Lindblad theory of linear response susceptibility and dispersive readout in minimal Kitaev junctions

Abstract

The field of hybrid superconductor-semiconductor quantum dots is advancing toward the development of functional devices that leverage the advantages of both types of materials. However, the inherent complexity of these devices demands a comprehensive theoretical framework for a complete understanding of their responses to external probes, readout and the dissipation arising from environmental coupling. We present a Lindblad-based linear response formalism that captures the multi-level nature of these devices, their probe-readout flexibility, and the non-unitary effects of finite-frequency response, including the so-called Sisyphus and Hermes dynamical susceptibilities. These arise from fluctuations in the rates and jump operators, and are hence absent in standard Kubo linear response treatments. We exemplify the framework using quantum dot-based Kitaev chain setups which are promising candidates for topologically protected Majorana-based parity qubits. Our results shed light onto the validity of the standard curvature-based approximation for fermionic parity and qubit readout, show that Hermes terms compensate decoherence in dispersive readout and implement important corrections beyond thermalized states.