarity conditions. Using the exact self-energies of elementary filter networks -- a series- and parallel-LC circuit and a simple representative bandpass filter consisting of their combination -- we calculate the generalized parametric gain factors. Compared with their Markovian counterpart, these gain profiles are strongly modified. We find bandwidth broadening not only in the established parameter regime, where the self-energy of the coupling is in resonance with the device and its real part has unity slope, but also within off-resonant parameter regimes where the real part of the self-energy is large. Our results offer insight for the bandwidth engineering of Josephson parametric devices using simple coupling networks.